The autocorrelation structure of the Markov-switching asymmetric power GARCH process
AbstractIn a recent paper, Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] proposed a generalization of the Markov-switching GARCH model of Haas etÂ al. [Haas, M., Mittnik, S., Paolella, M.S., 2004. A new approach to Markov-switching GARCH models. Journal of Financial Econometrics 2, 493-530] to allow for a nonlinear relation between past shocks and future volatility as well as for the leverage effect, which refers to the observation that stock market volatility reacts differently to positive and negative shocks. For the new model, Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] derived conditions for stationarity and the existence of moments. This article complements Liu's [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] results in two directions. First, a simple method for calculating the moments and the autocorrelation structure of the power-transformed absolute process is devised, which is of vital interest in applied GARCH modeling. Second, in an application to stock returns, the relevance of the extended Markov-switching GARCH process proposed by Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438], as compared to simpler versions, is illustrated.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 78 (2008)
Issue (Month): 12 (September)
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- GIOT, Pierre & LAURENT, Sébastien, 2001.
"Value-at-risk for long and short trading positions,"
CORE Discussion Papers
2001022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
- GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
- 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, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Timmermann, Allan, 2000.
"Moments of Markov switching models,"
Journal of Econometrics,
Elsevier, vol. 96(1), pages 75-111, May.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
- Brooks, Robert, 2007. "Power arch modelling of the volatility of emerging equity markets," Emerging Markets Review, Elsevier, vol. 8(2), pages 124-133, May.
- Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
- Bekaert, Geert & Wu, Guojun, 2000.
"Asymmetric Volatility and Risk in Equity Markets,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(1), pages 1-42.
- Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
- Francq, Christian & ZakoIÂ¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
- Liu, Ji-Chun, 2006. "On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1323-1330, July.
- Liu, Ji-Chun, 2006. "On The Tail Behaviors Of A Family Of Garch Processes," Econometric Theory, Cambridge University Press, vol. 22(05), pages 852-862, October.
- Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-16, July.
- Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
- Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
- Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Liu, Ji-Chun, 2007. "Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1428-1438, July.
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