statsmodels.tsa.statespace.kalman_filter.PredictionResults.standardized_forecasts_error

property PredictionResults.standardized_forecasts_error

Standardized forecast errors

Notes

The forecast errors produced by the Kalman filter are

vt∼N(0,Ft)

Hypothesis tests are usually applied to the standardized residuals

vts=Btvt∼N(0,I)

where Bt=Lt−1 and Ft=LtLt′; then Ft−1=(Lt′)−1Lt−1=Bt′Bt; Bt and Lt are lower triangular. Finally, Btvt∼N(0,BtFtBt′) and BtFtBt′=Lt−1LtLt′(Lt′)−1=I.

Thus we can rewrite vts=Lt−1vt or Ltvts=vt; the latter equation is the form required to use a linear solver to recover vts. Since Lt is lower triangular, we can use a triangular solver (?TRTRS).