AutoARIMA

Auto-(S)ARIMA(X) forecaster, from pmdarima package.

Quickstart

from sktime.forecasting.arima import AutoARIMA

estimator = AutoARIMA(start_p=2, d=None, start_q=2, max_p=5, max_d=2, max_q=5, start_P=1, D=None, start_Q=1, max_P=2, max_D=1, max_Q=2, max_order=5, sp=1, seasonal=True, stationary=False, information_criterion='aic', alpha=0.05, test='kpss', seasonal_test='ocsb', stepwise=True, n_jobs=1, start_params=None, trend=None, method='lbfgs', maxiter=50, offset_test_args=None, seasonal_test_args=None, suppress_warnings=False, error_action='warn', trace=False, random=False, random_state=None, n_fits=10, out_of_sample_size=0, scoring='mse', scoring_args=None, with_intercept=True, update_pdq=True, time_varying_regression=False, enforce_stationarity=True, enforce_invertibility=True, simple_differencing=False, measurement_error=False, mle_regression=True, hamilton_representation=False, concentrate_scale=False)

Parameters(46)

start_pint, optional (default=2)

The starting value of p, the order (or number of time lags) of the auto-regressive (“AR”) model. Must be a positive integer.

dint, optional (default=None)

The order of first-differencing. If None (by default), the value will automatically be selected based on the results of the test (i.e., either the Kwiatkowski-Phillips-Schmidt-Shin, Augmented Dickey-Fuller or the Phillips-Perron test will be conducted to find the most probable value). Must be a positive integer or None. Note that if d is None, the runtime could be significantly longer.

start_qint, optional (default=2)

The starting value of q, the order of the moving-average (“MA”) model. Must be a positive integer.

max_pint, optional (default=5)

The maximum value of p, inclusive. Must be a positive integer greater than or equal to start_p.

max_dint, optional (default=2)

The maximum value of d, or the maximum number of non-seasonal differences. Must be a positive integer greater than or equal to d.

max_qint, optional (default=5)

he maximum value of q, inclusive. Must be a positive integer greater than start_q.

start_Pint, optional (default=1)

The starting value of P, the order of the auto-regressive portion of the seasonal model.

Dint, optional (default=None)

The order of the seasonal differencing. If None (by default, the value will automatically be selected based on the results of the seasonal_test. Must be a positive integer or None.

start_Qint, optional (default=1)

The starting value of Q, the order of the moving-average portion of the seasonal model.

max_Pint, optional (default=2)

The maximum value of P, inclusive. Must be a positive integer greater than start_P.

max_Dint, optional (default=1)

The maximum value of D. Must be a positive integer greater than D.

max_Qint, optional (default=2)

The maximum value of Q, inclusive. Must be a positive integer greater than start_Q.

max_orderint, optional (default=5)

Maximum value of p+q+P+Q if model selection is not stepwise. If the sum of p and q is >= max_order, a model will not be fit with those parameters, but will progress to the next combination. Default is 5. If max_order is None, it means there are no constraints on maximum order.

spint, optional (default=1)

The period for seasonal differencing, sp refers to the number of periods in each season. For example, sp is 4 for quarterly data, 12 for monthly data, or 1 for annual (non-seasonal) data. Default is 1. Note that if sp == 1 (i.e., is non-seasonal), seasonal will be set to False. For more information on setting this parameter, see Setting sp. (link to http://alkaline-ml.com/pmdarima/tips_and_tricks.html#period)

seasonalbool, optional (default=True)

Whether to fit a seasonal ARIMA. Default is True. Note that if seasonal is True and sp == 1, seasonal will be set to False.

stationarybool, optional (default=False)

Whether the time-series is stationary and d should be set to zero.

information_criterionstr, optional (default=’aic’)

The information criterion used to select the best ARIMA model. One of pmdarima.arima.auto_arima.VALID_CRITERIA, (‘aic’, ‘bic’, ‘hqic’, ‘oob’).

alphafloat, optional (default=0.05)

Level of the test for testing significance.

teststr, optional (default=’kpss’)

Type of unit root test to use in order to detect stationarity if stationary is False and d is None.

seasonal_teststr, optional (default=’ocsb’)

This determines which seasonal unit root test is used if seasonal is True and D is None.

stepwisebool, optional (default=True)

Whether to use the stepwise algorithm outlined in Hyndman and Khandakar (2008) to identify the optimal model parameters. The stepwise algorithm can be significantly faster than fitting all (or a random subset of) hyper-parameter combinations and is less likely to over-fit the model.

n_jobsint, optional (default=1)

The number of models to fit in parallel in the case of a grid search (stepwise=False). Default is 1, but -1 can be used to designate “as many as possible”.

start_paramsarray-like, optional (default=None)

Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params.

trendstr, optional (default=None)

The trend parameter. If with_intercept is True, trend will be used. If with_intercept is False, the trend will be set to a no- intercept value.

methodstr, optional (default=’lbfgs’)

The method determines which solver from scipy.optimize is used, and it can be chosen from among the following strings:

• ‘newton’ for Newton-Raphson

• ‘nm’ for Nelder-Mead

• ‘bfgs’ for Broyden-Fletcher-Goldfarb-Shanno (BFGS)

• ‘lbfgs’ for limited-memory BFGS with optional box constraints

• ‘powell’ for modified Powell’s method

• ‘cg’ for conjugate gradient

• ‘ncg’ for Newton-conjugate gradient

• ‘basinhopping’ for global basin-hopping solver

The explicit arguments in fit are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. These can be passed as **fit_kwargs

maxiterint, optional (default=50)

The maximum number of function evaluations.

offset_test_argsdict, optional (default=None)

The args to pass to the constructor of the offset (d) test. See pmdarima.arima.stationarity for more details.

seasonal_test_argsdict, optional (default=None)

The args to pass to the constructor of the seasonal offset (D) test. See pmdarima.arima.seasonality for more details.

suppress_warningsbool, optional (default=False)

Many warnings might be thrown inside of statsmodels. If suppress_warnings is True, all of the warnings coming from ARIMA will be squelched.

error_actionstr, optional (default=’warn’)

If unable to fit an ARIMA due to stationarity issues, whether to warn (‘warn’), raise the ValueError (‘raise’) or ignore (‘ignore’). Note that the default behavior is to warn, and fits that fail will be returned as None. This is the recommended behavior, as statsmodels ARIMA and SARIMAX models hit bugs periodically that can cause an otherwise healthy parameter combination to fail for reasons not related to pmdarima.

tracebool, optional (default=False)

Whether to print status on the fits. A value of False will print no debugging information. A value of True will print some. Integer values exceeding 1 will print increasing amounts of debug information at each fit.

randombool, optional (default=’False’)

Similar to grid searches, auto_arima provides the capability to perform a “random search” over a hyper-parameter space. If random is True, rather than perform an exhaustive search or stepwise search, only n_fits ARIMA models will be fit (stepwise must be False for this option to do anything).

random_stateint, long or numpy RandomState, optional (default=None)

The PRNG for when random=True. Ensures replicable testing and results.

n_fitsint, optional (default=10)

If random is True and a “random search” is going to be performed, n_iter is the number of ARIMA models to be fit.

out_of_sample_sizeint, optional (default=0)

The number of examples from the tail of the time series to hold out and use as validation examples. The model will not be fit on these samples, but the observations will be added into the model’s endog and exog arrays so that future forecast values originate from the end of the endogenous vector. For instance:

y = [0, 1, 2, 3, 4, 5, 6] out_of_sample_size = 2 > Fit on: [0, 1, 2, 3, 4] > Score on: [5, 6] > Append [5, 6] to end of self.arima_res_.data.endog values

scoringstr, optional (default=’mse’)

If performing validation (i.e., if out_of_sample_size > 0), the metric to use for scoring the out-of-sample data. One of (‘mse’, ‘mae’)

scoring_argsdict, optional (default=None)

A dictionary of key-word arguments to be passed to the scoring metric.

with_interceptbool, optional (default=True)

Whether to include an intercept term.

update_pdqbool, optional (default=True)

whether to update pdq parameters in update True: model is refit on all data seen so far, potentially updating p,d,q False: model updates only ARIMA coefficients via likelihood, as in pmdarima

time_varying_regressionboolean, optional (default=False)

Whether or not coefficients on the exogenous regressors are allowed to vary over time.

enforce_stationarityboolean, optional (default=True)

Whether or not to transform the AR parameters to enforce stationarity in the auto-regressive component of the model. - enforce_invertibility: boolean, optional (default=True) Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model.

simple_differencingboolean, optional (default=False)

Whether or not to use partially conditional maximum likelihood estimation for seasonal ARIMA models. If True, differencing is performed prior to estimation, which discards the first \(s D + d\) initial rows but results in a smaller state-space formulation. If False, the full SARIMAX model is put in state-space form so that all datapoints can be used in estimation. Default is False.

measurement_error: boolean, optional (default=False)

Whether or not to assume the endogenous observations endog were measured with error. Default is False.

mle_regressionboolean, optional (default=True)

Whether or not to use estimate the regression coefficients for the exogenous variables as part of maximum likelihood estimation or through the Kalman filter (i.e. recursive least squares). If time_varying_regression is True, this must be set to False. Default is True.

hamilton_representationboolean, optional (default=False)

Whether or not to use the Hamilton representation of an ARMA process

• if True, uses the Hamilton representation.

• if False, uses the Harvey representation.

Default is False.

concentrate_scaleboolean, optional (default=False)

Whether or not to concentrate the scale out of the likelihood, scale = variance of the error term. This reduces the number of parameters estimated by maximum likelihood by one, but standard errors will then not be available for the scale parameter.

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.arima import AutoARIMA
>>> y = load_airline ()
>>> forecaster = AutoARIMA (
... sp = 12, d = 0, max_p = 2, max_q = 2, suppress_warnings = True
... )
>>> forecaster. fit (y) AutoARIMA(
... )
>>> y_pred = forecaster. predict (fh = [1, 2, 3 ])

References

1. [1 ] https://alkaline-ml.com/pmdarima/modules/generated/pmdarima.arima.AutoARIMA.html