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Wavelets in time-series analysis
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DOI：10.1098/rsta.1999.0445.png)
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Abstract
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This article reviews the role of wavelets in statistical time-series analysis. We survey work that emphasizes scale, such as estimation of variance, and the scale exponent of processes with a specific scale behaviour, such as 1/f processes. We present some of our own work on locally stationary wavelet (LSW) processes, which model both stationary and some kinds of non-stationary processes. Analysis of time-series assuming the LSW model permits identification of an evolutionary wavelet spectrum (EWS) that quantifies the variation in a time-series over a particular scale and at a particular time. We address estimation of the EWS and show how our methodology reveals phenomena of interest in an infant electrocardiogram series.
Keywords:
Allan variance
locally stationary time-series
long-memory processes
time-scale analysis
wavelet processes
wavelet spectrum
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