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A simulation study on the Markov regime-switching zero-drift GARCH model

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Abstract

A Zero-drift GARCH (ZD-GARCH) model is recently proposed to study conditional and unconditional heteroskedasticity together. Despite its attractive statistical properties, our research demonstrates that the stability test based on this model fails when structural changes are present. To overcome this issue, we allow the Markov regime-switching (MRS) feature within the ZD-GARCH framework and propose an MRS-ZD-GARCH model. A revised stability estimator is further derived. The effectiveness of our proposed approach to test the stability with and without structural changes is evidenced via simulation studies. Using the empirical data of the S&P 500, NASDAQ and Apple returns, we show that the new model can also outperform the ZD-GARCH model in practice and provide more informative results. Therefore, the MRS-ZD-GARCH model could be a widely useful tool to study the stability of financial data and help address risk management issues in other contexts.

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Notes

  1. In this paper, we focus on \(|y_t|^2\), which is the \(r=2\) case described in Li et al. (2018). Other common choices are also tested and lead to robust results, which are available upon request.

  2. Assume that the proportions of low- and high-persistence regimes are both 50%.

  3. We have also considered various settings with more than two groups of distinct state-dependent variables. Results of those additional scenarios are robust and available upon request.

  4. It can be shown that both state-dependent \(\gamma _{0}\) are close to 0. Thus, return sequences is essentially switching between two stable processes.

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Acknowledgements

The authors would also like to thank Tingting Cheng, Tao Zou and participants at the Macquarie University seminar for their helpful comments and suggestions on earlier versions of this paper. We particularly thank the Editors and two anonymous referees for providing valuable and insightful comments on earlier drafts. The usual disclaimer applies.

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  1. Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW, 2109, Australia

    Yanlin Shi

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Shi, Y. A simulation study on the Markov regime-switching zero-drift GARCH model. Ann Oper Res 330, 1–20 (2023). https://doi.org/10.1007/s10479-020-03832-0

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