Tracking Time-Varying Coefficient-Functions

Abstract

A conditional parametric ARX-model is an ARX-model in which the parameters are replaced by smooth functions of an, possibly multivariate, external input signal. These functions are called coefficientfunctions. A method, which estimates these functions adaptively and recursively, and hence allows for on-line tracking of the coefficientfunctions is suggested. Essentially, in its most simple form, this method is a combination of recursive least squares with exponential forgetting and local polynomial regression. However, it is argued, that it is appropriate to let the forgetting factor vary with the value of the external signal which is argument of the coefficient-functions. The properties of the modified method are studied by simulation. A particular feature is the this effective forgetting factor will adapt to the bandwidth used so that the effective number of observations behind the estimates will be almost independent of the actual bandwidth or of the type of bandwidth selection used ..