  This article develops a statistical test for the null hypothesis of strict
stationarity of a discrete time stochastic process in the frequency domain.
When the null hypothesis is true, the second order cumulant spectrum is zero at
all the discrete Fourier frequency pairs in the principal domain. The test uses
a window averaged sample estimate of the second order cumulant spectrum to
build a test statistic with an asymptotic complex standard normal distribution.
We derive the test statistic, study the properties of the test and demonstrate
its application using 137Cs gamma ray decay data. Future areas of research
include testing for strict stationarity of graph signals, with applications in
learning convolutional neural networks on graphs, denoising, and inpainting.
