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 structure of the circular autocorrelation function together with the circular partial autocorrelation function is found to be similar to 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.
翻译:本文考虑循环数据的平稳高阶马尔可夫过程。我们采用混合过渡分布(MTD)模型来表达圆上过程的过渡密度。基于Wehrly和Johnson的二元联合圆形模型,得出了下层圆形转移分布。当底层结合密度具有零正弦矩时,可以发现圆形自相关函数和圆形偏自相关函数的结构类似于实值自回归过程的自相关函数和部分自相关函数。通过对一些蒙特卡罗模拟和实际定向数据的应用来评估模型的有效性。