Walsh-function analysis of a certain class of time series

P. A. Morettin

Stochastic Processes and their Applications, 1974, vol. 2, issue 2, 183-193

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.

Date: 1974
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