A Markov regime switching approach to estimating the volatility of Johannesburg Stock Exchange (JSE) returns
-
DOIhttp://dx.doi.org/10.21511/imfi.16(1).2019.17
-
Article InfoVolume 16 2019, Issue #1, pp. 215-225
- Cited by
- 1984 Views
-
377 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
The study used the Markov regime switching model to investigate the presence of regimes in the volatility dynamics of the returns of JSE All-Share Index (ALSI). Volatility regimes are as a result of sudden changes in the underlying economy generating the market returns. In all, twelve candidate models were fitted to the data. Estimates from the regime switching model were compared to the industry standard non-switching GARCH (1,1) using the Deviance Information Criteria (DIC). The results show that the two-regime switching EGARCH model with skewed Student t innovations describes better the return of the JSE Index. Additionally, we backtest the model results in order to confirm our findings that the two-regime switching EGARCH is the best of the models for the sample period.
- Keywords
-
JEL Classification (Paper profile tab)G15, G17
-
References60
-
Tables4
-
Figures5
-
- Figure 1. Trend of JSE All-Share Index over the period January 2003 – December 2017
- Figure 2. The log returns of JSE All-Share Index over the period January 2003 – December 2017
- Figure 3. Histogram and the Q-Q plots of the returns
- Figure 4. Trace of MCMC samples for the parameters of the two-regime EGARCH model with skewed Student t innovations
- Figure 5. The smoothed probabilities of the high volatility regime
-
- Table 1. Summary statistics of the returns
- Table 2. Deviance Information Criteria of the models
- Table 3. Two-regime EGARCH with skewed Student t innovations
- Table 4. Results of the backtest
-
- Ardia, D., Bluteau, K., Boudt, K., Catania, L., & Trottier, D. (2016). Markov-Switching GARCH Models in R: The MSGARCH Package. Journal of Statistical Software, Forthcoming.
- Babikir, A., Gupta, R., Mwabutwa, C., & Owusu-Sekyere, E. (2012). Structural breaks and GARCH models of stock return volatility: The case of South Africa. Economic Modelling, 29(6), 2435-2443.
- Barndorff‐Nielsen, O. E., & Shephard, N. (2002). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17(5), 457-477.
- Bekaert, G., Erb, C. B., Harvey, C. R., & Viskanta, T. E. (1998). The behavior of emerging market returns. Emerging Market Capital Flows, 107-173.
- Bentes, S. (2014). Measuring persistence in stock market volatility using the FIGARCH approach. Physica A: Statistical Mechanics and its Applications, 408, 190-197.
- Billio, M., & Cavicchioli, M. (2017). Markov Switching GARCH Models: Filtering, Approximations and Duality. In M. Corazza, F. Legros, C. Perna & M. Sibillo (Eds.), Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 59-72). Cham: Springer.
- Black, F. (1976). Studies of Stock Price Volatility Changes. In Proceedings of the 1976 Meeting of the Business and Economic Statistics Section (pp. 177-181). Washington DC: American Statistical Association.
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
- Brooks, R. D., Davidson, S., & Faff, R. W. (1997). An examination of the effects of major political change on stock market volatility: the South African experience. Journal of International Financial Markets, Institutions and Money, 7(3), 255-275.
- Calvet, L. E., & Fisher, A. J. (2004). How to forecast long-run volatility: regime switching and the estimation of multifractal processes. Journal of Financial Econometrics, 2(1), 49-83.
- Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The econometrics of Financial Markets. Princeton University Press.
- Catania, L., Ardia, D., Bluteau, K., Boudt, K., & Trottier, D. A. (2018). Brian PetMarkov-Switching GARCH Models in R: The MSGARCH Package. Version 2.3.
- Chiarella, C., He, X. Z., Huang, W., & Zheng, H. (2012). Estimating behavioural heterogeneity under regime switching. Journal of Economic Behavior & Organization, 83(3), 446- 460.
- Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841-862.
- Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1(2), 223-236.
- Corsi, F., Mittnik, S., Pigorsch, C., & Pigorsch, U. (2008). The volatility of realized volatility. Econometric Reviews, 27(1-3), 46-78.
- Cosslett, S. R., & Lee, L. F. (1985). Serial correlation in latent discrete variable models. Journal of Econometrics, 27(1), 79-97.
- Csorgo, S., & Faraway, J. (1996). The exact and asymptotic distributions of Cramer-von Mises statistics. Journal of the Royal Statistical Society, Series B, 58(1), 221-234.
- Eichengreen, B., & Tong, H. (2003). Stock market volatility and monetary policy: what the historical record shows. Asset Prices and Monetary Policy, 108-142.
- Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 50(4), 987-1007.
- Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics, 22(4), 367-381.
- Engle, R. F., & Patton, A. J. (2007). What good is a volatility model? In Forecasting Volatility in the Financial Markets (3rd ed.) (pp. 47-63). Elsevier.
- Engle, R., & Rangel, J. G. (2008). The Spline GARCH Model for Low-Frequency Volatility and its Global Macroeconomic Causes. Review of Financial Studies, 21(3), 1187-1222.
- Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica: Journal of the Econometric Society, 57(6), 1317-1339.
- Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On The Relation between The Expected Value and The Volatility of Nominal Excess Return on stocks. Journal of Finance, 48(5), 1779- 1801.
- Goldfeld, S. M., & Quandt, R. E. (1973). A Markov model for switching regressions. Journal of econometrics, 1(1), 3-15.
- Gray, S. (1996). Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics, 42(1), 27-62.
- Gray, S. F. (1995). An analysis of conditional regime-switching models.
- Guo, Z. F., & Cao, L. (2011). A smooth transition GARCH model with asymmetric transition phases. Proceedings of the World Congress on Engineering, 1.
- Haario, H., Saksman, E., & Tamminen, J. (1999). Adaptive proposal distribution for random walk Metropolis algorithm. Computational Statistics, 14(3), 375-396.
- Haas, M., Mittnik, S., & Paolella, M. S. (2004). A new approach to Markov-switching GARCH models. Journal of Financial Econometrics, 2(4), 493-530.
- Hamilton, J. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384.
- Hamilton, J. D. (1990). Analysis of time series subject to changes in regime. Journal of Econometrics, 45(1-2), 39-70.
- Hamilton, J. D., & Susmel, R. (1994). Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64(1-2), 307-333.
- Hansen, P. R., & Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1,1)? Journal of Applied Econometrics, 20(7), 873-889.
- Hardy, M. R. (2001). A regime-switching model of long-term stock returns. North American Actuarial Journal, 5(2), 41-53.
- Jacquier, E., & Polson, N. (2011). Bayesian methods in finance. In J. Geweke, G. Koop & H. Van Diyk (Eds.), The Oxford Handbook of Bayesian Econometrics.
- Karatzas, I., & Shreve, S. (2012). Brownian motion and stochastic calculus, 113. Springer Science & Business Media.
- Klaassen, F. (2002). Improving GARCH volatility forecasts with regime-switching GARCH. In Advances in Markov-Switching Models (pp. 223-254). Physica-Verlag HD.
- Lamoureux, C. G., & Lastrapes, W. D. (1990). Heteroskedasticity in stock return data: Volume versus GARCH effects. The Journal of Finance, 45(1), 221-229.
- Liu, X., Margaritis, D., & Wang, P. (2012). Stock market volatility and equity returns: Evidence from a two-state Markov-switching model with regressors. Journal of Empirical Finance, 19(4), 483-496.
- Lux, T. (2008). The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. Journal of Business & Economic Statistics, 26(2), 194-210.
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
- Marx, C., & Struweg, J. (2015). Stagflation and the South African equity market. Procedia Economics and Finance, 30, 531-542.
- Muller, C., & Ward, M. (2013). Style-based effects on the Johannesburg Stock Exchange: A graphical time-series approach. Investment Analysts Journal, 77, 1-16.
- Nelson, D. B. (1991). Conditional Heteroscedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.
- Niyitegeka, O., & Tewar, D. D. (2013). Volatility clustering at the Johannesburg stock exchange: Investigation and analysis. Mediterranean Journal of Social Sciences, 4(14), 621-626.
- Nwogugu, M. (2006). Further critique of GARCH/ARMA/VAR/ EVT Stochastic-Volatility models and related approaches. Applied mathematics and computation, 182(2), 1735-1748.
- Oomen, R. (2005). Properties of bias-corrected realized variance under alternative sampling schemes. Journal of Financial Econometrics, 3(4), 555-577.
- R Core Team (2018). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
- Seleteng, M., Bittencourt, M., & Van Eyden, R. (2013). Non-linearities in inflation–growth nexus in the SADC region: A panel smooth transition regression approach. Economic Modelling, 30, 149-156.
- Shephard, N., & Sheppard, K. (2010). Realising the future: forecasting with high‐frequency‐based volatility (HEAVY) models. Journal of Applied Econometrics, 25(2), 197-231.
- Song, Y. (2014). Modelling regime switching and structural breaks with an infinite hidden Markov model. Journal of Applied Econometrics, 29(5), 825-842.
- Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583-639.
- Valadkhani, A., & O’Mahony, B. (2018). Identifying structural changes and regime switching in growing and declining inbound tourism markets in Australia. Current Issues in Tourism, 21(3), 277-300.
- Vihola, M. (2012). Robust Adaptive Metropolis Algorithm with Coerced Acceptance Rate. Statistics and Computing, 22(5), 997-1008.
- Whaley, R. (2013). Trading volatility: At what cost? Journal of Portfolio Management, 40(1), 95-108.
- Yalama, A., & Celik, S. (2013). Real or spurious long memory characteristics of volatility: Empirical evidence from an emerging market. Economic Modelling, 30, 67-72.
- Zhang, J. E., & Zhu, Y. (2006). VIX futures. Journal of Futures Markets, 26(6), 521-531.
- Zhang, L., Mykland, P. A., & Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 100(472), 1394-1411.