Circular autocorrelation of stationary circular Markov processes
Circular autocorrelation of stationary circular Markov processes
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平稳循环马尔可夫过程的循环自相关
DOI：
10.1007/s11203-016-9154-0
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
H.
中科院分区：
文献类型：
--
作者：
Abe;T.;Ogata;H.;Shiohama;T.;and Taniai;H.
考虑了平稳马尔可夫过程，研究了它的循环自相关函数。更具体地说，平稳马尔可夫循环过程的转移密度是由两个圆形分布定义的，我们阐明了当这些分布之一是均匀的，另一个是任意的圆形自相关的结构。给出了循环自相关函数自然估计的渐近性质。此外，我们考虑了三角函数的二元过程，并给出了它的谱密度矩阵的显式形式。通过将该模型应用于一系列风向数据，对模型的有效性进行了评估。
The stationary Markov process is considered and its circular autocorrelation function is investigated. More specifically, the transition density of the stationary Markov circular process is defined by two circular distributions, and we elucidate the structure of the circular autocorrelation when one of these distributions is uniform and the other is arbitrary. The asymptotic properties of the natural estimator of the circular autocorrelation function are derived. Furthermore, we consider the bivariate process of trigonometric functions and provide the explicit form of its spectral density matrix. The validity of the model was assessed by applying it to a series of wind direction data.