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Walsh-function analysis of a certain class of time series

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  • Morettin, P. A.

Abstract

This paper is concerned with investigating the use of the orthonormal system of Walsh functions in the analysis of a dyadic-stationary series. The main emphasis is on the finite Walsh transform of a sequence of values coming from such a series. Under a certain mixing condition, given in terms of the dyadic auto-covariance function of the series, we derive a central limit theorem for the finite Walsh transform. This, in turn, allows us to consider estimates of the Walsh spectrum, and we discuss briefly the Walsh periodogram.

Suggested Citation

  • Morettin, P. A., 1974. "Walsh-function analysis of a certain class of time series," Stochastic Processes and their Applications, Elsevier, vol. 2(2), pages 183-193, April.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:2:p:183-193
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    Cited by:

    1. M. Taniguchi & L. Zhao & P. Krishnaiah & Z. Bai, 1989. "Statistical analysis of dyadic stationary processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 205-225, June.

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