Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model
This paper presents a new multivariate GARCH model with time-varying conditional correlation structure which is a generalization of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model, which we name Hierarchical RSDC, is building with the hierarchical generalization of the hidden Markov model introduced by Fine et al. (1998). This can be viewed graphically as a tree-structure with different types of states. The first are called production states and they can emit observations, as in the classical Markov-Switching approach. The second are called abstract states. They can't emit observations but establish vertical and horizontal probabilities that define the dynamic of the hidden hierarchical structure. The main gain of this approach compared to the classical Markov-Switching model is to increase the granularity of the regimes. Our model is also compared to the new Double Smooth Transition Conditional Correlation GARCH model (DSTCC), a STAR approach for dynamic correlations proposed by Silvennoinen and Teräsvirta (2007). The reason is that under certain assumptions, the DSTCC and our model represent two classical competing approaches to modeling regime switching. We also perform Monte-Carlo simulations and we apply the model to two empirical applications studying the conditional correlations of selected stock returns. Results show that the Hierarchical RSDC provides a good measure of the correlations and also has an interesting explanatory power.
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- Nam, Kiseok & Pyun, Chong Soo & Arize, Augustine C., 2002. "Asymmetric mean-reversion and contrarian profits: ANST-GARCH approach," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 563-588, December.
- Kim, Chang-Jin, 1994.
"Dynamic linear models with Markov-switching,"
Journal of Econometrics,
Elsevier, vol. 60(1-2), pages 1-22.
- Smith, Daniel R, 2002. "Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 183-97, April.
- Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
- Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2002.
"Mixed normal conditional heteroskedasticity,"
CFS Working Paper Series
2002/10, Center for Financial Studies (CFS).
- Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
- Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany.
- Sheppard, Kevin & Cappiello, Lorenzo & Engle, Robert F., 2003.
"Asymmetric dynamics in the correlations of global equity and bond returns,"
Working Paper Series
0204, European Central Bank.
- Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
- Christina Amado & Timo Teräsvirta, 2008.
"Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure,"
CREATES Research Papers
2008-08, Department of Economics and Business Economics, Aarhus University.
- Cristina Amado & Timo Teräsvirta, 2008. "Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure," NIPE Working Papers 03/2008, NIPE - Universidade do Minho.
- Amado, Cristina & Teräsvirta, Timo, 2008. "Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure," SSE/EFI Working Paper Series in Economics and Finance 691, Stockholm School of Economics.
- Denis Pelletier, 2004.
"Regime Switching for Dynamic Correlations,"
Econometric Society 2004 North American Summer Meetings
230, Econometric Society.
- Berben, Robert-Paul & Jansen, W. Jos, 2005.
"Comovement in international equity markets: A sectoral view,"
Journal of International Money and Finance,
Elsevier, vol. 24(5), pages 832-857, September.
- R-P. Berben & W.J. Jansen, 2001. "Comovement in International Equity Markets: a Sectoral View," MEB Series (discontinued) 2001-11, Netherlands Central Bank, Monetary and Economic Policy Department.
- Robert-Paul Berben & W. Jos Jansen, 2003. "Comovement in international equity markets: A sectoral view," Finance 0310001, EconWPA.
- Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006.
"Multivariate GARCH models: a survey,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP 1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
- Sentana,E., 1995.
"Quadratic Arch Models,"
9517, Centro de Estudios Monetarios Y Financieros-.
- van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000.
"Smooth Transition Autoregressive Models - A Survey of Recent Developments,"
SSE/EFI Working Paper Series in Economics and Finance
380, Stockholm School of Economics, revised 17 Jan 2001.
- Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
- van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
- Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Hamilton, James D. & Susmel, Raul, 1994.
"Autoregressive conditional heteroskedasticity and changes in regime,"
Journal of Econometrics,
Elsevier, vol. 64(1-2), pages 307-333.
- Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
- Engle, Robert F & Sheppard, Kevin K, 2001.
"Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH,"
University of California at San Diego, Economics Working Paper Series
qt5s2218dp, Department of Economics, UC San Diego.
- Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
- Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
- Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
- Annastiina Silvennoinen & Timo Teräsvirta, 2005.
"Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations,"
Research Paper Series
168, Quantitative Finance Research Centre, University of Technology, Sydney.
- Silvennoinen, Annastiina & Teräsvirta, Timo, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," SSE/EFI Working Paper Series in Economics and Finance 577, Stockholm School of Economics, revised 01 Oct 2005.
- Fabio Trojani & Francesco Audrino, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369.
- Hsiang-Tai Lee & Jonathan Yoder, 2005.
"A Bivariate Markov Regime Switching GARCH Approach to Estimate Time Varying Minimum Variance Hedge Ratios,"
- Hsiang-Tai Lee & Jonathan Yoder, 2007. "A bivariate Markov regime switching GARCH approach to estimate time varying minimum variance hedge ratios," Applied Economics, Taylor & Francis Journals, vol. 39(10), pages 1253-1265.
- Palandri, Alessandro, 2009. "Sequential conditional correlations: Inference and evaluation," Journal of Econometrics, Elsevier, vol. 153(2), pages 122-132, December.
- Bohning, Dankmar & Seidel, Wilfried & Alfo, Macro & Garel, Bernard & Patilea, Valentin & Walther, Gunther, 2007. "Advances in Mixture Models," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5205-5210, July.
- Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-74, May-June.
- Ji-Chun Liu, 2006. "Stationarity of a Markov-Switching GARCH Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 573-593.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- Koutmos, Gregory, 1998. "Asymmetries in the Conditional Mean and the Conditional Variance: Evidence From Nine Stock Markets," Journal of Economics and Business, Elsevier, vol. 50(3), pages 277-290, May.
- Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
- Lanne, Markku & Saikkonen, Pentti, 2002.
"Nonlinear GARCH models for highly persistent volatility,"
SFB 373 Discussion Papers
2002,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, 07.
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