statsmodels.tsa.arima.model.ARIMA.fit

ARIMA.fit(start_params=None, transformed=True, includes_fixed=False, method=None, method_kwargs=None, gls=None, gls_kwargs=None, cov_type=None, cov_kwds=None, return_params=False, low_memory=False)[source]

Fit (estimate) the parameters of the model.

Parameters:

start_params : array_like, optional

Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params.

transformed : bool, optional

Whether or not start_params is already transformed. Default is True.

includes_fixed : bool, optional

If parameters were previously fixed with the fix_params method, this argument describes whether or not start_params also includes the fixed parameters, in addition to the free parameters. Default is False.

method : str, optional

The method used for estimating the parameters of the model. Valid options include ‘statespace’, ‘innovations_mle’, ‘hannan_rissanen’, ‘burg’, ‘innovations’, and ‘yule_walker’. Not all options are available for every specification (for example ‘yule_walker’ can only be used with AR(p) models).

method_kwargs : dict, optional

Arguments to pass to the fit function for the parameter estimator described by the method argument.

gls : bool, optional

Whether or not to use generalized least squares (GLS) to estimate regression effects. The default is False if method=’statespace’ and is True otherwise.

gls_kwargs : dict, optional

Arguments to pass to the GLS estimation fit method. Only applicable if GLS estimation is used (see gls argument for details).

cov_type : str, optional

The cov_type keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of:

  • ‘opg’ for the outer product of gradient estimator
  • ‘oim’ for the observed information matrix estimator, calculated using the method of Harvey (1989)
  • ‘approx’ for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix.
  • ‘robust’ for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the ‘oim’ method.
  • ‘robust_approx’ is the same as ‘robust’ except that the intermediate calculations use the ‘approx’ method.
  • ‘none’ for no covariance matrix calculation.

Default is ‘opg’ unless memory conservation is used to avoid computing the loglikelihood values for each observation, in which case the default is ‘oim’.

cov_kwds : dict or None, optional

A dictionary of arguments affecting covariance matrix computation.

opg, oim, approx, robust, robust_approx

  • ‘approx_complex_step’ : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True.
  • ‘approx_centered’ : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False.

return_params : bool, optional

Whether or not to return only the array of maximizing parameters. Default is False.

low_memory : bool, optional

If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Default is False.

Returns:

ARIMAResults

Examples

>>> mod = sm.tsa.arima.ARIMA(endog, order=(1, 0, 0))
>>> res = mod.fit()
>>> print(res.summary())