The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence

Abstract

The paper gives a unified approach to dealing with multiple long-memory time-series possessing a variety of singularities in their spectrum, based on the quasi-likelihood function. It proposes quasi-maximum-likelihood estimation and the quasi-likelihood ratio test for statistical inference purposes. A large-sample theory is given by means of a bracketing function approach under very general conditions, without the usual assumptions of Gaussianity or exact martingale differences for innovation processes. The paper also discusses the particular characteristic of modelling long-memory time-series which influences the type of the quasi-likelihood function and produces distinct differences in the asymptotic properties of related statistics.