Hybrid Waveform Diagnostics of Seasonal Time Series Models and Exponential Smoothing with the Application
Main Article Content
Abstract
The study aims to evaluate the effectiveness of wavelet analysis as a diagnostic tool for univariate time series models by comparing several traditional and wavelet-based methods. It also seeks to compare the performance of two different approaches for analyzing and forecasting univariate time series: traditional exponential smoothing and wavelet analysis. Additionally, the research explores the effectiveness of a hybrid model combining exponential smoothing and wavelet filters. These methods were applied to real-world data, with results showing that the hybrid model achieves higher predictive accuracy and excels in isolating noise and abrupt changes.
Article Details
Issue
Section
How to Cite
References
1. Abdul Rahim, Mushtaq Karim, Jawad, Ali Muhammad (2021), "Improving the Quality of Fit of the Binary Response Model with Practical Application on COVID-19 Patients," Department of Statistics, College of Administration and Economics, University of Karbala, Iraq.
2. Ahmed, Adeeb, Al-Jubaili, Ramia, (2021), "Forecasting Cow's Milk Production in Syria Using Exponential Smoothing," Al-Baath University Journal, Volume (43), Issue (26).
3. Al-Alja, Mabtoush, (2018), "The Effectiveness of the Box-Jengis and Holt-Winter Methods in Predicting Sales of the National Electricity and Gas Corporation "Sonelgaz" (Bitsemsilt Branch), Economic Researcher Journal (CHEEC), Volume (16), Issue (10).
4. Al-Jamal, Zakaria Yahya, Al-Omari, Hilal Anas, Saleh, Farah Abdul-Ghani, (2011), "Using Some Information Criteria in Determining the Best Multiplier Seasonal Model," Iraqi Journal of Statistical Sciences (19).
5. Al-Kalabi, Safaa Majeed Mutasher, (2018), "Using Some Different Forecasting Methods to Analyze the Number of Patients with Malignant Tumors," University of Karbala, College of Administration and Economics, Department of Statistics.
6. Al-Marshadi, Karar Hamza Hussein Ali, (2021), "Diagnosis and Estimation of Seasonal Time Series Models with Practical Application," College of Administration and Economics, University of Karbala.
7. Al-Muntasir, Zubaydah Salim, (2019), "Using Wavelet Transformation in Diagnosis," Misurata University, College of Engineering, Department of Electrical and Electronic Engineering.
8. Al-Rahim, Yusra Faisal, Suleiman, Ahmed Mohammed, (2012), "Audio Signal Purification Using Wavelet Transformation," Al-Rafidain Journal of Computer Science and Mathematics, Volume (9), Issue (2).
9. Hassan Raad Fadel, Tarad, Alaa Jaber, (2019), "Using the Wavelet Transformation and Difference Methods to Estimate a Semi-Parametric Model," Journal of Management and Economics, 2019, Issue 42.
10. Heyam Hayawi, Muzahem Al-Hashimi, Mohammed Alawjar.(2025),” Machine learning methods for modelling and predicting dust storms in Iraq”, STATISTICS, OPTIMIZATION AND INFORMATION COMPUTING, Vol.13(3), pp 1063–1075.
11. DOI:10.19139/soic-2310-5070-2122 http://www.iapress.org/index.php/soic/article/view/2122/1163
12. Heyam A. Hayawi, Shakar Maghdid Azeez, Sawen Othman Babakr and Taha Hussein Ali ,(2025),” ARX Time Series Model Analysis with Wavelets Shrinkage (Simulation Study)”, Pak. J. Statist. Vol. 41(2), 103-116.
https://www.pakjs.com/wp-content/uploads/2025/04/PJS-41201.pdf
13. Jaloul, Sharara, Asmahan, and Baqbaq Laili, (2021), "A Study of Wavelet Analysis of the Relationship between Oil Prices and Inflation in Algeria," Journal of Knowledge Groups, Volume (7), Issue (1).
14. Kadilar and Erdemir, (2003), "Modification of The Akaike Information Criterion to Account for seasonal Effects", Journal of Statistical Computation and Simulation, Vol. 73(2), PP. 135-143.
15. MAHMOUD, GH. (2010), "An Improvement single Exponential smoothing Method for Forecasting in Time Series", Iraqi Journal of statistical sciences, vol.10, Issue 18, 259-272.
16. Mahmoud, Rania Fikri, Ibrahim, Sahar Abdul Salam, (2022), "Using Exponential Smoothing Models in Predicting Wheat and Bean Crop Production," Arab Journal of Agricultural Sciences, Arab League Educational, Cultural and Scientific Organization.
17. Muhammad, Abdul Rahman Jassim, (2014), "Comparing Some Methods for Determining the Rank and Estimating the Parameters of the ARX Model with a Practical Application on the Exchange Rate of the Iraqi Dinar," Master's Thesis in Statistics, College of Administration and Economics, University of Baghdad.
18. Muzahem M. Al-Hashimi, Heyam A. Hayawi,(2023),” Nonlinear Model for Precipitation Forecasting in Northern Iraq using Machine Learning Algorithms”, International Journal of Mathematics and Computer Science 19 (1),171-179.
https://future-in-tech.net/19.1/R-Al-Hashimi.pdf
19. Muzahem M. Al-Hashimi, Heyam A. Hayawi, Mowafaq Al-Kassab,(2023)”A Comparative Study of Traditional Methods and Hybridization for Predicting Non-Stationary Sunspot Time Series”, International Journal of Mathematics and Computer Science 19 (1), 195–203.https://future-in-tech.net/19.1/R-MuzahemAl-Hashimi.pdf
20. Muzahem Al-Hashimi , Heyam Hayawi, Mohammed Alawjar.(2025),” Ensemble Method for Intervention Analysis to Predict the Water Resources of the Tigris River”, STATISTICS, OPTIMIZATION AND INFORMATION COMPUTING, Vol. 14, July 2025, pp144–161.
DOI: 10.19139/soic-2310-5070-2413
http://www.iapress.org/index.php/soic/article/view/2413/1307
21. Nassar, Hanaa Mohamed Mahmoud, (2023), "Forecasting Time Series Using the ARIMA-SVR Hybrid Model Based on Discrete Wavelet Transformation", Faculty of Commerce for Girls - Al-Azhar University.
22. Sarah K. Bleiler, (2008), "Orthogonal Filters and the Implications of wrapping on Discrete wavelet Transforms", Department of Mathematics, College of Arts and Sciences, university of South Florida.
23. Youssef, Bazin, Tawfiq, Tabbakh, (2022), "Comparison between Exponential Smoothing Models and the Box and Jenkins Methodology in Sales Forecasting - An Applied Study of NAFTAL Ghardaia Company", University of Ghardaia / Faculty of Economics, Management and Business Sciences/ Department of Economics.Hurvich.C., M. and Tsai, chi, (1989). Regression and Time Series Model Selection in small samples", Biometrika, 76, PP.297-307.