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This paper is concerned with the application of an asymptotic quasi-likelihoodpractical procedure to estimate the unknown parameters in linear stochastic models of the formyt=ft(θ)+Mt(θ)(t=1,2,..,T), where ft is a linear predictable process of θ and Mt is anerror term such that E(Mt|Ft−1)=0 and E(Mt2|Ft−1)<∞ and Fis a σ-field generatedfrom{ys}s≤t. For this model, to estimate the parameter θ∈Θ, the ordinary least squaresmethod 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 mathematicallyintractable. If the finite dimensional distribution of Mt is unknown, to obtain a good estimate ofθ an appropriate predictable process gt should be determined. In this paper, criteria for determininggt are introduced which, if satisfied, provide more accurate estimates of the parameters via theasymptotic quasi-likelihood method

A practical procedure for estimation of linear models via asymptotic quasi-likelihood