A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long-range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence...

We consider M-estimation of a location parameter for processes with zero autocorrelations but long-range dependence in volatility. The observed process is the product of i.i.d. Gaussian observations and a long-memory Gaussian process. For nonlinear estimators, the rate of convergence depends on...

This paper considers blockwise empirical likelihood for real-valued linear time processes which may exhibit either short- or long-range dependence. Empirical likelihood approaches intended for weakly dependent time series can fail in the presence of strong dependence. However, a modified...

We show that tests for a break in the persistence of a time series in the classical I(0)/I(1) framework have serious size distortions when the actual data-generating process (DGP) exhibits long-range dependencies. We prove that the limiting distribution of a CUSUM of squares-based test depends...