Models for circular data from time series spectra

Masanobu Taniguchi, Shogo Kato, Hiroaki Ogata*, Arthur Pewsey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex-valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high-order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra-generated models is illustrated in an analysis of wind direction data.

Original languageEnglish
Pages (from-to)808-829
Number of pages22
JournalJournal of Time Series Analysis
Issue number6
Publication statusPublished - 2020 Nov 1


  • Joint circular distributions
  • high-order spectral density
  • local asymptotic normality test
  • optimal inference
  • stationary processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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