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Forecasting Volatility under Fractality, Regime-Switching, Long Memory and Student-t Innovations

  • Thomas Lux
  • Leonardo Morales-Arias
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We examine the performance of volatility models that incorporate features such as long (short) memory, regime-switching and multifractality along with two competing distributional assumptions of the error component, i.e. Normal vs Student-t. Our precise contribution is twofold. First, we introduce a new model to the family of Markov-Switching Multifractal models of asset returns (MSM), namely, the Markov-Switching Multifractal model of asset returns with Student-t innovations (MSM-t). Second, we perform a comprehensive panel forecasting analysis of the MSM models as well as other competing volatility models of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) legacy. Our cross-sections consist of all-share equity indices, bond indices and real estate security indices at the country level. Furthermore, we investigate complementarities between models via combined forecasts. We find that: (i) Maximum Likelihood (ML) and Generalized Method of Moments (GMM) estimation are both suitable for MSM-t models, (ii) empirical panel forecasts of MSM-t models show an improvement over the alternative volatility models in terms of mean absolute forecast errors and that (iii) forecast combinations obtained from the different MSM and (FI)GARCH models considered appear to provide some improvement upon forecasts from single models

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Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1532.

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Length: 35 pages
Date of creation: Jul 2009
Handle: RePEc:kie:kieliw:1532
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  1. Thomas Lux & Taisei Kaizoji, 2006. "Forecasting Volatility and Volume in the Tokyo Stock Market: Long Memory, Fractality and Regime Switching," Working Papers wpn06-04, Warwick Business School, Finance Group.
  2. Liu, Ruipeng & Di Matteo, T. & Lux, Thomas, 2007. "True and apparent scaling: The proximity of the Markov-switching multifractal model to long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 35-42.
  3. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
  4. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
  5. Alessandro Rossi & Giampiero M. Gallo, 2002. "Volatility Estimation via Hidden Markov Models," Econometrics Working Papers Archive wp2002_14, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  6. Thomas Lux, 1996. "Long-term stochastic dependence in financial prices: evidence from the German stock market," Applied Economics Letters, Taylor & Francis Journals, vol. 3(11), pages 701-706.
  7. Brockwell, P. J. & Dahlhaus, R., 2004. "Generalized Levinson-Durbin and Burg algorithms," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 129-149.
  8. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, 01.
  9. Terence Mills, 1997. "Stylized facts on the temporal and distributional properties of daily FT-SE returns," Applied Financial Economics, Taylor & Francis Journals, vol. 7(6), pages 599-604.
  10. Laurent-Emmanuel Calvet & Adlai J. Fisher, 2001. "Forecasting multifractal volatility," Post-Print hal-00477952, HAL.
  11. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 49-83.
  12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  13. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
  14. I.-Yuan Chuang & Jin-Ray Lu & Pei-Hsuan Lee, 2007. "Forecasting volatility in the financial markets: a comparison of alternative distributional assumptions," Applied Financial Economics, Taylor & Francis Journals, vol. 17(13), pages 1051-1060.
  15. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
  16. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
  17. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
  18. Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," SSE/EFI Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
  19. 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.
  20. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
  21. 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.
  22. Aiolfi, Marco & Timmermann, Allan, 2006. "Persistence in forecasting performance and conditional combination strategies," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 31-53.
  23. Wu, Ping-Tsung & Shieh, Shwu-Jane, 2007. "Value-at-Risk analysis for long-term interest rate futures: Fat-tail and long memory in return innovations," Journal of Empirical Finance, Elsevier, vol. 14(2), pages 248-259, March.
  24. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  25. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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