Asymptotics for the conditional-sum-of-squares estimator in multivariate fractional time series models

This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses the multivariate non-cointegrated fractional ARIMA model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity, thus making the proof much more challenging than usual. The neighborhood around the critical point where uniform convergence fails is handled using a truncation argument.