Tracking time-varying coe cient-functions

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 coe cientfunctions. A method, which estimates these functions adaptively and recursively, and hence allows for on-line tracking of the coe cientfunctions 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 coe cient-functions. The properties of the modi ed method are studied by simulation. A particular feature is the this e ective forgetting factor will adapt to the bandwidth used so that the e ective number of observations behind the estimates will be almost independent of the actual bandwidth or of the type of bandwidth selection used ( xed or nearest neighbour). The choice of optimal bandwidth and forgetting is brie y discussed. Furthermore, a method for adaptive and recursive estimation in additive or varying-coe cient models is suggested. This method is a semi-parametric equivalent to the recursive prediction