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Modelling and forecasting by wavelets, and the application to exchange rates

Author

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  • H. Wong
  • Wai-Cheung Ip
  • Zhongjie Xie
  • Xueli Lui

Abstract

This paper investigates the modelling and forecasting method for non-stationary time series. Using wavelets, the authors propose a modelling procedure that decomposes the series as the sum of three separate components, namely trend, harmonic and irregular components. The estimates suggested in this paper are all consistent. This method has been used for the modelling of US dollar against DM exchange rate data, and ten steps ahead (2 weeks) forecasting are compared with several other methods. Under the Average Percentage of forecasting Error (APE) criterion, the wavelet approach is the best one. The results suggest that forecasting based on wavelets is a viable alternative to existing methods.

Suggested Citation

  • H. Wong & Wai-Cheung Ip & Zhongjie Xie & Xueli Lui, 2003. "Modelling and forecasting by wavelets, and the application to exchange rates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(5), pages 537-553.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:5:p:537-553
    DOI: 10.1080/0266476032000053664
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    Citations

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    Cited by:

    1. Lakhwinder Pal Singh & Ravi Teja Challa, 2016. "Integrated Forecasting Using the Discrete Wavelet Theory and Artificial Intelligence Techniques to Reduce the Bullwhip Effect in a Supply Chain," Global Journal of Flexible Systems Management, Springer;Global Institute of Flexible Systems Management, vol. 17(2), pages 157-169, June.
    2. Milan Bašta, 2014. "Additive Decomposition and Boundary Conditions in Wavelet-Based Forecasting Approaches," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2014(2), pages 48-70.
    3. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    4. Deniz Kenan Kılıç & Ömür Uğur, 2018. "Multiresolution analysis of S&P500 time series," Annals of Operations Research, Springer, vol. 260(1), pages 197-216, January.
    5. Indranil Ghosh & Tamal Datta Chaudhuri, 2017. "Fractal Investigation and Maximal Overlap Discrete Wavelet Transformation (MODWT)-based Machine Learning Framework for Forecasting Exchange Rates," Studies in Microeconomics, , vol. 5(2), pages 105-131, December.
    6. Ramazan Gencay & Ege Yazgan, 2017. "When Are Wavelets Useful Forecasters?," Working Papers 1704, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    7. Gandjon Fankem, Gislain Stéphane & Fouda Mbesa, Lucien Cédric, 2023. "Business cycle synchronization and African monetary union: A wavelet analysis," Journal of Macroeconomics, Elsevier, vol. 77(C).
    8. Joanna Janczura & Rafał Weron, 2012. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 385-407, July.
    9. António Rua, 2011. "A wavelet approach for factor‐augmented forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(7), pages 666-678, November.
    10. Weron, Rafal & Janczura, Joanna, 2010. "Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices," MPRA Paper 26628, University Library of Munich, Germany.
    11. Bruzda, Joanna, 2011. "Some aspects of the discrete wavelet analysis of bivariate spectra for business cycle synchronisation," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-46.
    12. Risse, Marian, 2019. "Combining wavelet decomposition with machine learning to forecast gold returns," International Journal of Forecasting, Elsevier, vol. 35(2), pages 601-615.
    13. Zhifeng Dai & Jie Kang & Hua Yin, 2023. "Forecasting equity risk premium: A new method based on wavelet de‐noising," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 4331-4352, October.
    14. Luís Aguiar-Conraria & Maria Joana Soares, 2014. "The Continuous Wavelet Transform: Moving Beyond Uni- And Bivariate Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 28(2), pages 344-375, April.
    15. Schlüter, Stephan & Deuschle, Carola, 2010. "Using wavelets for time series forecasting: Does it pay off?," FAU Discussion Papers in Economics 04/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    16. João Martins, 2022. "Bond Yields Movement Similarities and Synchronization in the G7: A Time–Frequency Analysis," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 18(2), pages 189-214, July.
    17. Joanna Bruzda, 2020. "The wavelet scaling approach to forecasting: Verification on a large set of Noisy data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 353-367, April.
    18. M. H. Lee & H. J. Sadaei & Suhartono, 2013. "Improving TAIEX forecasting using fuzzy time series with Box--Cox power transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(11), pages 2407-2422, November.
    19. Jakub Nowotarski & Jakub Tomczyk & Rafal Weron, 2013. "Modeling and forecasting of the long-term seasonal component of the EEX and Nord Pool spot prices," HSC Research Reports HSC/13/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    20. Abid, Fathi & Kaffel, Bilel, 2018. "Time–frequency wavelet analysis of the interrelationship between the global macro assets and the fear indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1028-1045.
    21. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    22. Fernandez, Viviana, 2007. "Wavelet- and SVM-based forecasts: An analysis of the U.S. metal and materials manufacturing industry," Resources Policy, Elsevier, vol. 32(1-2), pages 80-89.
    23. Boryana Bogdanova & Ivan Ivanov, 2016. "A wavelet-based approach to the analysis and modelling of financial time series exhibiting strong long-range dependence: the case of Southeast Europe," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 655-673, March.

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