Wavelets in time-series analysis

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.

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