Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting. (8th February 2017)

• Record Type: Journal Article
• Authors: Cardinali, Alessandro; Nason, Guy P.
• Other Names: Subba Rao Tata guestEditor.; Tunnicliffe Wilson Granville guestEditor.
• Is Part Of: Journal of time series analysis. Volume 38:Number 2(2017:Mar.)
• Page Start: 151
• Page End: 174
• Publication Date: 2017-02-08
• Subjects: Local stationarity -- wavelet packet -- locally stationary Fourier process -- locally stationary wavelet process; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12230
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : For non‐stationary time series, the fixed Fourier basis is no longer canonical. Rather than limit our basis choice to wavelet or Fourier functions, we propose the use of a library of non‐decimated wavelet packets from which we select a suitable basis (frame). Non‐decimated packets are preferred to decimated basis libraries so as to prevent information 'loss' at scales coarser than the finest. This article introduces a new class of locally stationary wavelet packet processes and a method to fit these to time series. We also provide new material on the boundedness of the inverse of the inner product operator of autocorrelation wavelet packet functions. We demonstrate the effectiveness of our modelling and basis selection on simulated series and Standard and Poor's 500 index series.