Premium
A NOTE ON THE APPLICATION OF THE KALMAN FILTER TO REGRESSION MODELS WITH SOME PARAMETERS VARYING OVER TIME AND OTHERS UNVARYING
Author(s) -
Hatanaka Michio
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01178.x
Subject(s) - kalman filter , observability , controllability , state vector , mathematics , regression , regression analysis , control theory (sociology) , state space representation , state space , statistics , computer science , algorithm , artificial intelligence , control (management) , physics , classical mechanics
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.