AN ENHANCED SHRINKAGE FUNCTION FOR DENOISING ECONOMIC TIME SERIES DATA USING WAVELET ANALYSIS
DOI:
https://doi.org/10.25271/sjuoz.2024.12.1.1223Keywords:
Wavelet Shrinkage Denoising, Arctangent Model, Financial Time Series Data, Noise Reduction, Stock Data, Shanghai Composite IndexAbstract
In the realm of economic (financial) time series analysis, accurate prediction holds paramount importance. However, these data often suffer from the presence of noise, particularly in highly random and non-stationary datasets like stock market data. Dealing with noisy data makes predicting noise-free economic models exceedingly challenging. This research paper introduces an innovative shrinkage (thresholding) function designed to improve the efficiency of wavelet shrinkage denoising in the context of financial time series data. The proposed function is constructed based on an arctangent model with adjustable parameters meticulously chosen to ensure the function maintains continuous differentiability. The application of this novel shrinkage function effectively reduces noise in stock data. Employing R program for data analysis and figure plotting, the performance of this approach is rigorously validated using closing price data from the Shanghai Composite Index, spanning the period from January 4, 2000 to August 28, 2023. The experimental results demonstrate that the proposed thresholding function outperforms classical shrinkage functions (hard, soft, and nonnegative garrote) in both continuous derivative property and denoising efficacy.
References
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, 14(2), pp.221-233.
Breiman, L. (1995). Better subset regression using the nonnegative garrote. Technometrics, 37, 373–384.
de Souza e Silva, E. G., Legey, L. F. L., & de Souza e Silva, E. A. (2010). Forecasting oil price trends using wavelets and hidden Markov models. Energy Economics, 32, 1507–1519.
Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika, 81(3), 425–455.
Donoho, D. L., & Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90(432), 1200–1224.
Donoho, D. L., & Johnstone, I. M. (1998). Minimax estimation via wavelet shrinkage. Annals of Statistics, 26(3), 879–921.
Gao, H. Y. (1998). Wavelet shrinkage denoising using the non-negative garrote. Journal of Computational and Graphical Statistics, 7(4), 469–488.
Gao, H. Y., & Bruce, A. G. (1997). WaveShrink with firm shrinkage. Statistica Sinica, 7, 855–874.
Gomes, J., & Velho, L. (2015). From Fourier analysis to wavelets. Basel, Switzerland: Springer.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In Proceedings of the royal society of London a: Mathematical, physical and engineering sciences (Vol. 454, pp. 903–995). The Royal Society.
Jarrah, M. and Derbali, M., 2023. Predicting Saudi Stock Market Index by Using Multivariate Time Series Based on Deep Learning. Applied Sciences, 13(14), p.8356.
Jiang, M. H., An, H. Z., Jia, X. L., & Sun, X. Q. (2017). The influence of global benchmark oil prices on the regional oil spot market in multi-period evolution. Energy, 118, 742–752.
Kolosinska, M. I., & Kolosinskyi, Y. Y. (2013). Analysis and forecast of the basic principles of tourist market development in Ukraine using the methods of economic-mathematical modeling. Actual Problems of Economics, 10(148), 222–227.
Li, S. T., & Kuo, S. C. (2008). Knowledge discovery in financial investment for forecasting and trading strategy through wavelet-based SOM networks. Expert Systems with Applications, 34, 935–951.
Neittaanmäki, P., Repin, S., & Tuovinen, T. (2016). Mathematical Modeling and optimization of complex structures. Basel, Switzerland: Springer.
Svarc, J., & Dabic, M. (2017). Evolution of the knowledge economy: A historical perspective with an application to the case of Europe. Journal of the Knowledge Economy, 8(1), 159–176.
Tiwari, A. K. (2013). Oil prices and the macroeconomy reconsideration for Germany: Using continuous wavelet. Economic Modelling, 30, 636–642.
Tiwari, A. K., & Kyophilavong, P. (2014). New evidence from the random walk hypothesis for BRICS stock indices: A wavelet unit root test approach. Economic Modelling, 43, 38–41.
Tiwari, A. K., Mutascu, M. I., & Albulescu, C. T. (2016). Continuous wavelet transform and rolling correlation of European stock markets. International Review of Economics and Finance, 42, 237–256.
Vacha, L., & Barunik, J. (2012). Co-movement of energy commodities revisited: Evidence from wavelet coherence analysis. Energy Economics, 34, 241–247.
Wu, Z. H., & Huang, N. E. (2009). Ensemble empirical model decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1(01), 1–14.
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Sameera A. Othman, Kurdistan M. Omar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work, with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online.
