FOURIER INFERENCE: SOME METHODS FOR THE ANALYSIS OF ARRAY AND NONGAUSSIAN SERIES DATA1

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Abstract
Fourier inference is a collection of analytic techniques and philosophic attitudes, for the analysis of data, wherein essential use is made of empirical Fourier transforms. This paper sets down some basic results concerning the finite Fourier transforms of stationary process data and then, to illustrate the approach, uses those results to develop procedures for: 1) estimating cloud and storm motion, 2) passive sonar and 3) fitting finite parameter models to nonGaussian time series via bispectral fitting. This last procedure is illustrated by an analysis of a stretch of Mississippi River runoff data. Examples 1), 2) refer to data having the form Y(xj, yj, t) for j = 1, …, J and t = 0, …, T‐l say, and view that data as part of a realization of a spatial‐temporal process. Such data has become common in geophysics generally and in hydrology particularly. The goal of this paper is to present some new statistical procedures pertinent to problems in the water sciences, equally it is to illustrate the genesis of those procedures and how their properties may be approximated.