This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs present in the principal domain of the cumulant spectrum. The test uses a frame (window) averaged sample estimate of the second order cumulant spectrum to build a test statistic that has an asymptotic complex standard normal distribution. 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.
Analyzing time series data for evidence of changes in market conditions is a problem central to development of a marketing information system. Examples are tracking field reports on competitors' prices and analyzing market share estimates computed from retail audits and consumer panel reports. These series may involve substantial random measurement error, and any changes, often small relative to this error, are difficult to detect promptly and accurately. One way to approach this problem is with techniques recently developed for handling time series with small stochastic mean shifts as well as random error. Two special procedures are compared in Monte Carlo analyses with a simpler data filtering and control-chart approach; the latter appears the most promising.