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Circular autocorrelation of stationary circular Markov processes

Author

Listed:
  • Toshihiro Abe

    (Nanzan University)

  • Hiroaki Ogata

    (Tokyo Metropolitan University)

  • Takayuki Shiohama

    (Tokyo University of Science)

  • Hiroyuki Taniai

    (Waseda University)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-016-9154-0
    DOI: 10.1007/s11203-016-9154-0
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    References listed on IDEAS

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    1. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    2. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    3. 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.
    4. Jones, M.C. & Pewsey, Arthur, 2005. "A Family of Symmetric Distributions on the Circle," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1422-1428, December.
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    Cited by:

    1. 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.
    2. Harvey, Andrew & Hurn, Stan & Palumbo, Dario & Thiele, Stephen, 2024. "Modelling circular time series," Journal of Econometrics, Elsevier, vol. 239(1).

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