Circular autocorrelation of stationary circular Markov processes

Toshihiro Abe, Hiroaki Ogata, Takayuki Shiohama, Hiroyuki Taniai

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

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

Fingerprint

Circular function
Autocorrelation
Markov Process
Autocorrelation Function
Spectral Density Matrix
Transition Density
Stationary Process
Asymptotic Properties
Estimator
Series
Arbitrary
Model

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Circular autocorrelation of stationary circular Markov processes. / Abe, Toshihiro; Ogata, Hiroaki; Shiohama, Takayuki; Taniai, Hiroyuki.

In: Statistical Inference for Stochastic Processes, 31.12.2016, p. 1-16.

Research output: Contribution to journalArticle

Abe, Toshihiro ; Ogata, Hiroaki ; Shiohama, Takayuki ; Taniai, Hiroyuki. / Circular autocorrelation of stationary circular Markov processes. In: Statistical Inference for Stochastic Processes. 2016 ; pp. 1-16.
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