Efficient inference in multivariate fractionally integrated time series models

Abstract

A computationally simple maximum likelihood procedure for multivariate fractionally integrated time series models is introduced. This allows, e.g., efficient estimation of the memory parameters of fractional models or efficient testing of the hypothesis that two or more series are integrated of the same possibly fractional order. In particular, we show the existence of a local time domain maximum likelihood estimator and its asymptotic normality, and under Gaussianity asymptotic efficiency. The likelihood‐based test statistics (Wald, likelihood ratio and Lagrange multiplier) are derived and shown to be asymptotically equivalent and chi‐squared distributed under local alternatives, and under Gaussianity locally most powerful. The finite sample properties of the likelihood ratio test are evaluated by Monte Carlo experiments, which show that rejection frequencies are very close to the asymptotic local power for samples as small as n= 100.