On backward periodic autoregressive processes

Hideaki Sakai and Shyuichi Ohno

Journal of Time Series Analysis, 1997, vol. 18, issue 4, 415-427

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.

Date: 1997
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