We study the asymptotic behaviour of frequency domain maximum likelihood estimators of mis-specified models of long memory Gaussian series. We show that even if the long memory structure of the time series is correctly specified, mis-specification of the short memory dynamics may result in...

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k=n ! 0. The test...