Euan McGonigle

(*TIME CHANGED) Modelling and estimation of nonstationary time series via wavelets and differencing

*The time of this seminar has changed.

Time series often possess complex and dynamic characteristics. Most time series observed in practice exhibit time-varying trend and autocovariance behaviour. Differencing is a commonly used technique to remove the trend, that allows for the estimation of the time-varying second order structure (of the differenced series). However, often we require inference on the second-order behaviour of the original series; for example, when performing trend estimation. In this talk, we propose a method using differencing to jointly estimate the time-varying trend and second-order structure of a time series, within the locally stationary wavelet framework of Nason et al. (2000). We discuss a wavelet-based estimator of the second-order structure of the original time series by employing differencing, and show how this can be incorporated into the estimation of the trend of the time series. We demonstrate the utility of the method by analysing a biomedical time series example.