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.<>