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Forecasting non-stationary time series by wavelet process modelling. (English) Zbl 1047.62085

Summary: Many time series in the applied sciences display a time-varying second order structure. 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.

MSC:

62M20 Inference from stochastic processes and prediction
65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65C60 Computational problems in statistics (MSC2010)
62P12 Applications of statistics to environmental and related topics
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