A Second Order Cumulant Spectrum Test That a Stochastic Process is Strictly Stationary and a Step Toward a Test for Graph Signal Strict Stationarity
This provides a method for testing strict stationarity in stochastic processes, with potential applications in graph signal processing, but it is incremental as it builds on existing frequency-domain approaches.
The authors developed a statistical test to determine if a discrete time stochastic process is strictly stationary by checking if the second order cumulant spectrum is zero in the frequency domain, and demonstrated it on 137Cs gamma ray decay data.
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.