Choosing an Appropriate Wavelet for VARX Time Series Model Analysis
DOI:
https://doi.org/10.33095/px3b7908Keywords:
Time Series; VARX Model; Optimal Wavelet; Level and Order Wavelet; Soft Rule; Universal Threshold.Abstract
The paper purports to improve the accuracy of VARX (vector autoregressive with exogenous variables) models adopted for economic time series analysis through wavelet transform techniques applied for noise reduction. The research assessed various wavelet types, including Coiflets, Daubechies, Symlets, Biorthogonal, and Reverse Biorthogonal, for the most appropriate wavelet to be used for improving the performance of the models. Furthermore, it made use of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for evaluating the efficacy of each wavelet in the dimension of noise reduction and predictive accuracy enhancement.
It is conclusively deduced that preprocessing through wavelet-based techniques markedly improves the reliability of VARX models, as it removes short-term noise without affecting the long-term trends in the economy. Application of Daubechies and Reverse Biorthogonal wavelets has emerged better in all size categories in reducing AIC and BIC values. Thus, the study lauds wavelet denoising techniques in associating industries with finance to provide sound arguments for policymakers and economists to analyze more accurately complex economic relations.
This work advances development in econometric modeling, detailing the importance of wavelet transformations in improving economic forecasts. Future studies should explore combining machine learning techniques with wavelet-based VARX models for further improvements in forecasting capabilities.
Downloads
References
Abdulqader, Q. M., & Ahmed, N. M. (2023). Enhancing the ARIMAX Model by Using the Bivariate Wavelet Denoising: Application on Road Traffic Accidents Data. Iraoi Journal of Statistical Sciences, 20(2).
Acquah, H. D. (2010). Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship. Journal of Development and Agricultural Economics, 2(1), 1–6.
Al-Doski, A. S., & Al-Waili, S. F. (2008). The reality of the Iraqi economy concerning the parallel sector. Prepared by the consulting office at Duhok University College with the support of the Center for International Private Enterprise (CIPE), Iraq - Duhok.
Ali, S., Murshed, S. M., & Papyrakis, E. (2023). Oil, export diversification and economic growth in Sudan: evidence from a VAR model. Mineral Economics, 36(1), 77-96. https://doi.org/10.1007/s13563-022-00310-w
Ali, T. H., Albarwari, N. H. S., & Ramadhan, D. L. (2023). Using the hybrid proposed method for quantile regression and multivariate wavelet in estimating the linear model parameters. Iraqi Journal of Statistical Sciences, 20(1), 9-24.
Ali, T. H., Mustafa, Q., & Raza, M. S. (2016). Reducing the orders of the mixed model (ARMA) before and after the wavelet de-noising with application. Journal of Humanity Sciences, 20, 433-442.
Ali, T. H., Raza, M. S., & Abdulqader, Q. M. (2024). VAR time series analysis using wavelet shrinkage with application. Science Journal of University of Zakho, 12(3), 345-355.
https://doi.org/10.25271/sjuoz.2024.12.3.1304
Ali, T. H., & Saleh, D. M. (2022). Proposed hybrid method for wavelet shrinkage with robust multiple linear regression model: With simulation study. Qalaai Zanist Journal, 7(1), 920-937.
Arouxet, M. B., Pastor, V. E., & Vampa, V. (2021). Using the wavelet transform for time series analysis. In Applications of Wavelet Multiresolution Analysis (pp. 59-74). Springer International Publishing.
Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261-304.
https://doi.org/10.1177/0049124104268644
Cazelles, B., Chavez, M., Berteaux, D., Ménard, F., Vik, J. O., Jenouvrier, S., & Stenseth, N. C. (2008). Wavelet analysis of ecological time series. Oecologia, 156, 287-304.
Central Bank of Iraq. (2024). Economic and statistical data. Retrieved from https://cbi.iq
Cohen, A., Daubechies, I., & Feauveau, J. C. (1992). Biorthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, 45(5), 485-560.
Dastgerdi, A. K., & Mercorelli, P. (2022). Investigating the effect of noise elimination on LSTM models for financial markets prediction using Kalman Filter and Wavelet Transform. WSEAS Transactions on Business and Economics, 19, 432-441.
https://doi.org/10.37394/23207.2022.19.39
Daubechies, I. (1992). Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics (SIAM). https://doi.org/10.1137/1.9781611970104
Donoho, D. L., & Johnstone, I. M. (1998). Minimax estimation via wavelet shrinkage. The Annals of Statistics, 26(3), 879-921. https://doi.org/10.1214/aos/1024691081
Gonçalves, M. A., Gonçalves, A. S., Franca, T. C., Santana, M. S., da Cunha, E. F., & Ramalho, T. C. (2022). Improved protocol for the selection of structures from molecular dynamics of organic systems in solution: The value of investigating different wavelet families. Journal of Chemical Theory and Computation, 18(10), 5810-5818.
Guo, T., Zhang, T., Lim, E., Lopez-Benitez, M., Ma, F., & Yu, L. (2022). A review of wavelet analysis and its applications: Challenges and opportunities. IEEE Access, 10, 58869-58903.
Haydier, E. A., Albarwari, N. H. S., & Ali, T. H. (2023). The Comparison Between VAR and ARIMAX Time Series Models in Forecasting. Iraqi Journal of Statistical Sciences, 20(2), 249-262.
Jalal, S. A., Saleh, D. M., Sedeeq, B. S., & Ali, T. H. (2024). Construction of the Daubechies wavelet chart for quality control of the single value. Iraqi Journal of Statistical Sciences, 21(1), 160-169. https://doi.org/10.33899/iqjoss.2024.183257
Karamikabir, H., Afshari, M., & Lak, F. (2021). Wavelet threshold based on Stein’s unbiased risk estimators of restricted location parameter in multivariate normal. Journal of Applied Statistics, 48(10), 1712-1729.
Kirillov, O. E. (2024). Application of the Wavelet Transform in the Analysis of Non-stationary Processes in Aerodynamic Experiments. Lobachevskii Journal of Mathematics, 45(5), 2058-2066. https://doi.org/10.1134/S1995080224602248
Li X, Liao K, He G, Zhao J. Research on improved wavelet threshold denoising method for non-contact force and magnetic signals. Electronics. 2023;12(5):1244. https://doi.org/10.3390/electronics12051244.
Liu, B., & Cheng, H. (2024). De-noising classification method for financial time series based on ICEEMDAN and wavelet threshold, and its application. EURASIP Journal on Advances in Signal Processing, 2024(1), 19.
Liu, B., & Cheng, H. (2024). De-noising classification method for financial time series based on ICEEMDAN and wavelet threshold, and its application. EURASIP Journal on Advances in Signal Processing, 2024(1), 19.
Lütkepohl, H. (2004). Applied time series econometrics. Cambridge University Press.
Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science & Business Media. p. 1-558
Mallat, S. (2009). The sparse way. In A wavelet tour of signal processing (3rd ed., pp. 1-795). Academic Press.
Mallat, S. (1999). Introduction to wavelets. In A wavelet tour of signal processing (pp. 1-532). Academic Press.
Omer, A. W., Sedeeq, B. S., & Ali, T. H. (2024). A proposed hybrid method for multivariate linear regression model and multivariate wavelets (Simulation study). Polytechnic Journal of Humanities and Social Sciences, 5(1), 112-124.
Parra, L. C., Ortubay, A. S., Nentwich, M., Madsen, J., & Babadi, B. (2024). VARX Granger analysis: Modeling, inference, and applications. arXiv preprint arXiv:2404.10834.
Percival, D. B., & Walden, A. T. (2000). Wavelet Methods for Time Series Analysis. Cambridge University Press. https://doi.org/10.1017/CBO9780511841040
Pesaran, M. H. (2015). Introduction to econometric models. In Time series and panel data econometrics (pp. 1-1024). Oxford University Press.
Rhif, M., Ben Abbes, A., Farah, I. R., Martínez, B., & Sang, Y. (2019). Wavelet transform application for/in non-stationary time-series analysis: A review. Applied Sciences, 9(7), 1345. http://dx.doi.org/10.3390/app9071345
Schulte, J. A. (2016). Wavelet analysis for non-stationary, nonlinear time series. Nonlinear Processes in Geophysics, 23(4), 257-267. https://doi.org/10.5194/npg-23-257-2016
Strang, G., & Nguyen, T. (1996). Introduction to wavelets and filter banks. In Wavelets and Filter Banks (pp. 1-515). Wellesley-Cambridge Press.
Tilak, T. N., & Krishnakumar, S. (2018). Reverse biorthogonal spline wavelets in undecimated transform for image denoising. Int. J. Comput. Sci. Eng, 6, 66-72.
Tsay, R. S. (2013). Multivariate time series analysis: with R and financial applications. John Wiley & Sons.
Published
Issue
Section
License
Copyright (c) 2025 Journal of Economics and Administrative Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Articles submitted to the journal should not have been published before in their current or substantially similar form or be under consideration for publication with another journal. Please see JEAS originality guidelines for details. Use this in conjunction with the points below about references, before submission i.e. always attribute clearly using either indented text or quote marks as well as making use of the preferred Harvard style of formatting. Authors submitting articles for publication warrant that the work is not an infringement of any existing copyright and will indemnify the publisher against any breach of such warranty. For ease of dissemination and to ensure proper policing of use, papers and contributions become the legal copyright of the publisher unless otherwise agreed.
The editor may make use of Turnitin software for checking the originality of submissions received.
