A simulation study on the Markov regime-switching zero-drift GARCH model
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A simulation study on the Markov regime-switching zero-drift GARCH model Yanlin Shi1 Accepted: 13 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Volatility modelling · Zero-drift GARCH · Regime switching · Heteroskedasticity
1 Introduction In the past few decades, GARCH model developed on the seminal works of Engle (1982) and Bollerslev (1986) has become a standard approach to study the volatility of time series in various fields of economics and finance [see, for example, Bali and Theodossiou (2007), Gerencsér and Orlovits (2012), Ho et al. (2013), Lu et al. (2014), Shi et al. (2016), Jawadi et al. (2018), among others]. The popularity of GARCH model is particularly due to its ability to capture characteristics of finance data like time varying heteroskedasticity and volatility clustering (French et al. 1987; Franses and van Dijk 1996; Marcucci 2005; Ho et al. 2016; Feng and Shi 2017b). However, despite the extensively investigated conditional volatility, less attempts have been made in the literature to capture conditional and unconditional heteroskedasticity together parametrically.
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Yanlin Shi [email protected] Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW 2109, Australia
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Annals of Operations Research
To fill this gap, a recent study by Li et al. (2018) propose a Zero-drift GARCH (ZDGARCH) model, by removing the drift term in the conditional variance equation of the classic GARCH model. This new model can nest the famous exponentially weighted moving average (EWMA) model developed by the RiskMetrics. Based on the EWMA model, companies like J.P. Morgan estimate the daily volatility of financial equities. In particular, the ZDGARCH process is always non-stationary, which is suitable for financial analysis with a long time span. In such cases, structural changes are inevitable for reasons like the potential presence of policy changes and other shocks in the real economy [see, for example, Ang and Timmermann (2011)]. Therefore, the unconditional variance can be
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