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A Wavelet‐Based Test for Stationarity
Author(s) -
Von Sachs Rainer,
Neumann Michael H.
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00200
Subject(s) - mathematics , series (stratigraphy) , covariance , wavelet , periodogram , haar wavelet , statistics , limit (mathematics) , econometrics , wavelet transform , discrete wavelet transform , mathematical analysis , computer science , artificial intelligence , paleontology , biology
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.