Novel wavelet models for nonstationary time series.

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In statistics, if a time series is stationary - meaning that its statistical properties, like the mean, do not change over time - there is a huge wealth of methods available to analyse the time series. However, it is normally the case that a time series is nonstationary. For example, a time series might display a trend - slow, long-running behaviour in the data. Nonstationary time series arise in many diverse areas, for example finance and environmental statistics, but these types of time series are less well-studied.The Numerical Algorithms Group (NAG), the industrial partner of the project, is a numerical software company that provides services to both industry and academia. There is an obvious demand to continually update and improve existing software libraries: statistical software for use with nonstationary time series is no exception.The main focus of the PhD is to develop new models for nonstationary time series using a mathematical concept known as wavelets. A wavelet is a "little wave" - it oscillates up and down but only for a short time. Wavelets allow us to capture the information in a time series by examining them at different scales or frequencies. The ultimate aim of the PhD is to develop a model for nonstationary time series that can be used to estimate both the mean and variance in a time series. Such a model could then be used, for example, to test for the presence of trend in a time series. In partnership with Numerical Algorithms Group (NAG).