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Prediction Based on a Multiscale Decomposition
Journal article

Prediction Based on a Multiscale Decomposition

  • Renaud, Olivier Faculté de Psychologie et Sciences de l'Education, Université de Genève, 40, Bd du Pont d'Arve, 1211 Genève 4, Switzerland
  • Starck, Jean-Luc DAPNIA/SEI-SAP, Service d'Astrophysique, CEA-Saclay, 91191 Gif sur Yvette, France
  • Murtagh, Fionn School of Computer Science, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland
  • 2012-1-5
Published in:
  • International Journal of Wavelets, Multiresolution and Information Processing. - World Scientific Pub Co Pte Lt. - 2003, vol. 01, no. 02, p. 217-232
English A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant "à trous" wavelet transform which has the advantage of being shift-invariant. The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies. We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.
Language
  • English
Open access status
closed
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Persistent URL
https://sonar.ch/global/documents/77854
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