ABSTRACT
In contrast, the Fourier transform is of interest to statisticians because it proves inordinately useful in the analysis of data and eases the development of various theoretical results. Noteworthy contributions to statistics have been made by Slutsky (1934), Cramer (1942), Good (1958), Yaglom (1961), Tukey (1963), Hannan ( 1965, 1966), Priestley ( 1965), Bloomfield (1976), Diaconnis (1988, 1989). Slutsky developed some of the statistical properties of the Fourier transform of a stretch of time series values. Cramer set down a Fourier representation (see Sec. 4.1) for stationary processes. The representation admitted many extensions and made transparent the effect of a variety of operations on processes. Good and Tukey indicated how the transform could be computed recursively and hence quickly in certain circumstances. Yaglom extended the domain of application to processes defined on compact and locally compact groups. Hannan considered problems for other groups than Yaglom and presented material relevant to practical applications. Priestley provided a frequency domain representation to describe nonstationary processes. Bloomfield made complicated results available to a broad audience. Diaconnis considered symmetric and permutation groups and the analysis of ordered data.
