Abstract
A nonparametric approach to analyzing a stationary binary time series X(n), n = 0, ±1, ±2, … taking values in 0, 1 is discussed. The analysis is accomplished in the spectral domain using the Walsh-Fourier transform which is based on Walsh functions. This seems to be a natural alternative to the trigonometric functions used in the usual spectral analysis since the Walsh functions take on only two values, +1 or − 1, (or “on” and “off”, as does the series X(n) itself). This approach enables the investigator to analyze a binary series in terms of square-waves and sequency (switches or changes per unit time) rather than sine-waves and frequency (cycles per unit time). We discuss (1) the basic theory of Walsh-Fourier analysis, (2) the computational aspects involved in calculating the discrete Walsh-Fourier transform, and (3) the analysis of simulated and real binary data in the sequency domain. We suggest that these methods would enhance the analysis of time series which take values in a discrete finite set.
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© 1987 D. Reidel Publishing Company
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Stoffer, D.S., Panchalingam, T. (1987). A Walsh-Fourier Approach to the Analysis of Binary Time Series. In: MacNeill, I.B., Umphrey, G.J., Carter, R.A.L., McLeod, A.I., Ullah, A. (eds) Time Series and Econometric Modelling. The University of Western Ontario Series in Philosophy of Science, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4790-0_12
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DOI: https://doi.org/10.1007/978-94-009-4790-0_12
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