Testing Gaussianity and Linearity For Random Fields in the Frequency Domain

J. Yuan

Journal of Time Series Analysis, 2000, vol. 21, issue 6, 723-737

Abstract: We consider tests of Gaussianity and linearity for random fields on Zd, where Z is the set of integers and d≥ 1. As in the time series case, the idea is to test the constancy (zero or otherwise) of the modulus of the kth‐order normalized spectrum (k > 2). We derive the asymptotic normality of the real part, the imaginary part and the modulus of the estimated normalized kth‐order spectrum at fixed frequencies. This leads to the formation of likelihood‐ratio tests. The test statistics are simple and intuitively plausible, and their asymptotic distributions are given in terms of deviations from Gaussianity and linearity.

Date: 2000
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