ABSTRACT 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.

Hiroaki Ogata

Takayuki Shiohama

Journal of Time Series Analysis

在过去的 30 年中，时间序列分析已成为数理统计中最重要和最广泛使用的分支之一。其应用领域从神经生理学到天体物理学，涵盖经济预测、生物数据研究、控制系统、信号处理与通信和振动工程等知名领域。《时间序列分析杂志》创刊于 1980 年，现已成为该领域的领先期刊，发表关于基础理论和应用的论文，以及涉及该主题主要领域最新进展的评论论文和关于理论发展的简短交流。编委由许多世界领先的时间序列分析专家组成。

Over the past 30 years, time series analysis has become one of the most important and widely used branches of mathematical statistics. Its applications span various fields, from neurophysiology to astrophysics, including economic forecasting, biological data research, control systems, signal processing and communication, and vibration engineering. The Journal of Time Series Analysis was established in 1980 and has since become a leading journal in this field, publishing research papers on fundamental theories and applications, as well as review articles on the latest developments in major areas related to the topic and brief communications on theoretical advancements. The editorial board consists of many of the world's leading experts in time series analysis.

在过去的30年中，时间序列分析已成为数理统计中最重要和最广泛使用的分支之一。它的应用领域涵盖了从神经生理学到天体物理学的多个领域，包括经济预测、生物数据研究、控制系统、信号处理与通信以及振动工程等。《Journal of Time Series Analysis》创刊于1980年，现已成为该领域的领先期刊，发表关于基础理论和应用的研究论文，以及涉及该主题主要领域最新进展的评论论文和关于理论发展的简短交流。期刊的编委会由许多世界领先的时间序列分析专家组成。

Category	Quartile
数学	4
数学, 数学跨学科应用	4
数学, 统计学与概率论	4

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

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	2