Statistical analysis of dyadic stationary processes

M. Taniguchi*, L. C. Zhao, P. R. Krishnaiah, Z. D. Bai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper we consider a multiple dyadic stationary process with the Walsh spectral density matrix fθ(λ), where θ is an unknown parameter vector. We define a quasi-maximum likelihood estimator {Mathematical expression} of θ, and give the asymptotic distribution of {Mathematical expression} under appropriate conditions. Then we propose an information criterion which determines the order of the model, and show that this criterion gives a consistent order estimate. As for a finite order dyadic autoregressive model, we propose a simpler order determination criterion, and discuss its asymptotic properties in detail. This criterion gives a strong consistent order estimate. In Section 5 we discuss testing whether an unknown parameter θ satisfies a linear restriction. Then we give the asymptotic distribution of the likelihood ratio criterion under the null hypothesis.

Original languageEnglish
Pages (from-to)205-225
Number of pages21
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
Publication statusPublished - 1989 Jun 1
Externally publishedYes


  • Dyadic stationary process
  • Walsh spectral density
  • information criterion
  • likelihood ratio criterion
  • quasi-maximum likelihood estimator

ASJC Scopus subject areas

  • Statistics and Probability


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