Before revision:  We derive the test statistic, study the size and power properties of the test , and demonstrate its implementation with intraday stock market return data. The test has conservative size properties and good power to detect varying variance and unit root in the presence of varying variance .
After revision:  We derive the test statistic, study the size and power 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 .