Testing that a Gaussian Process is Stationary

Abstract

A class of procedures is proposed for testing the stationarity of a Gaussian process or the homogeneity of independent processes. Requiring very limited prior knowledge of model structure, the methods can detect changes or differences in mean, in variance, in covariances and even in law. Although the theory of the stationarity test is worked out only for processes whose realizations are stationary over "epochs" separated by known change points, Monte Carlo evidence indicates that it can be useful also in detecting more general forms of nonstationarity. The test statistic is a quadratic form in differences among epoch means of certain "sensing" functions, the choice of which governs sensitivity to specific forms of nonstationarity or inhomogeneity. The applicability of the general asymptotic theory of the test is verified for two specific forms of sensing function, and small-sample properties of tests of each form are studied by means of simulation.