Estimating the Mean Direction of Strongly Dependent Circular Time Series

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 intervals for the mean direction are derived. Extensions to cases where the direction depends on explanatory variables are also considered. Simulations and a data example illustrate the proposed method.