### Abstract

A conditional parametric ARX-model is an ARX-model in which the
parameters re replaced by smooth functions of an, possibly
multivariate, externalinput signal. These functions are called
coefficient functions 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
shich is argument of the coeffieient-functions.The properties of
the modified method are sutdied by simulation. A particular
feature is that this effectiv forgetting factor will adapt to the
bandwidth used so that the effective number of observtions behind
the estimates will be almost independent of the actual bandwidth
or of the type of bandwidth selection used (fixed or nearest
neighbour). The choice of optimal bandwidth and forgetting is
briefly discussed. Furthermore, a method for adaptive nd recursive
estimation in additive or varying-coefficient models is suggested.
This method is a semi-parametric equivalent to the recursive
prediction error method.

Original language | English |
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Number of pages | 28 |
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Publication status | Published - 1999 |

## Cite this

Nielsen, H. A., Nielsen, T. S., Joensen, A. K., Madsen, H., & Holst, J. (1999).

*Tracking Time-Varying Coefficient-Functions*.