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.
翻译:本文考虑循环数据的固定高阶马尔科夫过程,应用混合转移分布(MTD)模型来表示它的循环转移密度。该模型的圆周转移分布基于Wehrly和Johnson的双变量圆周模型。当基础绑定密度的正弦矩为零时,圆形自相关函数和圆形偏自相关函数的结构与实值自回归过程的自相关函数和偏自相关函数相似。通过将模型应用于一些蒙特卡罗模拟和实际方向数据的评估,确定其有效性。