Abstract
This paper examines the efficacy of the least absolute shrinkage and selection operator (Lasso) and Ridge algorithms in improving the volatility forecasting of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models with exogenous covariates. Our study proposes a novel parameter estimation approach by combining a quasi-maximum-likelihood estimator (QMLE) with the Lasso and Ridge regularization methods. The other objective is to identify the most critical predictors that can enhance the volatility forecasting performance of various GARCH models. To demonstrate the effectiveness of our proposed algorithms, we conduct an empirical analysis of the US stock market. Our results indicate that by imposing a specific constraint on the penalty parameters, the Lasso and Ridge estimators can significantly enhance the volatility forecasting performance of different GARCH-type models.
Supported by Chiang Mai University.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Albu, L.L., Lupu, R., Călin, A.C.: Stock market asymmetric volatility and macroeconomic dynamics in Central and Eastern Europe. Procedia Econ. Finan. 22, 560–567 (2015)
Arouri, M., Estay, C., Rault, C., Roubaud, D.: Economic policy uncertainty and stock markets: long-run evidence from the US. Financ. Res. Lett. 18, 136–141 (2016)
Bahloul, W., Gupta, R.: Impact of macroeconomic news surprises and uncertainty for major economies on returns and volatility of oil futures. Int. Econ. 156, 247–253 (2018)
Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J. Econom. 31(3), 307–327 (1986)
Byun, S.J., Cho, H.: Forecasting carbon futures volatility using GARCH models with energy volatilities. Energy Econ. 40, 207–221 (2013)
Dittmann, I., Granger, C.W.: Properties of nonlinear transformations of fractionally integrated processes. J. Econom. 110(2), 113–133 (2002)
Glosten, L.R., Jagannathan, R., Runkle, D.E.: On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Financ. 48(5), 1779–1801 (1993)
Poon, S.H., Granger, C.W.: Forecasting volatility in financial markets: a review. J. Econ. Lit. 41(2), 478–539 (2003)
Hammoudeh, S., Dibooglu, S., Aleisa, E.: Relationships among US oil prices and oil industry equity indices. Int. Rev. Econ. Financ. 13(4), 427–453 (2004)
Hammoudeh, S., Yuan, Y.: Metal volatility in presence of oil and interest rate shocks. Energy Econ. 30(2), 606–620 (2008)
Han, H., Kristensen, D.: Asymptotic theory for the QMLE in GARCH-X models with stationary and nonstationary covariates. J. Bus. Econ. Stat. 32(3), 416–429 (2014)
Liao, R., Yamaka, W., Sriboonchitta, S.: Exchange rate volatility forecasting by hybrid neural network Markov switching Beta-t-EGARCH. IEEE Access 8, 207563–207574 (2020)
Maneejuk, P., Yamaka, W.: Significance test for linear regression: how to test without P-values? J. Appl. Stat. 48(5), 827–845 (2021)
McDonald, G.C.: Ridge regression. Wiley Interdiscip. Rev. Comput. Stat. 1(1), 93–100 (2009)
Medeiros, M.C., Mendes, E.F.: Adaptive LASSO estimation for ARDL models with GARCH innovations. Economet. Rev. 36(6–9), 622–637 (2017)
Narayan, P.K., Narayan, S.: Modelling oil price volatility. Energy Policy 35(12), 6549–6553 (2007)
Nelson, D.B.: Conditional heteroskedasticity in asset returns: a new approach. Econom. J. Econ. Soc. 59, 347–370 (1991)
Roubaud, D., Arouri, M.: Oil prices, exchange rates and stock markets under uncertainty and regime-switching. Finan. Res. Lett. 27, 28–33 (2018)
Sadorsky, P.: Modeling and forecasting petroleum futures volatility. Energy Econ. 28(4), 467–488 (2006)
Tully, E., Lucey, B.M.: A power GARCH examination of the gold market. Res. Int. Bus. Financ. 21(2), 316–325 (2007)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Stat Methodol. 58(1), 267–288 (1996)
Xu, Q., Bo, Z., Jiang, C., Liu, Y.: Does Google search index really help predicting stock market volatility? Evidence from a modified mixed data sampling model on volatility. Knowl. Based Syst. 166, 170–185 (2019)
Yamaka, W.: Sparse estimations in kink regression model. Soft. Comput. 25, 7825–7838 (2021)
Yoon, Y.J., Lee, S., Lee, T.: Adaptive LASSO for linear regression models with ARMA-GARCH errors. Commun. Stat. Simul. Comput. 46(5), 3479–3490 (2017)
Zhou, Z., Fu, Z., Jiang, Y., Zeng, X., Lin, L.: Can economic policy uncertainty predict exchange rate volatility? New evidence from the GARCH-MIDAS model. Financ. Res. Lett. 34, 101258 (2020)
Acknowledgements
This research work was partially supported by Chiang Mai University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Yamaka, W., Maneejuk, P., Thongkairat, S. (2023). Lasso and Ridge for GARCH-X Models. In: Huynh, VN., Le, B., Honda, K., Inuiguchi, M., Kohda, Y. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2023. Lecture Notes in Computer Science(), vol 14375. Springer, Cham. https://doi.org/10.1007/978-3-031-46775-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-031-46775-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-46774-5
Online ISBN: 978-3-031-46775-2
eBook Packages: Computer ScienceComputer Science (R0)