THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES

Maryam Jumaa Mousa; Munaf Yousif Hmood

THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES

Abstract

The essence of this article is that it has developed the Quantile GARCH-Distributed Lag (QGDL) model as a recent and superior model to the QARDL model. Although the QARDL model is only able to deal with asymmetric relationships in the quartiles and the assumption of homoscedasticity, our model is able to address this weakness using the simultaneous volatility clustering. The model that we propose is the most effective and correct in estimating the parameters in cases of changing conditional variance with time, which makes it the most appropriate measure to use in the analysis of extremely volatile financial time series.

Keywords

References

[1] Aldawsari, S. H., Tan, W. S., Elsherazy, T. A., Chang, B. H., Alzoubi, H. M., & Ognjanovic, I. (2024). A Quantile Dependence among Exchange Rate, Stock Prices and Oil Prices: An Empirical Evidence from India. Annals of Financial Economics, 19(03), 2450010, https://doi.org/10.1142/S2010495224500106
[2] Amagbo, R., Geman, H., & Peri, I. (2025). The Impact of Geopolitical Risk on the Volatility of Wheat Futures: A Quantile ARDL Approach. Commodities, 4(4), 28. https://doi.org/10.3390/commodities4040028
[3] Apergis, N. (2022). Evaluating tail risks for the US economic policy uncertainty. International Journal of Finance & Economics, 27(4), 3971-3989. https://doi.org/10.1002/ijfe.2354
[4] Bollerslev, T., Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11(2), 143–172. https://doi.org/10.1080/07474939208800229
[5] Cho, J. S., Kim, S. & Shin, Y. (2015). Quantile autoregressive distributed lag model with an application to pricing-to-market. Econometric Reviews, 34(3), 281–320. https://doi.org/10.1080/07474938.2012.744950
[6] Knight, K. (1998). Limiting distributions for L1 regression estimators under general conditions. Annals of Statistics, 26(2), 755–770.
[7] Koenker, R., Hallock, K. F. (2001). Quantile regression. Journal of economic perspectives, 15(4), 143-156. DOI: 10.1257/jep.15.4.143
[8] Lee, C. C., Yahya, F. ,Razzaq, A. (2022). The asymmetric effect of temperature, exchange rate, metals, and investor sentiments on solar stock price performance in China: evidence from QARDL approach. Environmental Science and Pollution Research, 29(52), 78588-78602.

[9] Mensi, W., Shahzad, S. J. H., Hammoudeh, S., Hkiri, B., & Al Yahyaee, K. H. (2019). Long-run relationships between US financial credit markets and risk factors: Evidence from the quantile ARDL approach. Finance Research Letters, 29, 101-110. https://doi.org/10.1016/j.frl.2019.03.007
[10] Newey, W. K. (1991). Uniform convergence in probability and stochastic equicontinuity. Econometrica, 59(4), 1161–1167. https://doi.org/10.2307/2938179
[11] Nor, M. I., Masron, T. A., & Alabdullah, T. T. Y. (2020). Macroeconomic fundamentals and the exchange rate volatility: empirical evidence from Somalia. Sage Open, 10(1), 2158244019898841.
[12] Olasehinde-Williams, G., Omotosho, R., & Bekun, F. V. (2024). Interest rate volatility and economic growth in Nigeria: New insight from the quantile autoregressive distributed lag (QARDL) model. Journal of the Knowledge Economy, 15(4), 20172-20195.
[13] Patrocinio, P. F., Reisen, V. A., Bondon, P., Monte, E. Z., & Danilevicz, I. M. (2024). M-quantile estimation for GARCH models. Computational Economics, 63(6), 2175–2192. https://doi.org/10.1007/s10614-023-10398-z.
[14] Ren, X., An, Y., & Jin, C. (2023). The asymmetric effect of geopolitical risk on China’s crude oil prices: new evidence from a QARDL approach. Finance Research Letters, 53, 103637. https://doi.org/10.1016/j.frl.2023.103637
[15] Sahin, G., & Sahin, A. (2023). An Empirical Examination of Asymmetry on Exchange Rate Spread Using the Quantile Autoregressive Distributed Lag (QARDL) Model. Journal of Risk and Financial Management, 16(1), 38. https://doi.org/10.3390/jrfm16010038 .
[16] Shahani, R., Maurya, Y. Do green Indices Show co-integrating Relation with Crude and Broader Market Indices during Shocks: Empirical Evidence from India using Quantile ARDL Approach. In INTERNATIONAL MANAGEMENT PERSPECTIVE CONFERENCE (p. 248).
[17] Shahzad, S. J. H., Hurley, D., & Ferrer, R. (2021). US stock prices and macroeconomic fundamentals: Fresh evidence using the quantile ARDL approach. International Journal of Finance & Economics, 26(3), 3569-3587. https://doi.org/10.1002/ijfe.1976
[18] Singh, K., Dhariwal, K. (2026). Impact of Distinct Uncertainty Types on the Returns of G20 Stock Indices Across Different Market Conditions: Evidence from Two-step Panel QARDL Approach. Journal of International Commerce, Economics and Policy, 17(02), 2550032.
[19] Sokhanvar, A., & Bouri, E. (2023). Commodity price shocks related to the war in Ukraine and exchange rates of commodity exporters and importers. Borsa Istanbul Review, 23(1), 44-54. https://doi.org/10.1016/j.bir.2022.09.001
[20] Tabash, M. I., Sheikh, U. A., Selmi, R., Al-Faryan, M. A. S., Hammoudeh, S. (2025). The asymmetric effects of European carbon emission trading system on European stock market returns: The moderating role of oil price uncertainty. International Review of Financial Analysis, 104, 104324.
[21] Uche, Effiom, L. (2021). Fighting capital flight in Nigeria: have we considered global uncertainties and exchange rate volatilities? Fresh insights via quantile ARDL model. SN Business and Economics, 1(6), 73.
[22] Umoru, D., Ekeoba, A. A., & Igbinovia, B. (2024). Dynamic adjustment between energy demand and productivity growth with exchange rate devaluation as a moderating variable. Amity Journal of Management, 12(2), 17-33.
[23] Vartholomatou, K., Pendaraki, K., & Tsagkanos, A. (2021). Corporate bonds, exchange rates and business strategy. International Journal of Banking, Accounting and Finance, 12(2), 97-117. https://doi.org/10.1504/IJBAAF.2021.114473
[24] Zhu, Q., Li, G., & Xiao, Z. (2021). Quantile estimation of regression models with GARCH-X errors. Statistica Sinica, 31(3), 1261–1284. https://doi.org/10.5705/ss.202019.0003.

Details

Primary Language

English

Subjects

Statistics (Other)

Journal Section

Research Article

Authors

Maryam Jumaa Mousa ^* This is me
0009-0003-9138-7967
Iraq

Munaf Yousif Hmood
0000-0002-1134-9078
Iraq

Publication Date

September 7, 2026

Submission Date

September 26, 2025

Acceptance Date

April 28, 2026

Published in Issue

Year 2026 Volume: 16 Number: 9

IZ

https://izlik.org/JA44RP57LE

Cite

RIS / Bibtex

APA

Jumaa Mousa, M., & Hmood, M. Y. (2026). THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES. TWMS Journal of Applied and Engineering Mathematics, 16(9), 1118-1134. https://izlik.org/JA44RP57LE

AMA

1.Jumaa Mousa M, Hmood MY. THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES. JAEM. 2026;16(9):1118-1134. https://izlik.org/JA44RP57LE

Chicago

Jumaa Mousa, Maryam, and Munaf Yousif Hmood. 2026. “THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES”. TWMS Journal of Applied and Engineering Mathematics 16 (9): 1118-34. https://izlik.org/JA44RP57LE.

EndNote

Jumaa Mousa M, Hmood MY (September 1, 2026) THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES. TWMS Journal of Applied and Engineering Mathematics 16 9 1118–1134.

IEEE

[1]M. Jumaa Mousa and M. Y. Hmood, “THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES”, JAEM, vol. 16, no. 9, pp. 1118–1134, Sept. 2026, [Online]. Available: https://izlik.org/JA44RP57LE

ISNAD

Jumaa Mousa, Maryam - Hmood, Munaf Yousif. “THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES”. TWMS Journal of Applied and Engineering Mathematics 16/9 (September 1, 2026): 1118-1134. https://izlik.org/JA44RP57LE.

JAMA

1.Jumaa Mousa M, Hmood MY. THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES. JAEM. 2026;16:1118–1134.

MLA

Jumaa Mousa, Maryam, and Munaf Yousif Hmood. “THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 9, Sept. 2026, pp. 1118-34, https://izlik.org/JA44RP57LE.

Vancouver

1.Maryam Jumaa Mousa, Munaf Yousif Hmood. THE QUANTILE GARCH-DISTRIBUTED LAG (QGDL) FRAMEWORK: A UNIFIED MODEL FOR HIGH-VOLATILITY TIME SERIES. JAEM [Internet]. 2026 Sep. 1;16(9):1118-34. Available from: https://izlik.org/JA44RP57LE