  The stationary higher-order Markov process for circular data is considered.
We employ the mixture transition distribution (MTD) model to express the
transition density of the process on the circle. 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 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.
