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Long memory and regime switching in the stochastic volatility modelling

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Abstract

This paper studies the confusion between the long memory and regime switching in the second moment via the stochastic volatility (SV) methodology. An illustrative proposition is firstly presented with simulation evidence to demonstrate that spurious long memory can be caused by a Markov regime-switching SV (MRS-SV) process, when a long memory SV (LMSV) model is employed. To address this, an MRS-LMSV model is developed using a simulation-based optimization method, namely the Markov-Chain Monte Carlo algorithm. Via systematically constructed simulation studies, the proposed model can effectively distinguish between LMSV and MRS-SV processes with consistent estimators of the long-memory parameter. An empirical study of the S&P 500 daily returns is then conducted which demonstrates the superiority of the MRS-LMSV model over LMSV and MRS-SV counterparties. It is verified that significant long memory only exists in the high-volatility state. Important financial implications can be made to improve the risk management operations in practice.

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References

  • Ang, A., & Timmermann, A. (2011). Regime changes and financial markets. Technical report, National Bureau of Economic Research.

  • Ardia, D. (2009). Bayesian estimation of a Markov-switching threshold asymmetric GARCH model with student-t innovations. The Econometrics Journal, 12(1), 105–126.

    Article  Google Scholar 

  • Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30.

    Article  Google Scholar 

  • Bali, T. G., & Theodossiou, P. (2007). A conditional-SGT-VaR approach with alternative GARCH models. Annals of Operations Research, 151(1), 241–267.

    Article  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

    Article  Google Scholar 

  • Bollerslev, T. (1987). A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics, 69(3), 542–547.

    Article  Google Scholar 

  • Breidt, F. J., Crato, N., & De Lima, P. (1998). The detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83(1–2), 325–348.

    Article  Google Scholar 

  • Brockwell, A. (2007). Likelihood-based analysis of a class of generalized long-memory time series models. Journal of Time Series Analysis, 28(3), 386–407.

    Article  Google Scholar 

  • Carstensen, K., Heinrich, M., Reif, M., & Wolters, M. H. (2020). Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model: An application to the German business cycle. International Journal of Forecasting, 36, 829–850.

    Article  Google Scholar 

  • Carvalho, C. M., & Lopes, H. F. (2007). Simulation-based sequential analysis of Markov switching stochastic volatility models. Computational Statistics & Data Analysis, 51(9), 4526–4542.

    Article  Google Scholar 

  • Chib, S., Nardari, F., & Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics, 108(2), 281–316.

    Article  Google Scholar 

  • Davidson, J. (2004). Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business & Economic Statistics, 22(1), 16–29.

    Article  Google Scholar 

  • Deo, R. S., & Hurvich, C. M. (2001). On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models. Econometric Theory, 17(4), 686–710.

    Article  Google Scholar 

  • Diebold, F. X., & Inoue, A. (2001). Long memory and regime switching. Journal of Econometrics, 105(1), 131–159.

    Article  Google Scholar 

  • Diebold, F. X., & Mariano, R. S. (2002). Comparing predictive accuracy. Journal of Business & Economic Statistics, 20(1), 134–144.

    Article  Google Scholar 

  • Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of variance of United Kingdom inflation. Economerica, 50(4), 987–1007.

    Article  Google Scholar 

  • Feng, L., & Shi, Y. (2017a). Fractionally integrated GARCH model with tempered stable distribution: A simulation study. Journal of Applied Statistics, 44(16), 2837–2857.

    Article  Google Scholar 

  • Feng, L., & Shi, Y. (2017b). A simulation study on the distributions of disturbances in the GARCH model. Cogent Economics & Finance, 5(1), 1355503.

    Article  Google Scholar 

  • Franses, P., & van Dijk, D. (1996). Forecasting stock volatility using (non-linear) GARCH models. Journal of Forecasting, 15, 229–235.

    Article  Google Scholar 

  • French, K. R., Schwert, G., & Stambaugh, R. F. (1987). Expected stock returns and volatility. Journal of Financial Economics, 19(1), 3–29.

    Article  Google Scholar 

  • Garman, M. B., & Klass, M. (1980). On the estimation of security price volatilities from. The Journal of Business, 53(1), 67–78.

    Article  Google Scholar 

  • Gerencsér, L., & Orlovits, Z. (2012). Real time estimation of stochastic volatility processes. Annals of Operations Research, 200(1), 223–246.

    Article  Google Scholar 

  • Gray, S. F. (1996). Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics, 42(1), 27–62.

    Article  Google Scholar 

  • Guidolin, M., & Timmermann, A. (2006). An econometric model of nonlinear dynamics in the joint distribution of stock and bond returns. Journal of Applied Econometrics, 21(1), 1–22.

    Article  Google Scholar 

  • Haas, M. (2009). Value-at-risk via mixture distributions reconsidered. Applied Mathematics and Computation, 215(6), 2103–2119.

    Article  Google Scholar 

  • Haas, M., Mittnik, S., & Paolella, M. S. (2004). A new approach to Markov-switching GARCH models. Journal of Financial Econometrics, 2(4), 493–530.

    Article  Google Scholar 

  • Haldrup, N., & Nielsen, M. Ø. (2006). A regime switching long memory model for electricity prices. Journal of Econometrics, 135(1), 349–376.

    Article  Google Scholar 

  • Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2), 357–384.

    Article  Google Scholar 

  • Harvey, A., Ruiz, E., & Shephard, N. (1994). Multivariate stochastic variance models. The Review of Economic Studies, 61(2), 247–264.

    Article  Google Scholar 

  • Harvey, A. C., & Shephard, N. (1996). Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business & Economic Statistics, 14(4), 429–434.

    Google Scholar 

  • Henneke, J. S., Rachev, S. T., Fabozzi, F. J., & Nikolov, M. (2011). MCMC-based estimation of Markov switching ARMA-GARCH models. Applied Economics, 43(3), 259–271.

    Article  Google Scholar 

  • Hillebrand, E. (2005). Neglecting parameter changes in GARCH models. Journal of Econometrics, 129(1–2), 121–138.

    Article  Google Scholar 

  • Ho, K. Y., & Shi, Y. (2020). Discussions on the spurious hyperbolic memory in the conditional variance and a new model. Journal of Empirical Finance, 55, 83–103.

    Article  Google Scholar 

  • Ho, K. Y., Shi, Y., & Zhang, Z. (2016). It takes two to tango: A regime-switching analysis of the correlation dynamics between the mainland Chinese and Hong Kong stock markets. Scottish Journal of Political Economy, 63(1), 41–65.

    Article  Google Scholar 

  • Jacquier, E., Polson, N. G., & Rossi, P. E. (2002). Bayesian analysis of stochastic volatility models. Journal of Business & Economic Statistics, 20(1), 69–87.

    Article  Google Scholar 

  • Jawadi, F., Louhichi, W., Cheffou, A. I., & Ameur, H. B. (2018). Modeling time-varying beta in a sustainable stock market with a three-regime threshold GARCH model. Annals of Operations Research, 281, 275–295.

    Article  Google Scholar 

  • Klaassen, F. (2002). Improving GARCH volatility forecasts with regime-switching GARCH. Empirical Economics, 27(2), 363–394.

    Article  Google Scholar 

  • Krämer, W. (2008). Long memory with Markov-switching GARCH. Economics Letters, 99(2), 390–392.

    Article  Google Scholar 

  • Lamoureux, C. G., & Lastrapes, W. D. (1990). Heteroskedasticity in stock return data: volume versus GARCH effects. Journal of Finance, 45(1), 221–229.

    Article  Google Scholar 

  • Lu, X. F., Lai, K. K., & Liang, L. (2014). Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model. Annals of Operations Research, 219(1), 333–357.

    Article  Google Scholar 

  • Marcucci, J. (2005). Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics & Econometrics,. https://doi.org/10.2202/1558-3708.1145.

    Article  Google Scholar 

  • Martens, M., De Pooter, M., Van Dijk, D. (2004). Modeling and forecasting S&P 500 volatility: Long memory, structural breaks and nonlinearity, tinbergen Institute Discussion Paper.

  • Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45(1–2), 239–265.

    Article  Google Scholar 

  • Mikosch, T., & Starica, C. (2004). Changes of structure in financial time series and the GARCH model. REVSTAT, 2(1), 41–73.

    Google Scholar 

  • Moore, T., & Wang, P. (2007). Volatility in stock returns for new EU member states: Markov regime switching model. International Review of Financial Analysis, 16(3), 282–292.

    Article  Google Scholar 

  • Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., & Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Physical Review E, 49(2), 1685.

    Article  Google Scholar 

  • Perron, P., & Qu, Z. (2010). Long-memory and level shifts in the volatility of stock market return indices. Journal of Business & Economic Statistics, 28(2), 275–290.

    Article  Google Scholar 

  • Ross, G. J., et al. (2015). Parametric and nonparametric sequential change detection in r: The CPM package. Journal of Statistical Software, 66(3), 1–20.

    Article  Google Scholar 

  • Shi, Y., & Feng, L. (2016). A discussion on the innovation distribution of the Markov regime-switching GARCH model. Economic Modelling, 53, 278–288.

    Article  Google Scholar 

  • Shi, Y., & Ho, K. Y. (2015). Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model. Journal of Banking & Finance, 61, S189–S204.

    Article  Google Scholar 

  • Smith, D. R. (2002). Markov-switching and stochastic volatility diffusion models of short-term interest rates. Journal of Business & Economic Statistics, 20(2), 183–197.

    Article  Google Scholar 

  • Tsay, W. J., & Härdle, W. K. (2009). A generalized ARFIMA process with Markov-switching fractional differencing parameter. Journal of Statistical Computation and Simulation, 79(5), 731–745.

    Article  Google Scholar 

  • Vo, M. T. (2009). Regime-switching stochastic volatility: Evidence from the crude oil market. Energy Economics, 31(5), 779–788.

    Article  Google Scholar 

  • Zheng, K., Li, Y., & Xu, W. (2019). Regime switching model estimation: Spectral clustering hidden Markov model. Annals of Operations Research,. https://doi.org/10.1007/s10479-019-03140-2.

    Article  Google Scholar 

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Acknowledgements

The authors would also like to thank the Macquarie University for the research support. We particularly thank the Guest Editor (Hasan Hüseyin Turan) 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. Long memory and regime switching in the stochastic volatility modelling. Ann Oper Res 320, 999–1020 (2023). https://doi.org/10.1007/s10479-020-03841-z

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