, Volume 55, Issue 4, pp 737-764

Forecasting non-stationary time series by wavelet process modelling

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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 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.

Financial supports from the contract ‘Projet d'Actions de Recherche Concertées’ no. 98/03-217 of the Belgian Government and from the IAP research network No. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) are gratefully acknowledged.