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Time series often possess complex characteristics and dynamics, from trends, and periodicities, to a time-varying second-order structure. Adequate modelling of such data is important for example in predicting future events or providing improved customer service and marketing strategies. Inappropriate assumptions can lead to incorrect conclusions being drawn.
Recently there has been much activity in so-called locally stationary models, which are able to capture evolving variability in time series data. The locally stationary wavelet model (LSW) by Nason et al (2000) has received much research focus in the time series literature, enabling the time-varying second-order structure to be more readily discovered and estimated.
One of the drawbacks of the LSW model is that it assumes the time series under analysis is zero-mean, which is unrealistic for the majority of time series encountered in practice. This talk describes a model which includes the attractive properties of the LSW model, but with the flexibility to incorporate trend, seasonal components and locally stationary mean structure as well as second order structure directly into the model.
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