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.