Forecasting non-stationary time series by wavelet process modelling

• Published in: Annals of the Institute of Statistical Mathematics Vol. 55; no. 4; pp. 737 - 764
• Main Authors: FRYZLEWICZ, Piotr, VAN BELLEGEM, Sébastien, VON SACHS, Rainer
• Format: Journal Article
• Language: English
• Published: Tokyo Kluwer 01-12-2003; Dordrecht Springer Nature B.V
• Subjects: Algorithms; Differential equations; Exact sciences and technology; Forecasting; Inference from stochastic processes; time series analysis; Mathematical models; Mathematics; Predictions; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic processes; Studies; Time series; United Kingdom > UK; Forecasting theory; Wavelet transformation; Prediction; Time series; Non stationary process; Yule Walker equation; Statistics
• ISSN: 0020-3157; 1572-9052
• DOI: 10.1007/BF02523391

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.