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


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

ar_paramsndarray, optional

Autoregressive parameters.

ma_paramsndarray, optional

Moving average parameters.

sigma2ndarray, optional

The ARMA innovation variance. Default is 1.

normalizeboolean, optional

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

prefixstr, 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.


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.


Mean square error for the innovations.