Circular autocorrelation of stationary circular Markov processes

Toshihiro Abe, Hiroaki Ogata*, Takayuki Shiohama, Hiroyuki Taniai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalStatistical Inference for Stochastic Processes
Publication statusAccepted/In press - 2016 Dec 31


  • Circular statistics
  • Time series models
  • Toroidal data
  • Wind direction
  • Wrapped cauchy distribution

ASJC Scopus subject areas

  • Statistics and Probability


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