Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2, pp. 286--304

THE TIME-VARYING PARAMETER MODEL: AN OPTIMAL CONTROL APPROACH USING TRAJECTORY SENSITIVITY METHODS

By

DILIP M. NACHANE and M. J. MANOHAR RAO, *University of Bombay*

SUMMARY. The problem of estimating parameters for a regression equation has often been characterized by the absence of precise knowledge regarding how these parameters can change over space or time. The paper discusses an alternative computational method for dealing with the time-varying parameter problem using optimal control theory which, by incorporating robustness considerations directly into the objective function via the Byrne-Burke trajectory sensitivity minimization method, explicitly associates sensitivity costs with each of the nominal trajectories and bears in mind that trajectory sensitivity reduction can be achieved only at the expense of tracking error. The problem of identifying an optimal trajectory is thus solved endogenously by assigning a cost effectiveness index to each of these solutions and choosing the one which minimizes this index from the set of ‘sensitivity-reducing’ trajectories.

*AMS (1980) subject classification.* 62J.

*Key words and phrases.* Trajectory sensitivity minimization, time-varying parameters, maximal sensitivity, tracking errors, robustness analysis.