Assessing nonstationary time series using wavelets
Brandon J. Whitcher · 1998
The discrete wavelet transform has be used extensively in the field of Statistics, mostly in the area of "denoising signals" or nonparametric regression. This thesis provides a new application for the discrete wavelet transform, assessing nonstationary events in time series -- especially long memory processes. Long memory processes are those which exhibit substantial correlations between events separated by a long period of time. Departures from stationarity in these heavily autocorrelated time series, such as an abrupt change in the variance at an unknown location or "bursts" of increased variability, can be detected and accurately located using discrete wavelet transforms -- both orthogonal and overcomplete. A cumulative sum of squares method, utilizing a Kolomogorov-Smirnov-type