Riccardo Biondini, Yan-Xia Lin, and Sifa Mvoi

Copyright © 1999 Riccardo Biondini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the application of an asymptotic quasi-likelihood practical procedure to estimate the unknown parameters in linear stochastic models of the form yt=ft(θ)+Mt(θ)(t=1,2,..,T) , where ft is a linear predictable process of θ and Mt is an error term such that E(Mt|Ft−1)=0 and E(Mt2|Ft−1)<∞ and F is a σ-field generated from{ys}s≤t . For this model, to estimate the parameter θ∈Θ, the ordinary least squares method is usually inappropriate (if there is only one observable path of {yt} and if E(Mt2|Ft−1) is not a constant) and the maximum likelihood method either does not exist or is mathematically intractable. If the finite dimensional distribution of Mt is unknown, to obtain a good estimate of θ an appropriate predictable process gt should be determined. In this paper, criteria for determining gt are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.