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 y t = f t ( θ ) + M t ( θ ) ( t = 1 , 2 , .. , T ) , where f t is a linear predictable process of θ and M t is an error term such that E ( M t | F t − 1 ) = 0 and E ( M t 2 | F t − 1 ) < ∞ and F is a σ -field generated from { y s } 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 { y t } and if E ( M t 2 | F t − 1 ) is not a constant) and the maximum likelihood method either does not exist or is mathematically intractable. If the finite dimensional distribution of M t is unknown, to obtain a good estimate of θ an appropriate predictable process g t should be determined. In this paper, criteria for determining g t are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.