A Wavelet‐Based Test for Stationarity

Rainer Von Sachs and Michael H. Neumann

Journal of Time Series Analysis, 2000, vol. 21, issue 5, 597-613

Abstract: We develop a test for stationarity of a time series against the alternative of a time‐varying covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time‐varying spectral density. Coefficients with respect to a Haar wavelet series expansion of such a time‐varying periodogram are an indicator of whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.

Date: 2000
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