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.