Models

Models currently supported by StatsForecast

StatsForecast offers a wide variety of statistical forecasting models grouped into the following categories:

• Auto Forecast: Automatic forecasting tools that search for the best parameters and select the best possible model. Useful for large collections of univariate time series. Includes: AutoARIMA, AutoETS, AutoTheta, AutoCES, AutoMFLES, AutoTBATS.

• ARIMA Family: AutoRegressive Integrated Moving Average models for capturing autocorrelations in time series data.

• Exponential Smoothing: Uses weighted averages of past observations where weights decrease exponentially into the past. Suitable for data with clear trend and/or seasonality.

• Baseline Models: Classical models for establishing baselines: HistoricAverage, Naive, RandomWalkWithDrift, SeasonalNaive, WindowAverage, SeasonalWindowAverage.

• Sparse or Intermittent: Models suited for series with very few non-zero observations: ADIDA, CrostonClassic, CrostonOptimized, CrostonSBA, IMAPA, TSB.

• Multiple Seasonalities: Models suited for signals with more than one clear seasonality. Useful for low-frequency data like electricity and logs: MSTL, MFLES, TBATS.

• Theta Models: Fit two theta lines to a deseasonalized time series using different techniques: Theta, OptimizedTheta, DynamicTheta, DynamicOptimizedTheta.

• ARCH/GARCH Family: Models for time series exhibiting non-constant volatility over time. Commonly used in finance.

• Machine Learning: Wrapper for scikit-learn models to be used with StatsForecast.

Automatic Forecasting

AutoARIMA

AutoARIMA

AutoARIMA(d=None, D=None, max_p=5, max_q=5, max_P=2, max_Q=2, max_order=5, max_d=2, max_D=1, start_p=2, start_q=2, start_P=1, start_Q=1, stationary=False, seasonal=True, ic='aicc', stepwise=True, nmodels=94, trace=False, approximation=False, method=None, truncate=None, test='kpss', test_kwargs=None, seasonal_test='seas', seasonal_test_kwargs=None, allowdrift=True, allowmean=True, blambda=None, biasadj=False, season_length=1, distribution='normal', alias='AutoARIMA', prediction_intervals=None)

Bases: _TS

AutoARIMA model.

Automatically selects the best ARIMA (AutoRegressive Integrated Moving Average) model using an information criterion. Default is Akaike Information Criterion (AICc).

Parameters:

Name	Type	Description	Default
d	Optional[int]	Order of first-differencing.	None
D	Optional[int]	Order of seasonal-differencing.	None
max_p	int, default=5	Max autorregresives p.	5
max_q	int, default=5	Max moving averages q.	5
max_P	int, default=2	Max seasonal autorregresives P.	2
max_Q	int, default=2	Max seasonal moving averages Q.	2
max_order	int, default=5	Max p+q+P+Q value if not stepwise selection.	5
max_d	int, default=2	Max non-seasonal differences.	2
max_D	int, default=1	Max seasonal differences.	1
start_p	int, default=2	Starting value of p in stepwise procedure.	2
start_q	int, default=2	Starting value of q in stepwise procedure.	2
start_P	int, default=1	Starting value of P in stepwise procedure.	1
start_Q	int, default=1	Starting value of Q in stepwise procedure.	1
stationary	bool, default=False	If True, restricts search to stationary models.	False
seasonal	bool, default=True	If False, restricts search to non-seasonal models.	True
ic	str, default=“aicc”	Information criterion to be used in model selection.	‘aicc’
stepwise	bool, default=True	If True, will do stepwise selection (faster).	True
nmodels	int, default=94	Number of models considered in stepwise search.	94
trace	bool, default=False	If True, the searched ARIMA models is reported.	False
approximation	Optional[bool], default=False	If True, conditional sums-of-squares estimation, final MLE.	False
method	Optional[str]	Fitting method between maximum likelihood or sums-of-squares.	None
truncate	Optional[bool]	Observations truncated series used in model selection.	None
test	str, default=“kpss”	Unit root test to use. See ndiffs for details.	‘kpss’
test_kwargs	Optional[str]	Unit root test additional arguments.	None
seasonal_test	str, default=“seas”	Selection method for seasonal differences.	‘seas’
seasonal_test_kwargs	Optional[dict]	Seasonal unit root test arguments.	None
allowdrift	bool, default=True	If True, drift models terms considered.	True
allowmean	bool, default=True	If True, non-zero mean models considered.	True
blambda	Optional[float]	Box-Cox transformation parameter.	None
biasadj	bool, default=False	Use adjusted back-transformed mean Box-Cox.	False
season_length	int, default=1	Number of observations per unit of time. Ex: 24 Hourly data.	1
alias	str, default=“AutoARIMA”	Custom name of the model.	‘AutoARIMA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

AutoARIMA.fit

fit(y, X=None)

Fit the AutoARIMA model.

Fit an AutoARIMA to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
AutoARIMA		AutoARIMA fitted model.

AutoARIMA.predict

predict(h, X=None, level=None)

Predict with fitted AutoArima.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoARIMA.predict_in_sample

predict_in_sample(level=None)

Access fitted AutoArima insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoARIMA.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient AutoARIMA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenpus of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x) optional exogenous.	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool, default=False	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoETS

AutoETS

AutoETS(season_length=1, model='ZZZ', damped=None, phi=None, alias='AutoETS', prediction_intervals=None, distribution='normal')

Bases: _TS

Automatic Error, Trend, Seasonal Model.

Automatically selects the best ETS (Error, Trend, Seasonality) model using an information criterion. Default is Akaike Information Criterion (AICc), while particular models are estimated using maximum likelihood. The state-space equations can be determined based on their $M$ multiplicative, $A$ additive, $Z$ optimized or $N$ ommited components. The model string parameter defines the ETS equations: E in [$M, A, Z$], T in [$N, A, M, Z$], and S in [$N, A, M, Z$].

For example when model=‘ANN’ (additive error, no trend, and no seasonality), ETS will explore only a simple exponential smoothing.

If the component is selected as ‘Z’, it operates as a placeholder to ask the AutoETS model to figure out the best parameter.

Parameters:

Name	Type	Description	Default
season_length	int, default=1	Number of observations per unit of time. Ex: 24 Hourly data.	1
model	str, default=“ZZZ”	Controlling state-space-equations.	‘ZZZ’
damped	bool	A parameter that ‘dampens’ the trend.	None
phi	float	Smoothing parameter for trend damping. Only used when damped=True.	None
alias	str, default=“AutoETS”	Custom name of the model.	‘AutoETS’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

AutoETS.fit

fit(y, X=None)

Fit the Exponential Smoothing model.

Fit an Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
AutoETS		Exponential Smoothing fitted model.

AutoETS.predict

predict(h, X=None, level=None)

Predict with fitted Exponential Smoothing.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenpus of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoETS.predict_in_sample

predict_in_sample(level=None)

Access fitted Exponential Smoothing insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoETS.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenpus of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool, default=False	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoCES

AutoCES

AutoCES(season_length=1, model='Z', alias='CES', prediction_intervals=None, distribution='normal')

Bases: _TS

Complex Exponential Smoothing model.

Automatically selects the best Complex Exponential Smoothing model using an information criterion. Default is Akaike Information Criterion (AICc), while particular models are estimated using maximum likelihood. The state-space equations can be determined based on their $S$ simple, $P$ parial, $Z$ optimized or $N$ ommited components. The model string parameter defines the kind of CES model: $N$ for simple CES (withous seasonality), $S$ for simple seasonality (lagged CES), $P$ for partial seasonality (without complex part), $F$ for full seasonality (lagged CES with real and complex seasonal parts).

If the component is selected as ‘Z’, it operates as a placeholder to ask the AutoCES model to figure out the best parameter.

Parameters:

Name	Type	Description	Default
season_length	int, default=1	Number of observations per unit of time. Ex: 24 Hourly data.	1
model	str, default=“Z”	Controlling state-space-equations.	‘Z’
alias	str, default=“CES”	Custom name of the model.	‘CES’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

AutoCES.fit

fit(y, X=None)

Fit the Complex Exponential Smoothing model.

Fit the Complex Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
AutoCES		Complex Exponential Smoothing fitted model.

AutoCES.predict

predict(h, X=None, level=None)

Predict with fitted Exponential Smoothing.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoCES.predict_in_sample

predict_in_sample(level=None)

Access fitted Exponential Smoothing insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoCES.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient Complex Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenpus of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool, default=False	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTheta

AutoTheta

AutoTheta(season_length=1, decomposition_type='multiplicative', model=None, alias='AutoTheta', prediction_intervals=None, distribution='normal')

Bases: _TS

AutoTheta model.

Automatically selects the best Theta (Standard Theta Model (‘STM’), Optimized Theta Model (‘OTM’), Dynamic Standard Theta Model (‘DSTM’), Dynamic Optimized Theta Model (‘DOTM’)) model using mse.

Parameters:

Name	Type	Description	Default
season_length	int, default=1	Number of observations per unit of time. Ex: 24 Hourly data.	1
decomposition_type	str, default=“multiplicative”	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.	‘multiplicative’
model	Optional[str]	Controlling Theta Model. By default searchs the best model.	None
alias	str, default=“AutoTheta”	Custom name of the model.	‘AutoTheta’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

AutoTheta.fit

fit(y, X=None)

Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
AutoTheta		AutoTheta fitted model.

AutoTheta.predict

predict(h, X=None, level=None)

Predict with fitted AutoTheta.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTheta.predict_in_sample

predict_in_sample(level=None)

Access fitted AutoTheta insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoTheta.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool, default=False	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoMFLES

AutoMFLES

AutoMFLES(test_size, season_length=None, n_windows=2, config=None, step_size=None, metric='smape', verbose=False, prediction_intervals=None, alias='AutoMFLES')

Bases: _TS

AutoMFLES

Parameters:

Name	Type	Description	Default
test_size	int	Forecast horizon used during cross validation.	required
season_length	int or list of int, optional, default=None	Number of observations per unit of time. Ex: 24 Hourly data.	None
n_windows	int, default=2	Number of windows used for cross validation.	2
config	dict, optional, default=None	Mapping from parameter name (from the init arguments of MFLES) to a list of values to try. If None, will use defaults.	None
step_size	int, optional, default=None	Step size between each cross validation window. If None will be set to test_size.	None
metric	str, default=‘smape’	Metric used to select the best model. Possible options are: ‘smape’, ‘mape’, ‘mse’ and ‘mae’.	‘smape’
verbose	bool, default=False	Print debugging information.	False
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None
alias	str, default=‘AutoMFLES’	Custom name of the model.	‘AutoMFLES’

AutoMFLES.fit

fit(y, X=None)

Fit the model

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array-like, optional, default=None	Exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
AutoMFLES	AutoMFLES	Fitted AutoMFLES object.

AutoMFLES.predict

predict(h, X=None, level=None)

Predict with fitted AutoMFLES.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array-like, optional, default=None	Exogenous of shape (h, n_x).	None
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoMFLES.predict_in_sample

predict_in_sample(level=None)

Access fitted AutoMFLES insample predictions.

Parameters:

Name	Type	Description	Default
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoMFLES.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient AutoMFLES predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
h	int	Forecast horizon.	required
X	array - like	Insample exogenous of shape (t, n_x).	None
X_future	array - like	Exogenous of shape (h, n_x).	None
level	List[int]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool, default=False	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTBATS

AutoTBATS

AutoTBATS(season_length, use_boxcox=None, bc_lower_bound=0.0, bc_upper_bound=1.0, use_trend=None, use_damped_trend=None, use_arma_errors=True, alias='AutoTBATS')

Bases: _TS

AutoTBATS model.

Automatically selects the best TBATS model from all feasible combinations of the parameters use_boxcox, use_trend, use_damped_trend, and use_arma_errors. Selection is made using the AIC. Default value for use_arma_errors is True since this enables the evaluation of models with and without ARMA errors.

Parameters:

Name	Type	Description	Default
seasonal_periods	int or list of int	Number of observations per unit of time. Ex: 24 Hourly data.	required
use_boxcox	bool, default=None	Whether or not to use a Box-Cox transformation. By default tries both.	None
bc_lower_bound	float, default=0.0	Lower bound for the Box-Cox transformation.	0.0
bc_upper_bound	float, default=1.0	Upper bound for the Box-Cox transformation.	1.0
use_trend	bool, default=None	Whether or not to use a trend component. By default tries both.	None
use_damped_trend	bool, default=None	Whether or not to dampen the trend component. By default tries both.	None
use_arma_errors	bool, default=True	Whether or not to use a ARMA errors. Default is True and this evaluates both models.	True
alias	str	Custom name of the model.	‘AutoTBATS’

AutoTBATS.fit

fit(y, X=None)

Fit TBATS model.

Fit TBATS model to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	numpy.array, optional, default=None	Ignored	None

Returns:

Name	Type	Description
self		TBATS model.

AutoTBATS.predict

predict(h, X=None, level=None)

Predict with fitted TBATS model.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTBATS.predict_in_sample

predict_in_sample(level=None)

Access fitted TBATS model predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTBATS.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient TBATS model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ARIMA Family

ARIMA

ARIMA

ARIMA(order=(0, 0, 0), season_length=1, seasonal_order=(0, 0, 0), include_mean=True, include_drift=False, include_constant=None, blambda=None, biasadj=False, method='CSS-ML', fixed=None, distribution='normal', alias='ARIMA', prediction_intervals=None)

Bases: _TS

ARIMA model.

AutoRegressive Integrated Moving Average model.

Parameters:

Name	Type	Description	Default
order	tuple, default=(0, 0, 0)	A specification of the non-seasonal part of the ARIMA model: the three components (p, d, q) are the AR order, the degree of differencing, and the MA order.	(0, 0, 0)
season_length	int, default=1	Number of observations per unit of time. Ex: 24 Hourly data.	1
seasonal_order	tuple, default=(0, 0, 0)	A specification of the seasonal part of the ARIMA model. (P, D, Q) for the AR order, the degree of differencing, the MA order.	(0, 0, 0)
include_mean	bool, default=True	Should the ARIMA model include a mean term? The default is True for undifferenced series, False for differenced ones (where a mean would not affect the fit nor predictions).	True
include_drift	bool, default=False	Should the ARIMA model include a linear drift term? (i.e., a linear regression with ARIMA errors is fitted.)	False
include_constant	bool, optional, default=None	If True, then includ_mean is set to be True for undifferenced series and include_drift is set to be True for differenced series. Note that if there is more than one difference taken, no constant is included regardless of the value of this argument. This is deliberate as otherwise quadratic and higher order polynomial trends would be induced.	None
blambda	float, optional, default=None	Box-Cox transformation parameter.	None
biasadj	bool, default=False	Use adjusted back-transformed mean Box-Cox.	False
method	str, default=‘CSS-ML’	Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.	‘CSS-ML’
fixed	dict, optional, default=None	Dictionary containing fixed coefficients for the arima model. Example: {'ar1': 0.5, 'ma2': 0.75}. For autoregressive terms use the ar{i} keys. For its seasonal version use sar{i}. For moving average terms use the ma{i} keys. For its seasonal version use sma{i}. For intercept and drift use the intercept and drift keys. For exogenous variables use the ex_{i} keys.	None
alias	str	Custom name of the model.	‘ARIMA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

ARIMA.fit

fit(y, X=None)

Fit the model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		Fitted model.

ARIMA.predict

predict(h, X=None, level=None)

Predict with fitted model.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ARIMA.predict_in_sample

predict_in_sample(level=None)

Access fitted insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

ARIMA.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory efficient predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x) optional exogenous.	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoRegressive

AutoRegressive

AutoRegressive(lags, include_mean=True, include_drift=False, blambda=None, biasadj=False, method='CSS-ML', fixed=None, alias='AutoRegressive', prediction_intervals=None)

Bases: ARIMA

Simple Autoregressive model.

Parameters:

Name	Type	Description	Default
lags	int or list	Number of lags to include in the model. If an int is passed then all lags up to lags are considered. If a list, only the elements of the list are considered as lags.	required
include_mean	bool, default=True	Should the AutoRegressive model include a mean term? The default is True for undifferenced series, False for differenced ones (where a mean would not affect the fit nor predictions).	True
include_drift	bool, default=False	Should the AutoRegressive model include a linear drift term? (i.e., a linear regression with AutoRegressive errors is fitted.)	False
blambda	float, optional, default=None	Box-Cox transformation parameter.	None
biasadj	bool, default=False	Use adjusted back-transformed mean Box-Cox.	False
method	str, default=‘CSS-ML’	Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.	‘CSS-ML’
fixed	dict, optional, default=None	Dictionary containing fixed coefficients for the AutoRegressive model. Example: {'ar1': 0.5, 'ar5': 0.75}. For autoregressive terms use the ar{i} keys.	None
alias	str	Custom name of the model.	‘AutoRegressive’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

AutoRegressive.fit

fit(y, X=None)

Fit the model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		Fitted model.

AutoRegressive.predict

predict(h, X=None, level=None)

Predict with fitted model.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoRegressive.predict_in_sample

predict_in_sample(level=None)

Access fitted insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

AutoRegressive.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory efficient predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x) optional exogenous.	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Exponential Smoothing

SimpleExponentialSmoothing

SimpleExponentialSmoothing

SimpleExponentialSmoothing(alpha, alias='SES', prediction_intervals=None)

Bases: _TS

SimpleExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations, the one-step forecast is given by: $\\hat{y}_{t+1} = \\alpha y_t + (1-\\alpha) \\hat{y}_{t-1}$

The rate $0 \\leq \\alpha \\leq 1$ at which the weights decrease is called the smoothing parameter. When $\\alpha = 1$, SES is equal to the naive method.

Parameters:

Name	Type	Description	Default
alpha	float	Smoothing parameter.	required
alias	str	Custom name of the model.	‘SES’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

SimpleExponentialSmoothing.fit

fit(y, X=None)

Fit the SimpleExponentialSmoothing model.

Fit an SimpleExponentialSmoothing to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		SimpleExponentialSmoothing fitted model.

SimpleExponentialSmoothing.predict

predict(h, X=None, level=None)

Predict with fitted SimpleExponentialSmoothing.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SimpleExponentialSmoothing.predict_in_sample

predict_in_sample()

Access fitted SimpleExponentialSmoothing insample predictions.

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

SimpleExponentialSmoothing.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SimpleExponentialSmoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SimpleExponentialSmoothingOptimized

SimpleExponentialSmoothingOptimized

SimpleExponentialSmoothingOptimized(alias='SESOpt', prediction_intervals=None)

Bases: _TS

SimpleExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations, the one-step forecast is given by: $\\hat{y}_{t+1} = \\alpha y_t + (1-\\alpha) \\hat{y}_{t-1}$

The smoothing parameter $\\alpha^\*$ is optimized by square error minimization.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model.	‘SESOpt’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None

SimpleExponentialSmoothingOptimized.fit

fit(y, X=None)

Fit the SimpleExponentialSmoothingOptimized model.

Fit an SimpleExponentialSmoothingOptimized to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
SimpleExponentialSmoothingOptimized		SimpleExponentialSmoothingOptimized fitted model.

SimpleExponentialSmoothingOptimized.predict

predict(h, X=None, level=None)

Predict with fitted SimpleExponentialSmoothingOptimized.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SimpleExponentialSmoothingOptimized.predict_in_sample

predict_in_sample()

Access fitted SimpleExponentialSmoothingOptimized insample predictions.

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

SimpleExponentialSmoothingOptimized.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SimpleExponentialSmoothingOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalExponentialSmoothing

SeasonalExponentialSmoothing

SeasonalExponentialSmoothing(season_length, alpha, alias='SeasonalES', prediction_intervals=None)

Bases: _TS

SeasonalExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations and season $s$, the one-step forecast is given by: $\\hat{y}_{t+1,s} = \\alpha y_t + (1-\\alpha) \\hat{y}_{t-1,s}$

Parameters:

Name	Type	Description	Default
alpha	float	Smoothing parameter.	required
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	required
alias	str	Custom name of the model.	‘SeasonalES’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None

SeasonalExponentialSmoothing.fit

fit(y, X=None)

Fit the SeasonalExponentialSmoothing model.

Fit an SeasonalExponentialSmoothing to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
SeasonalExponentialSmoothing		SeasonalExponentialSmoothing fitted model.

SeasonalExponentialSmoothing.predict

predict(h, X=None, level=None)

Predict with fitted SeasonalExponentialSmoothing.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalExponentialSmoothing.predict_in_sample

predict_in_sample()

Access fitted SeasonalExponentialSmoothing insample predictions.

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

SeasonalExponentialSmoothing.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SeasonalExponentialSmoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalExponentialSmoothingOptimized

SeasonalExponentialSmoothingOptimized

SeasonalExponentialSmoothingOptimized(season_length, alias='SeasESOpt', prediction_intervals=None)

Bases: _TS

SeasonalExponentialSmoothingOptimized model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations and season $s$, the one-step forecast is given by: $\\hat{y}_{t+1,s} = \\alpha y_t + (1-\\alpha) \\hat{y}_{t-1,s}$

The smoothing parameter $\\alpha^\*$ is optimized by square error minimization.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	required
alias	str	Custom name of the model.	‘SeasESOpt’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None

SeasonalExponentialSmoothingOptimized.fit

fit(y, X=None)

Fit the SeasonalExponentialSmoothingOptimized model.

Fit an SeasonalExponentialSmoothingOptimized to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
SeasonalExponentialSmoothingOptimized		SeasonalExponentialSmoothingOptimized fitted model.

SeasonalExponentialSmoothingOptimized.predict

predict(h, X=None, level=None)

Predict with fitted SeasonalExponentialSmoothingOptimized.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalExponentialSmoothingOptimized.predict_in_sample

predict_in_sample()

Access fitted SeasonalExponentialSmoothingOptimized insample predictions.

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

SeasonalExponentialSmoothingOptimized.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SeasonalExponentialSmoothingOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Holt

Holt

Holt(season_length=1, error_type='A', alias='Holt', prediction_intervals=None)

Bases: AutoETS

Holt’s method.

Also known as double exponential smoothing, Holt’s method is an extension of exponential smoothing for series with a trend. This implementation returns the corresponding ETS model with additive (A) or multiplicative (M) errors (so either ‘AAN’ or ‘MAN’).

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 12 Monthly data.	1
error_type	str	The type of error of the ETS model. Can be additive (A) or multiplicative (M).	’A’
alias	str	Custom name of the model.	‘Holt’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

HoltWinters

HoltWinters

HoltWinters(season_length=1, error_type='A', alias='HoltWinters', prediction_intervals=None)

Bases: AutoETS

Holt-Winters’ method.

Also known as triple exponential smoothing, Holt-Winters’ method is an extension of exponential smoothing for series that contain both trend and seasonality. This implementation returns the corresponding ETS model with additive (A) or multiplicative (M) errors (so either ‘AAA’ or ‘MAM’).

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 12 Monthly data.	1
error_type	str	The type of error of the ETS model. Can be additive (A) or multiplicative (M).	’A’
alias	str	Custom name of the model.	‘HoltWinters’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

Baseline Models

HistoricAverage

HistoricAverage

HistoricAverage(alias='HistoricAverage', prediction_intervals=None)

Bases: _TS

HistoricAverage model.

Also known as mean method. Uses a simple average of all past observations. Assuming there are $t$ observations, the one-step forecast is given by:

$$\hat{y}_{t+1} = \frac{1}{t} \sum_{j=1}^t y_j$$

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model.	‘HistoricAverage’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

HistoricAverage.fit

fit(y, X=None)

Fit the HistoricAverage model.

Fit an HistoricAverage to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		HistoricAverage fitted model.

r

HistoricAverage.predict

predict(h, X=None, level=None)

Predict with fitted HistoricAverage.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

HistoricAverage.predict_in_sample

predict_in_sample(level=None)

Access fitted HistoricAverage insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

HistoricAverage.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient HistoricAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not to return insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Naive

Naive

Naive(alias='Naive', prediction_intervals=None)

Bases: _TS

Naive model.

All forecasts have the value of the last observation: $\\hat{y}\_{t+1} = y_t$ for all $t$

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “Naive”.	’Naive’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Defaults to None.	None

Naive.fit

fit(y, X=None)

Fit the Naive model.

Fit an Naive to a time series (numpy.array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		Naive fitted model.

Naive.predict

predict(h, X=None, level=None)

Predict with fitted Naive.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Naive.predict_in_sample

predict_in_sample(level=None)

Access fitted Naive insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions.

Naive.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient Naive predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n,).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

RandomWalkWithDrift

RandomWalkWithDrift

RandomWalkWithDrift(alias='RWD', prediction_intervals=None)

Bases: _TS

RandomWalkWithDrift model.

A variation of the naive method allows the forecasts to change over time. The amout of change, called drift, is the average change seen in the historical data.

$$\hat{y}_{t+1} = y_t+\frac{1}{t-1}\sum_{j=1}^t (y_j-y_{j-1}) = y_t+ \frac{y_t-y_1}{t-1}$$

From the previous equation, we can see that this is equivalent to extrapolating a line between the first and the last observation.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model.	‘RWD’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

RandomWalkWithDrift.fit

fit(y, X=None)

Fit the RandomWalkWithDrift model.

Fit an RandomWalkWithDrift to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required

Returns:

Name	Type	Description
self		RandomWalkWithDrift fitted model.

r

RandomWalkWithDrift.predict

predict(h, X=None, level=None)

Predict with fitted RandomWalkWithDrift.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

RandomWalkWithDrift.predict_in_sample

predict_in_sample(level=None)

Access fitted RandomWalkWithDrift insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

RandomWalkWithDrift.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient RandomWalkWithDrift predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n,).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalNaive

SeasonalNaive

SeasonalNaive(season_length, alias='SeasonalNaive', prediction_intervals=None)

Bases: _TS

Seasonal naive model.

A method similar to the naive, but uses the last known observation of the same period (e.g. the same month of the previous year) in order to capture seasonal variations.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	required
alias	str	Custom name of the model.	‘SeasonalNaive’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

SeasonalNaive.fit

fit(y, X=None)

Fit the SeasonalNaive model.

Fit an SeasonalNaive to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		SeasonalNaive fitted model.

r

SeasonalNaive.predict

predict(h, X=None, level=None)

Predict with fitted Naive.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalNaive.predict_in_sample

predict_in_sample(level=None)

Access fitted SeasonalNaive insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

r

SeasonalNaive.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SeasonalNaive predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

WindowAverage

WindowAverage

WindowAverage(window_size, alias='WindowAverage', prediction_intervals=None)

Bases: _TS

WindowAverage model.

Uses the average of the last $k$ observations, with $k$ the length of the window. Wider windows will capture global trends, while narrow windows will reveal local trends. The length of the window selected should take into account the importance of past observations and how fast the series changes.

Parameters:

Name	Type	Description	Default
window_size	int	Size of truncated series on which average is estimated.	required
alias	str	Custom name of the model.	‘WindowAverage’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None

r

WindowAverage.fit

fit(y, X=None)

Fit the WindowAverage model.

Fit an WindowAverage to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		WindowAverage fitted model.

WindowAverage.predict

predict(h, X=None, level=None)

Predict with fitted WindowAverage.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

WindowAverage.predict_in_sample

predict_in_sample()

Access fitted WindowAverage insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	required

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

WindowAverage.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient WindowAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x).	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x).	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalWindowAverage

SeasonalWindowAverage

SeasonalWindowAverage(season_length, window_size, alias='SeasWA', prediction_intervals=None)

Bases: _TS

SeasonalWindowAverage model.

An average of the last $k$ observations of the same period, with $k$ the length of the window.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	required
window_size	int	Size of truncated series on which average is estimated.	required
alias	str	Custom name of the model.	‘SeasWA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None

r

SeasonalWindowAverage.fit

fit(y, X=None)

Fit the SeasonalWindowAverage model.

Fit an SeasonalWindowAverage to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
SeasonalWindowAverage		SeasonalWindowAverage fitted model.

SeasonalWindowAverage.predict

predict(h, X=None, level=None)

Predict with fitted SeasonalWindowAverage.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x).	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SeasonalWindowAverage.predict_in_sample

predict_in_sample()

Access fitted SeasonalWindowAverage insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals.	required

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

SeasonalWindowAverage.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient SeasonalWindowAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n,).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not to return insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Sparse or Intermittent Models

ADIDA

ADIDA

ADIDA(alias='ADIDA', prediction_intervals=None)

Bases: _TS

ADIDA model.

Aggregate-Dissagregate Intermittent Demand Approach: Uses temporal aggregation to reduce the number of zero observations. Once the data has been agregated, it uses the optimized SES to generate the forecasts at the new level. It then breaks down the forecast to the original level using equal weights.

ADIDA specializes on sparse or intermittent series are series with very few non-zero observations. They are notoriously hard to forecast, and so, different methods have been developed especifically for them.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “ADIDA”.	’ADIDA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Defaults to None.	None

ADIDA.fit

fit(y, X=None)

Fit the ADIDA model.

Fit an ADIDA to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
ADIDA		ADIDA fitted model.

ADIDA.predict

predict(h, X=None, level=None)

Predict with fitted ADIDA.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ADIDA.predict_in_sample

predict_in_sample(level=None)

Access fitted ADIDA insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

ADIDA.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient ADIDA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n,).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not to return insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonClassic

CrostonClassic

CrostonClassic(alias='CrostonClassic', prediction_intervals=None)

Bases: _TS

CrostonClassic model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by:

$$\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$$

where $\\hat{z}\_t$ and $\\hat{p}\_t$ are forecasted using SES. The smoothing parameter of both components is set equal to 0.1

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “CrostonClassic”.	’CrostonClassic’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Defaults to None.	None

CrostonClassic.fit

fit(y, X=None)

Fit the CrostonClassic model.

Fit an CrostonClassic to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
CrostonClassic		CrostonClassic fitted model.

CrostonClassic.predict

predict(h, X=None, level=None)

Predict with fitted CrostonClassic.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonClassic.predict_in_sample

predict_in_sample(level=None)

Access fitted CrostonClassic insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

CrostonClassic.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient CrostonClassic predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not returns insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonOptimized

CrostonOptimized

CrostonOptimized(alias='CrostonOptimized', prediction_intervals=None)

Bases: _TS

CrostonOptimized model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by:

$$\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$$

A variation of the classic Croston’s method where the smooting paramater is optimally selected from the range $[0.1,0.3]$. Both the non-zero demand $z_t$ and the inter-demand intervals $p_t$ are smoothed separately, so their smoothing parameters can be different.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “CrostonOptimized”.	’CrostonOptimized’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals. Defaults to None.	None

CrostonOptimized.fit

fit(y, X=None)

Fit the CrostonOptimized model.

Fit an CrostonOptimized to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
CrostonOptimized		CrostonOptimized fitted model.

CrostonOptimized.predict

predict(h, X=None, level=None)

Predict with fitted CrostonOptimized.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonOptimized.predict_in_sample

predict_in_sample(level=None)

Access fitted CrostonOptimized insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

CrostonOptimized.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient CrostonOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not returns insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonSBA

CrostonSBA

CrostonSBA(alias='CrostonSBA', prediction_intervals=None)

Bases: _TS

CrostonSBA model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by:

$$\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$$

A variation of the classic Croston’s method that uses a debiasing factor, so that the forecast is given by:

$$\hat{y}_t = 0.95 \frac{\hat{z}_t}{\hat{p}_t}$$

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “CrostonSBA”.	’CrostonSBA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Defaults to None.	None

CrostonSBA.fit

fit(y, X=None)

Fit the CrostonSBA model.

Fit an CrostonSBA to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
CrostonSBA		CrostonSBA fitted model.

CrostonSBA.predict

predict(h, X=None, level=None)

Predict with fitted CrostonSBA.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

CrostonSBA.predict_in_sample

predict_in_sample(level=None)

Access fitted CrostonSBA insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

CrostonSBA.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient CrostonSBA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not to return insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

IMAPA

IMAPA

IMAPA(alias='IMAPA', prediction_intervals=None)

Bases: _TS

IMAPA model.

Intermittent Multiple Aggregation Prediction Algorithm: Similar to ADIDA, but instead of using a single aggregation level, it considers multiple in order to capture different dynamics of the data. Uses the optimized SES to generate the forecasts at the new levels and then combines them using a simple average.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model. Defaults to “IMAPA”.	’IMAPA’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Defaults to None.	None

IMAPA.fit

fit(y, X=None)

Fit the IMAPA model.

Fit an IMAPA to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
IMAPA		IMAPA fitted model.

IMAPA.predict

predict(h, X=None, level=None)

Predict with fitted IMAPA.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

IMAPA.predict_in_sample

predict_in_sample(level=None)

Access fitted IMAPA insample predictions.

Parameters:

Name	Type	Description	Default
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

IMAPA.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient IMAPA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional insample exogenous of shape (t, n_x). Defaults to None.	None
X_future	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None
fitted	bool	Whether or not to return insample predictions. Defaults to False.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

TSB

TSB

TSB(alpha_d, alpha_p, alias='TSB', prediction_intervals=None)

Bases: _TS

TSB model.

Teunter-Syntetos-Babai: A modification of Croston’s method that replaces the inter-demand intervals with the demand probability $d_t$, which is defined as follows.

$$d_t = \begin{cases} 1 & \text{if demand occurs at time t} \\ 0 & \text{otherwise.} \end{cases}$$

Hence, the forecast is given by

$$\hat{y}_t= \hat{d}_t\hat{z_t}$$

Both $d_t$ and $z_t$ are forecasted using SES. The smooting paramaters of each may differ, like in the optimized Croston’s method.

Parameters:

Name	Type	Description	Default
alpha_d	float	Smoothing parameter for demand.	required
alpha_p	float	Smoothing parameter for probability.	required
alias	str	Custom name of the model. Defaults to “TSB”.	’TSB’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals. Defaults to None.	None

TSB.fit

fit(y, X=None)

Fit the TSB model.

Fit an TSB to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	ndarray	Clean time series of shape (t, ).	required
X	Optional[ndarray]	Optional exogenous variables. Defaults to None.	None

Returns:

Name	Type	Description
TSB		TSB fitted model.

TSB.predict

predict(h, X=None, level=None)

Predict with fitted TSB.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	Optional[ndarray]	Optional exogenous of shape (h, n_x). Defaults to None.	None
level	Optional[List[int]]	Confidence levels (0-100) for prediction intervals. Defaults to None.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

TSB.predict_in_sample

predict_in_sample(level=None)

Access fitted TSB insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

TSB.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient TSB predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Multiple Seasonalities

MSTL

MSTL

MSTL(season_length, trend_forecaster=AutoETS(model='ZZN'), stl_kwargs=None, alias='MSTL', prediction_intervals=None)

Bases: _TS

MSTL model.

The MSTL (Multiple Seasonal-Trend decomposition using LOESS) decomposes the time series in multiple seasonalities using LOESS. Then forecasts the trend using a custom non-seaonal model and each seasonality using a SeasonalNaive model.

Parameters:

Name	Type	Description	Default
season_length	Union[int, List[int]]	Number of observations per unit of time. For multiple seasonalities use a list.	required
trend_forecaster	model, default=AutoETS(model=‘ZZN’)	StatsForecast model used to forecast the trend component.	AutoETS(model=‘ZZN’)
stl_kwargs	dict	Extra arguments to pass to statsmodels.tsa.seasonal.STL. The period and seasonal arguments are reserved.	None
alias	str	Custom name of the model.	‘MSTL’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

MSTL.fit

fit(y, X=None)

Fit the MSTL model.

Fit MSTL to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
self		MSTL fitted model.

MSTL.predict

predict(h, X=None, level=None)

Predict with fitted MSTL.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

MSTL.predict_in_sample

predict_in_sample(level=None)

Access fitted MSTL insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

MSTL.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient MSTL predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

MFLES

MFLES

MFLES(season_length=None, fourier_order=None, max_rounds=50, ma=None, alpha=1.0, decay=-1.0, changepoints=True, n_changepoints=0.25, seasonal_lr=0.9, trend_lr=0.9, exogenous_lr=1.0, residuals_lr=1.0, cov_threshold=0.7, moving_medians=False, min_alpha=0.05, max_alpha=1.0, trend_penalty=True, multiplicative=None, smoother=False, robust=None, verbose=False, prediction_intervals=None, alias='MFLES')

Bases: _TS

MFLES model.

A method to forecast time series based on Gradient Boosted Time Series Decomposition which treats traditional decomposition as the base estimator in the boosting process. Unlike normal gradient boosting, slight learning rates are applied at the component level (trend/seasonality/exogenous).

The method derives its name from some of the underlying estimators that can enter into the boosting procedure, specifically: a simple Median, Fourier functions for seasonality, a simple/piecewise Linear trend, and Exponential Smoothing.

Parameters:

Name	Type	Description	Default
season_length	int or list of int	Number of observations per unit of time. Ex: 24 Hourly data. Default None.	None
fourier_order	int	How many fourier sin/cos pairs to create, the larger the number the more complex of a seasonal pattern can be fitted. A lower number leads to smoother results. This is auto-set based on seasonal_period. Default None.	None
max_rounds	int	The max number of boosting rounds. The boosting will auto-stop but depending on other parameters such as rs_lr you may want more rounds. Generally more rounds means a smoother fit. Default 50.	50
ma	int	The moving average order to use, this is auto-set based on internal logic. Passing 4 would fit a 4 period moving average on the residual component. Default None.	None
alpha	float	The alpha which is used in fitting the underlying LASSO when using piecewise functions. Default 1.0.	1.0
decay	float	Effects the slopes of the piecewise-linear basis function. Default -1.0.	-1.0
changepoints	boolean	Whether to fit for changepoints if all other logic allows for it. If False, MFLES will not ever fit a piecewise trend. Default True.	True
n_changepoints	int or float	Number (if int) or proportion (if float) of changepoint knots to place. The default of 0.25 will place 0.25 * (series length) number of knots. Default 0.25.	0.25
seasonal_lr	float	A shrinkage parameter (0 < seasonal_lr <= 1) which penalizes the seasonal fit. A value of 0.9 will flatly multiply the seasonal fit by 0.9 each boosting round, this can be used to allow more signal to the exogenous component. Default 0.9.	0.9
trend_lr	float	A shrinkage parameter (0 < trend_lr <= 1) which penalizes the linear trend fit A value of 0.9 will flatly multiply the linear fit by 0.9 each boosting round, this can be used to allow more signal to the seasonality or exogenous components. Default 0.9.	0.9
exogenous_lr	float	The shrinkage parameter (0 < exogenous_lr <= 1) which controls how much of the exogenous signal is carried to the next round. Default 1.0.	1.0
residuals_lr	float	A shrinkage parameter (0 < residuals_lr <= 1) which penalizes the residual smoothing. A value of 0.9 will flatly multiply the residual fit by 0.9 each boosting round, this can be used to allow more signal to the seasonality or linear components. Default 1.0.	1.0
cov_threshold	float	The deseasonalized cov is used to auto-set some logic, lowering the cov_threshold will result in simpler and less complex residual smoothing. If you pass something like 1000 then there will be no safeguards applied. Default 0.7.	0.7
moving_medians	bool	The default behavior is to fit an initial median to the time series. If True, then it will fit a median per seasonal period. Default False.	False
min_alpha	float	The minimum alpha in the SES ensemble. Default 0.05.	0.05
max_alpha	float	The maximum alpha used in the SES ensemble. Default 1.0.	1.0
trend_penalty	bool	Whether to apply a simple penalty to the linear trend component, very useful for dealing with the potentially dangerous piecewise trend. Default True.	True
multiplicative	bool	Auto-set based on internal logic. If True, it will simply take the log of the time series. Default None.	None
smoother	bool	If True, then a simple exponential ensemble will be used rather than auto settings. Default False.	False
robust	bool	If True then MFLES will fit using more reserved methods, i.e. not using piecewise trend or moving average residual smoother. Auto-set based on internal logic. Default None.	None
verbose	bool	Print debugging information. Default False.	False
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None
alias	str	Custom name of the model. Default ‘MFLES’.	‘MFLES’

MFLES.fit

fit(y, X=None)

Fit the model

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Exogenous of shape (t, n_x). Default None.	None

Returns:

Name	Type	Description
self	MFLES	Fitted MFLES object.

MFLES.predict

predict(h, X=None, level=None)

Predict with fitted MFLES.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Exogenous of shape (h, n_x). Default None.	None
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

MFLES.predict_in_sample

predict_in_sample(level=None)

Access fitted SklearnModel insample predictions.

Parameters:

Name	Type	Description	Default
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

MFLES.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient MFLES predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
h	int	Forecast horizon.	required
X	array - like	Insample exogenous of shape (t, n_x).	None
X_future	array - like	Exogenous of shape (h, n_x).	None
level	List[int]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions. Default False.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

TBATS

TBATS

TBATS(season_length, use_boxcox=True, bc_lower_bound=0.0, bc_upper_bound=1.0, use_trend=True, use_damped_trend=False, use_arma_errors=False, alias='TBATS')

Bases: AutoTBATS

Trigonometric Box-Cox transform, ARMA errors, Trend and Seasonal components (TBATS) model.

TBATS is an innovations state space model framework used for forecasting time series with multiple seasonalities. It uses a Box-Cox tranformation, ARMA errors, and a trigonometric representation of the seasonal patterns based on Fourier series.

The name TBATS is an acronym for the key features of the model: Trigonometric, Box-Cox transform, ARMA errors, Trend, and Seasonal components.

Parameters:

Name	Type	Description	Default
season_length	Union[int, List[int]]	Number of observations per unit of time. Ex: 24 Hourly data.	required
use_boxcox	Optional[bool]	Whether or not to use a Box-Cox transformation. Default True.	True
bc_lower_bound	float	Lower bound for the Box-Cox transformation. Default 0.0.	0.0
bc_upper_bound	float	Upper bound for the Box-Cox transformation. Default 1.0.	1.0
use_trend	Optional[bool]	Whether or not to use a trend component. Default True.	True
use_damped_trend	Optional[bool]	Whether or not to dampen the trend component. Default False.	False
use_arma_errors	bool	Whether or not to use a ARMA errors. Default False.	False
alias	str	Custom name of the model. Default ‘TBATS’.	‘TBATS’

Theta Family

Theta

Theta

Theta(season_length=1, decomposition_type='multiplicative', alias='Theta', prediction_intervals=None)

Bases: AutoTheta

Standard Theta Method.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data. Default 1.	1
decomposition_type	str	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’. Default ‘multiplicative’.	‘multiplicative’
alias	str	Custom name of the model. Default ‘Theta’.	‘Theta’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Default None.	None

OptimizedTheta

OptimizedTheta

OptimizedTheta(season_length=1, decomposition_type='multiplicative', alias='OptimizedTheta', prediction_intervals=None)

Bases: AutoTheta

Optimized Theta Method.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data. Default 1.	1
decomposition_type	str	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’. Default ‘multiplicative’.	‘multiplicative’
alias	str	Custom name of the model. Default ‘OptimizedTheta’.	‘OptimizedTheta’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals. Default None.	None

DynamicTheta

DynamicTheta

DynamicTheta(season_length=1, decomposition_type='multiplicative', alias='DynamicTheta', prediction_intervals=None)

Bases: AutoTheta

Dynamic Standard Theta Method.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	1
decomposition_type	str	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.	‘multiplicative’
alias	str	Custom name of the model.	‘DynamicTheta’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

DynamicOptimizedTheta

DynamicOptimizedTheta

DynamicOptimizedTheta(season_length=1, decomposition_type='multiplicative', alias='DynamicOptimizedTheta', prediction_intervals=None)

Bases: AutoTheta

Dynamic Optimized Theta Method.

Parameters:

Name	Type	Description	Default
season_length	int	Number of observations per unit of time. Ex: 24 Hourly data.	1
decomposition_type	str	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.	‘multiplicative’
alias	str	Custom name of the model.	‘DynamicOptimizedTheta’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

ARCH/GARCH Family

GARCH

GARCH

GARCH(p=1, q=1, alias='GARCH', prediction_intervals=None)

Bases: _TS

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model.

A method for modeling time series that exhibit non-constant volatility over time. The GARCH model assumes that at time $t$, $y_t$ is given by:

$$y_t = v_t \sigma_t$$

with

$$\sigma_t^2 = w + \sum_{i=1}^p a_i y_{t-i}^2 + \sum_{j=1}^q b_j \sigma_{t-j}^2.$$

Here $v_t$ is a sequence of iid random variables with zero mean and unit variance. The coefficients $w$, $a_i$, $i=1,...,p$, and $b_j$, $j=1,...,q$ must satisfy the following conditions:

1. $w > 0$ and $a_i, b_j \\geq 0$ for all $i$ and $j$.

2. $\\sum\_{k=1}^{max(p,q)} a_k + b_k < 1$. Here it is assumed that $a_i=0$ for $i>p$ and $b_j=0$ for $j>q$.

The ARCH model is a particular case of the GARCH model when $q=0$.

Parameters:

Name	Type	Description	Default
p	int	Number of lagged versions of the series.	1
q	int	Number of lagged versions of the volatility.	1
alias	str	Custom name of the model.	‘GARCH’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

GARCH.fit

fit(y, X=None)

Fit GARCH model.

Fit GARCH model to a time series (numpy array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required

Returns:

Name	Type	Description
self		GARCH model.

GARCH.predict

predict(h, X=None, level=None)

Predict with fitted GARCH model.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

GARCH.predict_in_sample

predict_in_sample(level=None)

Access fitted GARCH model predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

GARCH.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient GARCH model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n, ).	required
h	int	Forecast horizon.	required
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not returns insample predictions.	False

Returns:

Name	Type	Description
forecasts	dict	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ARCH

ARCH

ARCH(p=1, alias='ARCH', prediction_intervals=None)

Bases: GARCH

Autoregressive Conditional Heteroskedasticity (ARCH) model.

A particular case of the GARCH(p,q) model where $q=0$. It assumes that at time $t$, $y_t$ is given by:

$$y_t = \epsilon_t \sigma_t$$

with

$$\sigma_t^2 = w0 + \sum_{i=1}^p a_i y_{t-i}^2$$

Here $\\epsilon_t$ is a sequence of iid random variables with zero mean and unit variance. The coefficients $w$ and $a_i$, $i=1,...,p$ must be nonnegative and $\\sum\_{k=1}^p a_k < 1$.

Parameters:

Name	Type	Description	Default
p	int	Number of lagged versions of the series.	1
alias	str	Custom name of the model.	‘ARCH’
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.	None

Machine Learning

SklearnModel

SklearnModel

SklearnModel(model, prediction_intervals=None, alias=None)

Bases: _TS

scikit-learn model wrapper

Parameters:

Name	Type	Description	Default
model	BaseEstimator	scikit-learn estimator	required
prediction_intervals	Optional[ConformalIntervals]	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.	None
alias	str	Custom name of the model. If None will use the model’s class.	None

SklearnModel.fit

fit(y, X)

Fit the model.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Exogenous of shape (t, n_x).	required

Returns:

Name	Type	Description
SklearnModel	SklearnModel	Fitted SklearnModel object.

SklearnModel.predict

predict(h, X, level=None)

Predict with fitted SklearnModel.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Exogenous of shape (h, n_x).	required
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

SklearnModel.predict_in_sample

predict_in_sample(level=None)

Access fitted SklearnModel insample predictions.

Parameters:

Name	Type	Description	Default
level	List[int]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

SklearnModel.forecast

forecast(y, h, X, X_future, level=None, fitted=False)

Memory Efficient SklearnModel predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
h	int	Forecast horizon.	required
X	array - like	Insample exogenous of shape (t, n_x).	required
X_future	array - like	Exogenous of shape (h, n_x).	required
level	List[int]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict	Dict[str, Any]	Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Fallback Models

These models are used as fallbacks when other models fail during forecasting.

ConstantModel

ConstantModel

ConstantModel(constant, alias='ConstantModel')

Bases: _TS

Constant Model.

Returns Constant values.

Parameters:

Name	Type	Description	Default
constant	float	Custom value to return as forecast.	required
alias	str	Custom name of the model.	‘ConstantModel’

ConstantModel.fit

fit(y, X=None)

Fit the Constant model.

Fit an Constant Model to a time series (numpy.array) y.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (t, ).	required
X	array - like	Optional exogenous of shape (t, n_x).	None

Returns:

Name	Type	Description
ConstantModel		Constant fitted model.

ConstantModel.predict

predict(h, X=None, level=None)

Predict with fitted ConstantModel.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
X	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ConstantModel.predict_in_sample

predict_in_sample(level=None)

Access fitted Constant Model insample predictions.

Parameters:

Name	Type	Description	Default
level	List[float]	Confidence levels (0-100) for prediction intervals.	None

Returns:

Name	Type	Description
dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

ConstantModel.forecast

forecast(y, h, X=None, X_future=None, level=None, fitted=False)

Memory Efficient Constant Model predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.

Parameters:

Name	Type	Description	Default
y	array	Clean time series of shape (n,).	required
h	int	Forecast horizon.	required
X	array - like	Optional insample exogenous of shape (t, n_x).	None
X_future	array - like	Optional exogenous of shape (h, n_x).	None
level	List[float]	Confidence levels (0-100) for prediction intervals.	None
fitted	bool	Whether or not to return insample predictions.	False

Returns:

Name	Type	Description
dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ZeroModel

ZeroModel

ZeroModel(alias='ZeroModel')

Bases: ConstantModel

Returns Zero forecasts.

Returns Zero values.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model.	‘ZeroModel’

NaNModel

NaNModel

NaNModel(alias='NaNModel')

Bases: ConstantModel

NaN Model.

Returns NaN values.

Parameters:

Name	Type	Description	Default
alias	str	Custom name of the model.	‘NaNModel’

Usage Examples

Basic Model Usage

from statsforecast import StatsForecast
from statsforecast.models import AutoARIMA, Naive
from statsforecast.utils import generate_series

# Generate example data
df = generate_series(n_series=10)

# Create StatsForecast instance with models
sf = StatsForecast(
    models=[
        AutoARIMA(season_length=7),
        Naive()
    ],
    freq='D'
)

# Forecast
forecasts = sf.forecast(df=df, h=7)

Using Multiple Models

from statsforecast import StatsForecast
from statsforecast.models import (
    AutoARIMA,
    AutoETS,
    SeasonalNaive,
    Theta,
    HistoricAverage
)

# Combine multiple models for comparison
models = [
    AutoARIMA(season_length=12),
    AutoETS(season_length=12),
    SeasonalNaive(season_length=12),
    Theta(season_length=12),
    HistoricAverage()
]

sf = StatsForecast(models=models, freq='M', n_jobs=-1)
forecasts = sf.forecast(df=df, h=12, level=[80, 95])

Model with Prediction Intervals

from statsforecast import StatsForecast
from statsforecast.models import AutoARIMA
from statsforecast.utils import ConformalIntervals

# Create model with conformal prediction intervals
model = AutoARIMA(
    season_length=12,
    prediction_intervals=ConformalIntervals(n_windows=2, h=12),
    alias='ConformalAutoARIMA'
)

sf = StatsForecast(models=[model], freq='M')
forecasts = sf.forecast(df=df, h=12, level=[80, 95])

Sparse/Intermittent Data

from statsforecast import StatsForecast
from statsforecast.models import (
    CrostonOptimized,
    ADIDA,
    IMAPA,
    TSB
)

# Models specialized for sparse/intermittent data
sparse_models = [
    CrostonOptimized(),
    ADIDA(),
    IMAPA(),
    TSB(alpha_d=0.2, alpha_p=0.2)
]

sf = StatsForecast(models=sparse_models, freq='D')
forecasts = sf.forecast(df=sparse_df, h=30)

Multiple Seasonalities

from statsforecast import StatsForecast
from statsforecast.models import MSTL, AutoTBATS

# For data with multiple seasonal patterns
models = [
    MSTL(season_length=[24, 168]),  # Hourly with daily and weekly seasonality
    AutoTBATS(season_length=[24, 168])
]

sf = StatsForecast(models=models, freq='H')
forecasts = sf.forecast(df=hourly_df, h=168)

ARCH/GARCH for Volatility

from statsforecast import StatsForecast
from statsforecast.models import GARCH, ARCH

# Models for financial data with volatility
volatility_models = [
    GARCH(p=1, q=1),
    ARCH(p=1)
]

sf = StatsForecast(models=volatility_models, freq='D')
forecasts = sf.forecast(df=financial_df, h=30)

Using Scikit-learn Models

from statsforecast import StatsForecast
from statsforecast.models import SklearnModel
from sklearn.ensemble import RandomForestRegressor
from sklearn.linear_model import Ridge

# Wrap scikit-learn models
models = [
    SklearnModel(RandomForestRegressor(n_estimators=100), alias='RF'),
    SklearnModel(Ridge(alpha=1.0), alias='Ridge')
]

sf = StatsForecast(models=models, freq='D')
forecasts = sf.forecast(df=df, h=14)

Model Selection Tips

• For automatic selection: Start with AutoARIMA or AutoETS
• For baseline comparison: Use Naive, SeasonalNaive, or HistoricAverage
• For seasonal data: Use models with season_length parameter
• For sparse data: Use Croston family or ADIDA
• For multiple seasonalities: Use MSTL or TBATS
• For volatile data: Use GARCH or ARCH
• For ensemble approaches: Combine multiple models and compare performance

References

For detailed information on the statistical models and algorithms, please refer to the source code and the original academic papers referenced in the docstrings.