Title: Nonparametric changes in variance detection using localised estimates
Authors: Rebecca Killick - Lancaster University (United Kingdom) [presenting]
Jamie-Leigh Chapman - Lancaster University (United Kingdom)
Idris Eckley - Lancaster University (United Kingdom)
Abstract: A nonparametric method of detecting changes in variance is developed for the case where assumptions of normality and independence are not appropriate. This may be the case in applications in renewable energy, finance and biomedical research. We develop a nonparametric method using the Locally Stationary Wavelet (LSW) model to provide a local estimate of the variance of a time series. If a time series has constant variance, then its local variance function will have constant mean and variance over time. However, if this variance is piecewise constant, then the structure of the variance function will also be piecewise constant. To this end, we can use the wavelet transformation to identify changes in variance in a fully non-parametric setting. We will demonstrate the efficacy of our approach through simulations studies where we compare against the most commonly used approaches in a variety of settings. The proposed method performs particular well in cases where the data contains outliers, heavy tails and/or autocorrelation. As the wavelet transformation separates out the variance from the autocorrelation the methodology is very fast compared to other approaches where the ARMA likelihood is required to account for the autocorrelation in a series. We demonstrate this on a large real world example.