A further note on flexible least squares and Kalman filtering

Tucci (1990) logically errs when he attempts to equate the flexible least squares (FLS) approach [Kalaba and Tesfatsion (KT) (1989)] with Kalman filtering. FLS addresses a multicriteria model specification problem which does not require probability assumptions either for its motivation or for its solution: the characterization of the set of all state sequence estimates which achieve vector-minimal incompatibility between imperfectly specified theoretical relations and process observations. Kalman filtering is a point estimation technique for determining the most probable state sequence estimate for a stochastic model assumed to be correctly and completely specified. To illustrate, consider the simple time-varying linear regression problem analyzed both in KT (1989) and in Tucci (1990). Scalar observations yi,..., yr have been obtained on an economic process which is not yet well understood. For simplicity, a linear relation is postulated between the observation y, and a vector X, of given regressor variables at each time t, of the form y, = x;bt, t=l 9..., T. Although it is recognized that some systematic time variation i