Walsh-Fourier Analysis and its Statistical Applications

The aim of this article is to acquaint statisticians and practitioners, whose research activities require statistical methodology, with the statistical theory and applications of Walsh-Fourier analysis. It has been suggested that Walsh spectral analysis is suited to (albeit not restricted to) the analysis of discrete-valued and categorical-valued time series, and of time series that contain sharp discontinuities. I explain the need for Walsh-Fourier analysis, review the history and properties of Walsh functions, and outline the existing Walsh-Fourier theory for real-time stationary time series. I discuss various statistical applications based on the Walsh-Fourier transform and provide an annotated bibliography.