Estimating Functions for Circular Time Series Models

In this article, we describe an estimating function (EF) approach for circular time series models. We construct EFs based on conditional trigonometric moments of the circular discrete-time stochastic processes and provide closed form expressions for the optimal EF of the model parameters and its associated Godambe information. When the conditional circular mean and concentration are functions of the same parameters of interest, we show that the combined EF is more informative than its component sine and cosine EFs. We discuss recursive estimation of circular model parameters and illustrate the approach on two well known circular time series models.