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A Markov process for circular data

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  • Shogo Kato

Abstract

Summary. We propose a discrete time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. A further discussion is given on some submodels, in particular on the stationary process. The proposed model is compared with some existing Markov processes for circular data. Some statistical issues of the model, such as statistical inference, model selection and diagnostic checks, are considered. Finally, an application of the model to wind direction data is provided.

Suggested Citation

  • Shogo Kato, 2010. "A Markov process for circular data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 655-672, November.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:5:p:655-672
    DOI: 10.1111/j.1467-9868.2010.00748.x
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    References listed on IDEAS

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    1. M. Jones, 2004. "The Möbius distribution on the disc," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 733-742, December.
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    Cited by:

    1. Fatemeh Hassanzadeh, 2021. "A smoothing spline model for multimodal and skewed circular responses: Applications in meteorology and oceanography," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    2. Fangpo Wang & Alan E. Gelfand, 2014. "Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1565-1580, December.
    3. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.
    4. Xiaoping Zhan & Tiefeng Ma & Shuangzhe Liu & Kunio Shimizu, 2018. "Markov-Switching Linked Autoregressive Model for Non-continuous Wind Direction Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 410-425, September.
    5. Toshihiro Abe & Hiroaki Ogata & Takayuki Shiohama & Hiroyuki Taniai, 2017. "Circular autocorrelation of stationary circular Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 275-290, October.
    6. Manolopoulou, Ioanna & Kepler, Thomas B. & Merl, Daniel M., 2012. "Mixtures of Gaussian wells: Theory, computation, and application," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3809-3820.
    7. Louis-Paul Rivest & Thierry Duchesne & Aurélien Nicosia & Daniel Fortin, 2016. "A general angular regression model for the analysis of data on animal movement in ecology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 445-463, April.
    8. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    9. Harvey, Andrew & Hurn, Stan & Palumbo, Dario & Thiele, Stephen, 2024. "Modelling circular time series," Journal of Econometrics, Elsevier, vol. 239(1).

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