Tests for nonstationarity

Most practical random processes are more or less nonstationary. The concept of stationarity appears to be merely a mathematical model. The question then is how to decide the ‘‘degree’’ of nonstationarity underlined in a given time series. This report explains how and why estimated evolutionary spectra of the time series can be used to test the nonstationarity for the random processes; the methods are essentially the modification and extension of Priestley’s evolutionary spectrum test technique. Various test models are further proposed in this paper including ‘‘two‐way’’ and ‘‘three‐way’’ tests using both discrete (or equispaced) frequency and/or frequency bands. The techniques developed are applied to both synthetic and practical acoustic data captured from aircraft fly‐over events.