Efficient Inference in Multivariate Fractionally Integrated Time Series Models

We consider statistical inference for multivariate fractionally integrated time series models using a computationally simple conditional likelihood procedure which has recently been shown to be efficient in the univariate case. We show that those results generalize to the present multivariate setup, e.g. allowing us to efficiently estimate the memory parameters of vector ARFIMA models or test if two or more series are integrated of the same possibly fractional order. In particular, we show that all the desirable properties from standard statistical analysis apply for the time domain maximum likelihood estimator and related test statistics, i.e. consistency, standard asymptotic distributional properties, and under Gaussianity asymptotic efficiency. 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.