Gaussianity test for zero-skewed real and complex data

Bispectrum based tests for Gaussianity of stationary processes such as Hinich´s (1982) or Subba Rao and Gabr´s (1980) test are not able to detect symmetric alternatives. Methods that use additionally the trispectrum have been proposed to decide whether a stationary process is Gaussian. Testing the trispectrum for zero is a complicated task from a computational as well as statistical point of view. Epps (1987) proposed a test for Gaussianity that is based on the differences between components of the sample and Gaussian characteristic functions of a real-valued stationary process. The aim of this paper is to extend Epps´ idea to the complex case and to apply the test to the characterisation of backscattered clutter in over-the-horizon radar (OTHR). In OTHR, the complex signal is zero-skewed, and the amount of data available is small. In this case, a test for Gaussianity based on higher-order spectra is inappropriate.