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Averaging Heterogeneous Autoregression Models with Heteroskedastic Errors: Theory and an Application to Cryptocurrency Volatility Forecasting

Ziwen Gao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China; and University of Chinese Academy of Sciences, China)

Steven F. Lehrer (Queen’s University, Canada; and NBER, USA)

Tian Xie (College of Business, Shanghai University of Finance and Economics, China)

Xinyu Zhang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China)

Essays in Honor of Subal Kumbhakar

ISBN: 978-1-83797-874-8, eISBN: 978-1-83797-873-1

Publication date: 5 April 2024

Abstract

Motivated by empirical features that characterize cryptocurrency volatility data, the authors develop a forecasting strategy that can account for both model uncertainty and heteroskedasticity of unknown form. The theoretical investigation establishes the asymptotic optimality of the proposed heteroskedastic model averaging heterogeneous autoregressive (H-MAHAR) estimator under mild conditions. The authors additionally examine the convergence rate of the estimated weights of the proposed H-MAHAR estimator. This analysis sheds new light on the asymptotic properties of the least squares model averaging estimator under alternative complicated data generating processes (DGPs). To examine the performance of the H-MAHAR estimator, the authors conduct an out-of-sample forecasting application involving 22 different cryptocurrency assets. The results emphasize the importance of accounting for both model uncertainty and heteroskedasticity in practice.

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Acknowledgements

Acknowledgments

We are very grateful to the editors and the referees for their insightful comments that greatly improved our chapter. Lehrer wishes to thank SSHRC for research support. Xie’s research is supported by the Natural Science Foundation of China (No. 72173075), the Shanghai Research Center for Data Science and Decision Technology, and the Fundamental Research Funds for the Central Universities. Zhang gratefully acknowledges research support from the National Natural Science Foundation of China (71925007, 72091212, and 12288201) and the CAS Project for Young Scientists in Basic Research (YSBR-008).

Citation

Gao, Z., Lehrer, S.F., Xie, T. and Zhang, X. (2024), "Averaging Heterogeneous Autoregression Models with Heteroskedastic Errors: Theory and an Application to Cryptocurrency Volatility Forecasting", Parmeter, C.F., Tsionas, M.G. and Wang, H.-J. (Ed.) Essays in Honor of Subal Kumbhakar (Advances in Econometrics, Vol. 46), Emerald Publishing Limited, Leeds, pp. 99-131. https://doi.org/10.1108/S0731-905320240000046006

Publisher

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Emerald Publishing Limited