Statistics Seminar: Introducing the Mean Locally Stationary Wavelet Process and its applications

Presenter: Rebecca Killick (Statistics, Lancaster University)

Title: Introducing the Mean Locally Stationary Wavelet Process and its applications

Microsoft Teams Meeting

Summary:

Most time series observed in practice exhibit first as well as second-order nonstationarity. In this presentation, we propose a novel framework for modelling series with simultaneous time-varying first and second-order structure, removing the restrictive zero-mean assumption of locally stationary wavelet processes and extending the applicability of the locally stationary wavelet model to include trend components. We develop an associated estimation theory for both first and second-order time series quantities and show that our estimators achieve good properties in isolation of each other by making appropriate assumptions on the series trend. We demonstrate the utility of the method by analysing global mean sea temperature time series, highlighting the impact of the changing climate as well as an application to the bioluminescence of micro-worms.