A practical procedure for estimation of linear models via asymptotic quasi-likelihood. Issue 1 (1999) - Biondini, Riccardo; Lin, Yan-Xia; Mvoi, Sifa
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 formy t = f t ( θ ) + M t ( θ ) ( t = 1, 2, .., T ), wheref t is a linear predictable process ofθ andM t is an error term such thatE ( M t | F t − 1 ) = 0 andE ( M t 2 | F t − 1 ) < ∞ andF is aσ -field generated from y s s ≤ t . For this model, to estimate the parameterθ ∈ Θ, the ordinary least squares method is usually inappropriate (if there is only one observable path of y t and ifE ( 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 ofM t is unknown, to obtain a good estimate ofθ an appropriate predictable processg t should be determined. In this paper, criteria for determiningg t are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.