Fryzlewicz, Piotr, van Bellegem, Sébastien and von Sachs, Rainer
Forecasting non-stationary time series by wavelet process modelling.
Annals of the Institute of Statistical Mathematics, 55
Many time series in the applied sciences display a time-varying second order structure. In this article, we address the problem of how to forecast these nonstationary time series by means of non-decimated wavelets. Using the class of Locally Stationary Wavelet processes, we introduce a new predictor based on wavelets and derive the prediction equations as a generalisation of the Yule-Walker equations. We propose an automatic computational procedure for choosing the parameters of the forecasting algorithm. Finally, we apply the prediction algorithm to a meteorological time series.
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