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)

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

Parameters

endogndarray

The observed time-series process.

ar_paramsndarray, optional

Autoregressive coefficients, not including the zero lag.

ma_paramsndarray, 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).

sigma2ndarray, optional

The ARMA innovation variance. Default is 1.

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.

Returns

scoreobsarray

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.