Article Sidebar

Download
PDF
Statistic
Read Counter : 82 Download : 60

Main Article Content

Abstract

This research discussed a hybrid Maximal Overlap Discrete Wavelet Transform (MODWT)-Autoregressive Moving Average (ARMA) model by combining the MODWT and the ARMA models to deal with the nonstationary and long-range dependence (LRD) time series. Theoretically, the details series obtained by MODWT are stationary and short-range dependent (SRD). Then, the general form of the MODWT-ARMA model was derived. In the experimental study, the daily Indonesia stock exchange LQ45 index time series was used to assess the performance of the hybrid model. Finally, the Mean Squared Error (MSE) and Mean Absolute Percent Error (MAPE) comparison with DWT-ARMA, ARIMA, and exponential smoothing models indicates that this combined model effectively improves forecasting accuracy. Based on the result of the analysis, the score of MSE of the MODWT-ARMA model was 51.42533, the score of the DWT-ARMA model was 180.1799, the score of the ARIMA model was 168.7863, and the score of the exponential smoothing model was 168.7824. At the same time, the score of MAPE in the MODWT-ARMA model was 0.00580797, the score of the DWT-ARMA model was 0.01106721, the score of the ARIMA model was 0.01070074, and the score of the exponential smoothing model was 0.01069591.

Keywords

time series LQ45 forecasting DWT MODWT-ARMA

Article Details

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
How to Cite
Hermansah. (2024). Hybrid MODWT-ARMA Model for Indonesia Stock Exchange LQ45 Index Forecasting . Enthusiastic : International Journal of Applied Statistics and Data Science, 4(1), 51–57. https://doi.org/10.20885/enthusiastic.vol4.iss1.art5
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. G.E.P. Box and G.M. Jenkins, Time Series Analysis Forecasting and Control. California, USA: Holden-Day, 1970.
  2. W.W.S. Wei, Time Series Analysis: Univariate and Multivariate Methods, 2nd ed. Boston, USA: Pearson Addison Wesley, 2006.
  3. P.J. Brockwell and A.R. Davis, Time Series Theory and Methods. New York, USA: Springer Verlag, 1991.
  4. D. Rosadi, Analisis Runtun Waktu dan Aplikasinya dengan R. Yogyakarta, Indonesia: Gadjah Mada University Press, 2014.
  5. G.P. Nason, Wavelet Methods in Statistics with R. New York, USA: Springer, 2008.
  6. D.B. Percival and A.T. Walden, Wavelet Methods for Time Series Analysis. Cambridge, United Kingdom: Cambridge University Press, 2000.
  7. J.S. Walker, A Primer on Wavelets and their Scientific Applications, 2nd ed. New York, USA: Taylor and Francis Group, 2008.
  8. R.K. Paul, Prajneshu, and H. Ghosh, “Wavelet Frequency Domain Approach for Modelling and Forecasting of Indian Monsoon Rainfall Time Series Data,” Journal of The Indian Society of Agricultural Statistics, Vol. 67, No. 3, pp. 319–327, 2013.
  9. O. Renaud, J.L. Starck, and F. Murtagh, “Prediction Based on a Multiscale Decomposition,” International Journal of Wavelet, Multiresolution and Information Processing, Vol. 1, No. 2, pp. 217–232, 2003.
  10. S.A. Wadi, A. Hamarsheh, and H. Alwadi, “Maximum Overlapping Discrete Wavelet Transform in Forecasting Banking Sector,” Applied Mathematical Sciences, Vol. 7, No. 80, pp. 3995–4002, 2013, doi: 10.12988/ams.2013.36305.
  11. L. Zhu, Y. Wang, and Q. Fan, “MODWT-ARMA Model for Time Series Prediction,” Journal of Applied Mathematical Modelling, Vol. 38, No. 5–6, pp. 1859–1865, Mar. 2014, doi: 10.1016/j.apm.2013.10.002.
  12. R.K.A. Paul and P. Anjoy, “Modeling Fractionally Integrated Maximum Temperature Series in India in Presence of Structural Break,” Theory and Applied Climatology, Vol. 134, pp. 241–249, 2018, doi: 10.1007/s00704-017-2271-x.
  13. R.J. Hyndman and Y. Khandakar, “Automatic Time Series Forecasting: The Forecast Package for R,” Journal of Statistical Software, Vol. 27, No. 3, pp. 1–22, 2008, doi: 10.18637/jss.v027.i03.
  14. R.J. Hyndman, A.B. Koehler, R.D. Snyder, and S. Grose, “A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods,” International Journal of Forecasting, Vol. 18, No. 3, pp. 439–454, Jul.–Sep. 2002, doi: 10.1016/S0169-2070(01)00110-8.
  15. G.P. Nason and R.V. Sachs, “Wavelets in Time Series Analysis,” Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 357, No. 760, pp. 2511–2526, Sep. 1999.
  16. M. Aminghafari and J.M. Poggi, “Forecasting Time Series Using Wavelets,” International Journal of Wavelets, Multiresolution and Information Processing, Vol. 5, No. 5, pp. 709–724, 2007, doi: 0.1142/S0219691307002002.
  17. M. Aminghafari and J.M. Poggi, “Nonstationary Time Series Forecasting Using Wavelets and Kernel Smoothing,” Communications in Statistics-Theory and Methods, Vol. 41, No. 3, pp. 485–499, 2012, doi: 10.1080/03610926.2010.529532.