Forecasting non-stationary time series by wavelet process modelling

Fryzlewicz, P;Van Bellegem, Sébastien;von Sachs, Rainer
(2003) Annals of the Institute of Statistical Mathematics — Vol. 55, n° 4, p. 737-764 (2003)

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Abstract
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 non-stationary 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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Fryzlewicz, P., Van Bellegem, S., & von Sachs, R. (2003). Forecasting non-stationary time series by wavelet process modelling. Annals of the Institute of Statistical Mathematics, 55(4), 737-764. https://doi.org/10.1007/BF02523391 (Original work published 2003)