pyramid.arima.auto_arima(y, exogenous=None, 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=10, m=1, seasonal=True, stationary=False, information_criterion='aic', alpha=0.05, test='kpss', seasonal_test='ch', stepwise=True, n_jobs=1, start_params=None, trend='c', method=None, transparams=True, solver='lbfgs', maxiter=50, disp=0, callback=None, offset_test_args=None, seasonal_test_args=None, suppress_warnings=False, error_action='warn', trace=False, random=False, random_state=None, n_fits=10, return_valid_fits=False, out_of_sample_size=0, scoring='mse', scoring_args=None, **fit_args)[source][source]

Automatically discover the optimal order for an ARIMA model.

The auto_arima function seeks to identify the most optimal parameters for an ARIMA model, and returns a fitted ARIMA model. This function is based on the commonly-used R function, forecast::auto.arima [3].

The auro_arima function works by conducting differencing tests (i.e., Kwiatkowski–Phillips–Schmidt–Shin, Augmented Dickey-Fuller or Phillips–Perron) to determine the order of differencing, d, and then fitting models within ranges of defined start_p, max_p, start_q, max_q ranges. If the seasonal optional is enabled, auto_arima also seeks to identify the optimal P and Q hyper- parameters after conducting the Canova-Hansen to determine the optimal order of seasonal differencing, D.

In order to find the best model, auto_arima optimizes for a given information_criterion, one of {‘aic’, ‘aicc’, ‘bic’, ‘hqic’, ‘oob’} (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, Hannan-Quinn Information Criterion, or “out of bag”–for validation scoring–respectively) and returns the ARIMA which minimizes the value.

Note that due to stationarity issues, auto_arima might not find a suitable model that will converge. If this is the case, a ValueError will be thrown suggesting stationarity-inducing measures be taken prior to re-fitting or that a new range of order values be selected. Non- stepwise (i.e., essentially a grid search) selection can be slow, especially for seasonal data. Stepwise algorithm is outlined in Hyndman and Khandakar (2008).


y : array-like or iterable, shape=(n_samples,)

The time-series to which to fit the ARIMA estimator. This may either be a Pandas Series object (statsmodels can internally use the dates in the index), or a numpy array. This should be a one-dimensional array of floats, and should not contain any np.nan or np.inf values.

exogenous : array-like, shape=[n_obs, n_vars], optional (default=None)

An optional 2-d array of exogenous variables. If provided, these variables are used as additional features in the regression operation. This should not include a constant or trend. Note that if an ARIMA is fit on exogenous features, it must be provided exogenous features for making predictions.

start_p : int, 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.

d : int, 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_q : int, optional (default=2)

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

max_p : int, optional (default=5)

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

max_d : int, 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_q : int, optional (default=5)

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

start_P : int, optional (default=1)

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

D : int, 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_Q : int, optional (default=1)

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

max_P : int, optional (default=2)

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

max_D : int, optional (default=1)

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

max_Q : int, optional (default=2)

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

max_order : int, optional (default=10)

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.

m : int, optional (default=1)

The period for seasonal differencing, m refers to the number of periods in each season. For example, m is 4 for quarterly data, 12 for monthly data, or 1 for annual (non-seasonal) data. Default is 1. Note that if m == 1 (i.e., is non-seasonal), seasonal will be set to False. For more information on setting this parameter, see Setting m.

seasonal : bool, optional (default=True)

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

stationary : bool, optional (default=False)

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

information_criterion : str, optional (default=’aic’)

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

alpha : float, optional (default=0.05)

Level of the test for testing significance.

test : str, optional (default=’kpss’)

Type of unit root test to use in order to detect stationarity if stationary is False and d is None. Default is ‘kpss’ (Kwiatkowski–Phillips–Schmidt–Shin).

seasonal_test : str, optional (default=’ch’)

This determines which seasonal unit root test is used if seasonal is True and D is None. Default is ‘ch’ (Canova-Hansen).

stepwise : bool, 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_jobs : int, 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_params : array-like, optional (default=None)

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

transparams : bool, optional (default=True)

Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done.

method : str, one of {‘css-mle’,’mle’,’css’}, optional (default=None)

This is the loglikelihood to maximize. If “css-mle”, the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If “mle”, the exact likelihood is maximized via the Kalman Filter. If “css” the conditional sum of squares likelihood is maximized. All three methods use start_params as starting parameters. See above for more information. If fitting a seasonal ARIMA, the default is ‘lbfgs’

trend : str or iterable, optional (default=’c’)

Parameter controlling the deterministic trend polynomial \(A(t)\). Can be specified as a string where ‘c’ indicates a constant (i.e. a degree zero component of the trend polynomial), ‘t’ indicates a linear trend with time, and ‘ct’ is both. Can also be specified as an iterable defining the polynomial as in numpy.poly1d, where [1,1,0,1] would denote \(a + bt + ct^3\).

solver : str or None, optional (default=’lbfgs’)

Solver to be used. The default is ‘lbfgs’ (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are ‘bfgs’, ‘newton’ (Newton-Raphson), ‘nm’ (Nelder-Mead), ‘cg’ - (conjugate gradient), ‘ncg’ (non-conjugate gradient), and ‘powell’. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs.

maxiter : int, optional (default=50)

The maximum number of function evaluations. Default is 50.

disp : int, optional (default=0)

If True, convergence information is printed. For the default ‘lbfgs’ solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case.

callback : callable, optional (default=None)

Called after each iteration as callback(xk) where xk is the current parameter vector. This is only used in non-seasonal ARIMA models.

offset_test_args : dict, optional (default=None)

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

seasonal_test_args : dict, optional (default=None)

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

suppress_warnings : bool, 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_action : str, 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 pyramid.

trace : bool, optional (default=False)

Whether to print status on the fits. Note that this can be very verbose…

random : bool, 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_state : int, long or numpy RandomState, optional (default=None)

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

n_fits : int, 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.

return_valid_fits : bool, optional (default=False)

If True, will return all valid ARIMA fits in a list. If False (by default), will only return the best fit.

out_of_sample_size : int, optional (default=0)

The ARIMA class can fit only a portion of the data if specified, in order to retain an “out of bag” sample score. This is 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 values

scoring : str, 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_args : dict, optional (default=None)

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

**fit_args : dict, optional (default=None)

A dictionary of keyword arguments to pass to the method.


Fitting with stepwise=False can prove slower, especially when seasonal=True.


[R31]R’s auto-arima source code:
[R32]R’s auto-arima documentation: