A NOTE ON THE APPLICATION OF THE KALMAN FILTER TO REGRESSION MODELS WITH SOME PARAMETERS VARYING OVER TIME AND OTHERS UNVARYING

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.