A Mixture Transition Distribution Modeling for Higher-Order Circular Markov Processes

This study considers the stationary higher-order Markov process for circular data by employing the mixture transition distribution modeling. The underlying circular transition distribution is based on Wehrly and Johnson's bivariate joint circular models. The structures of the circular autocorrelation function, together with the circular partial autocorrelation function, are investigated. They are found to be similar to those of the autocorrelation and partial autocorrelation functions of the real-valued autoregressive process when the underlying binding density has zero sine moments. The validity of the model is assessed by applying it to some Monte Carlo simulations and real directional data.