Sequential Change-Point Detection Methods for Nonstationary Time Series

Abstract

We present two new spectral-based methods for detection of changes in autocorrelation structure in a continuous-valued time series in an online process monitoring setting. Our methods are based on the idea that changes in the autocorrelation structure are reflected by changes in the Fourier or wavelet-based spectrum and can be detected by comparing estimated spectra of adjacent blocks of the series. To be effective for slowly changing spectral structure, the methods are extended to allow information from more than one past block to be used in determining whether a change has occurred, in such a way as to minimize computational burden. Through simulation, we evaluate the performance of our methods and find that they can provide reliable and timely detection of changes in covariance structure in an online monitoring framework. We illustrate the methods using electroencephalogram traces (brain waves) and run-time computer performance metrics.