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.

Return type:

ARIMAResults

Examples

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