A Wavelet‐Based Test for Stationarity

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.