statsmodels.tsa.innovations.arma_innovations.arma_scoreobs

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

Compute the score per observation (gradient of the loglikelihood function)

Parameters:

endog : ndarray

The observed time-series process.

ar_params : ndarray, optional

Autoregressive coefficients, not including the zero lag.

ma_params : ndarray, optional

Moving average coefficients, not including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition).

sigma2 : ndarray, optional

The ARMA innovation variance. Default is 1.

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:

scoreobs : array

Score per observation, evaluated at the given parameters.

Notes

This is a numerical approximation, calculated using first-order complex step differentiation on the arma_loglike method.