There exist several estimators of the memory parameter in long-memory time series models with mean µ and the spectrum specified only locally near zero frequency. In this paper we give a lower bound for the rate of convergence of any estimator of the memory parameter as a function of the degree...

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asumptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d, we extend these results to include possibly...

Band spectrum regression is considered for cointegrated time series with long memory innovations. The estimates we advocate are shown to be consistent when cointegrating relationships among stationary variables are investigated, while OLS are inconsistent due to correlation between the regressor...

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown, asymptotic distribution theory for estimates of parameters, including the...