WALSH‐FOURIER ANALYSIS OF DISCRETE‐VALUED TIME SERIES

Abstract : An approach to the analyses of discrete-valued time series is discussed. The analyses are accomplished in the spectral domain using the Walsh-Fourier transform which is based on Walsh functions. This approach will enable an investigator of discrete systems to analyze the data in terms of square-waveforms and sequency rather than sine-waves and frequency. This document develops a general signal-plus-noise type model for discrete-valued time series in which Walsh-Fourier spectral analysis is of interest. The author considers the problems of detecting whether or not a common signal exists in repeated measures on discrete-valued time series and in discrete-valued processes collected in an experimental design. It is shown that these models may depend on unknown regression parameters and consistent estimates of these parameters based on the finite Walsh-Fourier transform are developed. Applications to certain Markov models are given, however, the methods presented also apply to non-Markov cases. (Author)

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