Acta Oeconomica Pragensia 2018, 26(1):5-24 | DOI: 10.18267/j.aop.592

Time series forecasting with a prior wavelet-based denoising step

Milan Bašta
University of Economics, Prague, Faculty of Informatics and Statistics

We provide an extensive study assessing whether a prior wavelet-based denoising step enhances the forecast accuracy of standard forecasting models. Many combinations of attribute values of the thresholding (denoising) algorithm are explored together with several traditional forecasting models used in economic time series forecasting. The results are evaluated using M3 competition yearly time series. We conclude that the performance of a forecasting model combined with the prior denoising step is generally not recommended, which implies that a straightforward generalisation of some of the results available in the literature (which found the denoising step to be beneficial) is not possible. Even if cross-validation is used to select the value of the threshold, a superior performance of the forecasting model with the prior denoising step does not generally follow.

Keywords: wavelets, noise, evaluating forecasts, automatic forecasting
JEL classification: C15, C22, C49, C53

Published: February 1, 2018  Show citation

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Bašta, M. (2018). Time series forecasting with a prior wavelet-based denoising step. Acta Oeconomica Pragensia, 26(1), 5-24. doi: 10.18267/j.aop.592
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    References

    1. Alrumaih, R. M. and Al-Fawzan, M. A. (2002). Time Series Forecasting Using Wavelet Denoising: An Application to Saudi Stock Index. Journal of King Saud University. Engineering Sciences, 2(14), pp. 221-234. Go to original source...
    2. Bašta, M. (2014). Additive Decomposition and Boundary Conditions in Wavelet-based Forecasting Approaches. Acta Oeconomica Pragensia, 22(2), pp. 48-70, https://doi.org/10.18267/j.aop.431 Go to original source...
    3. Bergmeir, C. and Benítez, J. M. (2012). On the Use of Cross-validation for Time Series Predictor Evaluation. Information Sciences, 191, pp. 192-213, https://doi.org/10.1016/j.ins.2011.12.028 Go to original source...
    4. Boto-Giralda, D., Díaz-Pernas, F. J., González-Ortega, D., Díez-Higuera, J. F., Antón-Rodríguez, M., Martínez-Zarzuela, M. and Torre-Díez, I. (2010). Wavelet-Based Denoising for Traffic Volume Time Series Forecasting with Self-Organizing Neural Networks. Computer-Aided Civil and Infrastructure Engineering, 25(7), pp. 530-545, https://doi.org/10.1111/j.1467-8667.2010.00668.x Go to original source...
    5. Bruzda, J. (2014). Forecasting via wavelet denoising: the random signal case. In: M. Gallegatti and W. Semmler, eds., Wavelet applications in economics and finance, 1st ed. New York: Springer, pp. 187-225. Go to original source...
    6. Coifman, R. R. and Donoho, D. L. (1995). Translation-invariant de-noising. In: A. Antoniadis and G. Oppenheim G., eds., Wavelets and Statistics. Lecture Notes in Statistics, vol. 103. New York: Springer, pp. 125-150, https://doi.org/10.1007/978-1-4612-2544-7_9 Go to original source...
    7. Donoho, D. L. and Johnstone, J. M. (1994). Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika, 81(3), pp. 425-455, https://doi.org/10.1093/biomet/81.3.425 Go to original source...
    8. Ferbar, L., Čreslovnik, D., Mojškerc, B. and Rajgelj, M. (2009). Demand Forecasting Methods in a Supply Chain: Smoothing and Denoising. International Journal of Production Economics, 118(1), pp. 49-54, https://doi.org/10.1016/j.ijpe.2008.08.042 Go to original source...
    9. Hastie, T., Tibshirani, R. and Friedman, J. (2011). The elements of statistical learning: data mining, inference, and prediction. 2nd ed. New York: Springer.
    10. Hyndman, R. J. and Athanasopoulos, G. (2013). Forecasting: principles and practice. Melbourne: OTexts.
    11. Hyndman, R. J. and Khandakar, Y. (2008). Automatic Time Series Forecasting: The Forecast Package for R. Journal of Statistical Software, 27(3), https://doi.org/10.18637/jss.v000.i00 Go to original source...
    12. Hyndman, R. J. and Koehler, A. B. (2006). Another Look at Measures of Forecast Accuracy. International Journal of Forecasting, 22(4), pp. 679-688, https://doi.org/10.1016/j.ijforecast.2006.03.001 Go to original source...
    13. Hyndman, R. J. (2013a). forecast: Forecasting functions for time series and linear models. R package version 4.7. Available at: https://cran.r-project.org/web/packages/forecast/index.html [Accessed 15 Apr. 2015].
    14. Hyndman, R. J. (2013b). Mcomp: Data from the M-competitions. R package version 2.05. Available at: https://cran.r-project.org/web/packages/Mcomp/index.html [Accessed 25 Nov. 2015].
    15. Lotrič, U. (2004). Wavelet Based Denoising Integrated into Multilayered Perceptron. Neurocomputing, 62, pp. 179-196, https://doi.org/10.1016/j.neucom.2004.02.003 Go to original source...
    16. Makridakis, S., Andersen, A., Carbone, R., Fildes, R., Hibon, M., Lewandowski, R., Newton, J., Parzen, E. and Winkler, R. (1982). The Accuracy of Extrapolation (Time Series) Methods: Results of a Forecasting Competition. Journal of Forecasting, 1(2), pp. 111-153, https://doi.org/ 10.1002/for.3980010202 Go to original source...
    17. Makridakis, S., Chatfield, C., Hibon, M., Lawrence, M., Mills, T., Ord, K. and Simmons, L. F. (1993). The M2-competition: A Real-Time Judgmentally Based Forecasting Study. International Journal of Forecasting, 9(1), pp. 5-22, https://doi.org/10.1016/0169-2070(93)90044-N Go to original source...
    18. Makridakis, S. and Hibon, M. (2000). The M3-Competition: Results, Conclusions and Implications. International Journal of Forecasting, 16(4), pp. 451-476, https://doi.org/10.1016/S0169-2070(00)00057-1 Go to original source...
    19. Miller, C. J., Genovese, C., Nichol, R. C., Wasserman, L., Connolly, A., Reichart, D., Hopkins, A., Schneider, J. and Moore, A. (2001). Controlling the False-discovery Rate in Astrophysical Data Analysis. The Astronomical Journal, 122, pp. 3492-3505, https://doi.org/10.1086/324109 Go to original source...
    20. Olmeda, I. and Fernández, E. (2000). Filtering With Wavelets May Be Worse Than You Think. Computing in Economics and Finance 2000, 150, Society for Computational Economics.
    21. Percival, D. B. and Walden, A. T. (2006). Wavelet methods for time series analysis. Cambridge: Cambridge University Press.
    22. R Core Team (2015). R: A Language and Environment for Statistical Computing, [online]. R Foundation for Statistical Computing, Vienna, Austria. Available at: https://www.R-project.org [Accessed 13 Jan. 2016].
    23. Schlüter, S. and Deuschle, C. (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.
    24. Shmueli, G. (2010). To Explain or to Predict? Statistical Science, 25(3), pp. 289-310, https://doi.org/10.1214/10-STS330 Go to original source...
    25. Tashman, L. J. (2000). Out-of-sample Tests of Forecasting Accuracy: An Analysis and Review. International Journal of Forecasting, 16(4), pp. 437-450, https://doi.org/10.1016/S0169-2070(00)00065-0 Go to original source...
    26. Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing. 3rd ed. Oxford: Academic Press. Go to original source...

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