A practical procedure for estimation of linear models via asymptotic quasi-likelihood
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 , where is a linear predictable process of and is an error term such that and and is a -field generated from . For this model, to estimate the parameter , the ordinary least squares method is usually inappropriate (if there is only one observable path of and if is not a constant) and the maximum likelihood method either does not exist or is mathematically intractable. If the finite dimensional distribution of is unknown, to obtain a good estimate of an appropriate predictable process should be determined. In this paper, criteria for determining are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.