A NOTE ON THE APPLICATION OF THE KALMAN FILTER TO REGRESSION MODELS WITH SOME PARAMETERS VARYING OVER TIME AND OTHERS UNVARYING
Michio Hatanaka · Australian Journal of Statistics · 1980
Summary The Kalman filter has been applied to estimation of the time‐varying vector of regression parameters. I investigate the case where a portion of elements of the vector is invariant over time while others are varying as generated by the nonstationary, random walk model. Combined with the regression model it yields a state‐space model in which observability holds but controllability does not. Under Grenan‐der's condition on the exogenous variables I shall show that the estimate of the time‐invariant portion is consistent, despite the seemingly unfavorable circumstances mentioned above, with the order equal to the reciprocal of sample size.