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.

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).