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On backward periodic autoregressive processes

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  • Hideaki Sakai
  • Shyuichi Ohno

Abstract

It has been shown that there is a one‐to‐one correspondence between a multivariate autoregress ive (AR) process and a scalar periodic AR process. So we can analyze periodic processes by the theory of multivariate AR processes and vice versa. Multivariate AR processes have been widely studied and the Levinson–Whittle–Wiggins–Robinson algorithm is well known for obtaining the predictor coeffic ient matrices. In addition, the circular Levinson algorithm has been derived for obtaining the coefficients of periodic AR processes. In this paper, we construct backward periodic AR processes from the auxiliary coefficients used in this algorithm. A numerical example is also presented and the statistical properties of the estimated coefficients of backward periodic AR processes based on a sample of finite size are derived.

Suggested Citation

  • Hideaki Sakai & Shyuichi Ohno, 1997. "On backward periodic autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 415-427, July.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:4:p:415-427
    DOI: 10.1111/1467-9892.00059
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    Cited by:

    1. Abdelhakim Aknouche, 2017. "Periodic autoregressive stochastic volatility," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 139-177, July.
    2. Aknouche, Abdelhakim, 2013. "Periodic autoregressive stochastic volatility," MPRA Paper 69571, University Library of Munich, Germany, revised 2015.

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