statsmodels.regression.recursive_ls.RecursiveLSResults.resid_recursive¶

RecursiveLSResults.resid_recursive¶

Recursive residuals

Returns:¶

resid_recursivearray_like

An array of length nobs holding the recursive residuals.

Notes

These quantities are defined in, for example, Harvey (1989) section 5.4. In fact, there he defines the standardized innovations in equation 5.4.1, but in his version they have non-unit variance, whereas the standardized forecast errors computed by the Kalman filter here assume unit variance. To convert to Harvey’s definition, we need to multiply by the standard deviation.

Harvey notes that in smaller samples, “although the second moment of the \(\tilde \sigma_*^{-1} \tilde v_t\)’s is unity, the variance is not necessarily equal to unity as the mean need not be equal to zero”, and he defines an alternative version (which are not provided here).