Time Series

Annals of the Institute of Statistical Mathematics

, Volume 55, Issue 4, pp 737-764

First online:

Forecasting non-stationary time series by wavelet process modelling

  • Piotr FryzlewiczAffiliated withDepartment of Mathematics, University of Bristol
  • , Sébastien Van BellegemAffiliated withInstitut de statistique, Université catholique de Louvain
  • , Rainer von SachsAffiliated withInstitut de statistique, Université catholique de Louvain

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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 stationarity non-decimated wavelets prediction time-modulated processes Yule-Walker equations