WALSH‐FOURIER ANALYSIS OF DISCRETE‐VALUED TIME SERIES

David S. Stoffer

Journal of Time Series Analysis, 1987, vol. 8, issue 4, 449-467

Abstract: 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 analyse the data in terms of square waveforms and sequency rather than sine waves and frequency. We develop a general signal‐plus‐noise type model for discrete‐valued time series in which Walsh‐Fourier spectral analysis is of interest. We consider the problems of detecting whether a common signal exists in repeated measures on discrete‐valued time series and in discrete‐valued processes collected in an experimental design. We show that these models may depend on unknown regression parameters and we develop consistent estimates of these parameters based on the finite Walsh‐Fourier transform. Applications to certain Markov models are given; however, the methods presented also apply to non‐Markov cases.

Date: 1987
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