A direct approach to time-varying modelling

We consider the on-line identification of continuously adaptive autoregressive (AR) models for observed data records which are realizations of non-stationary stochastic processes. Emphasis is placed on the treatment of arbitrary non-stationarities and the use of realistic assumptions in this operation. Because of these two objectives, usual adaptation procedures or description techniques are not well suited to the problem, which motivates the investigation of a new (direct) approach to time-varying parameter estimation. The cost criterion considered is a constrained least squares cost functional which incorporates with equal weight all instantaneous errors up to the current time of observation. The constraint is specified from limited a priori knowledge about the nature of the non-stationarity, namely the expected maximum rate of change (MRC) of the model parameters.