statsmodels.tsa.innovations.arma_innovations.arma_innovations

statsmodels.tsa.innovations.arma_innovations.arma_innovations(endog, ar_params=None, ma_params=None, sigma2=1, normalize=False, prefix=None)[source]

Compute innovations using a given ARMA process

Parameters:

endog : ndarray

The observed time-series process, may be univariate or multivariate.

ar_params : ndarray, optional

Autoregressive parameters.

ma_params : ndarray, optional

Moving average parameters.

sigma2 : ndarray, optional

The ARMA innovation variance. Default is 1.

normalize : boolean, optional

Whether or not to normalize the returned innovations. Default is False.

prefix : str, optional

The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally.

Returns:

innovations : ndarray

Innovations (one-step-ahead prediction errors) for the given endog series with predictions based on the given ARMA process. If normalize=True, then the returned innovations have been “whitened” by dividing through by the square root of the mean square error.

innovations_mse : ndarray

Mean square error for the innovations.