Annals of the Institute of Statistical Mathematics

, Volume 55, Issue 4, pp 737–764

Forecasting non-stationary time series by wavelet process modelling

  • Piotr Fryzlewicz
  • Sébastien Van Bellegem
  • Rainer von Sachs
Time Series

DOI: 10.1007/BF02523391

Cite this article as:
Fryzlewicz, P., Van Bellegem, S. & von Sachs, R. Ann Inst Stat Math (2003) 55: 737. doi:10.1007/BF02523391

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.

Key words and phrases

Local stationaritynon-decimated waveletspredictiontime-modulated processesYule-Walker equations

Copyright information

© The Institute of Statistical Mathematics 2003

Authors and Affiliations

  • Piotr Fryzlewicz
    • 1
  • Sébastien Van Bellegem
    • 2
  • Rainer von Sachs
    • 2
  1. 1.Department of MathematicsUniversity of BristolBristolUK
  2. 2.Institut de statistiqueUniversité catholique de LouvainBelgium