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Estimating Functions for Circular Time Series Models

Author

Listed:
  • Aerambamoorthy Thavaneswaran

    (University of Manitoba)

  • Nalini Ravishanker

    (University of Connecticut)

Abstract

In this article, we describe an estimating function (EF) approach for circular time series models. We construct EFs based on conditional trigonometric moments of the circular discrete-time stochastic processes and provide closed form expressions for the optimal EF of the model parameters and its associated Godambe information. When the conditional circular mean and concentration are functions of the same parameters of interest, we show that the combined EF is more informative than its component sine and cosine EFs. We discuss recursive estimation of circular model parameters and illustrate the approach on two well known circular time series models.

Suggested Citation

  • Aerambamoorthy Thavaneswaran & Nalini Ravishanker, 2023. "Estimating Functions for Circular Time Series Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 198-213, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-020-00237-w
    DOI: 10.1007/s13171-020-00237-w
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    References listed on IDEAS

    as
    1. Saralees Nadarajah & Yuanyuan Zhang, 2017. "Wrapped: An R package for circular data," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-26, December.
    2. Aerambamoorthy Thavaneswaran & Nalini Ravishanker & You Liang, 2015. "Generalized duration models and optimal estimation using estimating functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 129-156, February.
    3. Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
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