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Title: Recent developments in nonstationary time series modelling with application to the environmental sciences Authors:  Matthew Nunes - University of Bath (United Kingdom) [presenting]
Euan McGonigle - University of Bristol (United Kingdom)
Rebecca Killick - Lancaster University (United Kingdom)
Abstract: In many application areas, including the environmental sciences, time series often show second-order characteristics which vary over time. Modelling and estimating this structure is vital for understanding and characterising the evolution of underlying processes. However, many processes also exhibit a first-order (trend) structure. Trend estimation in time series is often performed without consideration of the second-order nonstationary structure; on the other hand, it is common to remove trends prior to nonstationary time series analysis, risking inaccurate estimation of second-order properties. We introduce trend locally stationary wavelet (T-LSW) processes, a modelling framework which extends previous work to capture both first- and second-order nonstationarity, and describe an estimation scheme for the time series quantities, which ensures bias and consistency. We illustrate our model with climatic data examples and outline avenues of further work of interest to practitioners in the environmental sciences.