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Viterbi-Based Estimation for Markov Switching GARCH Model

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  • Robert J. Elliott
  • John W. Lau
  • Hong Miao
  • Tak Kuen Siu

Abstract

We outline a two-stage estimation method for a Markov-switching Generalized Autoregressive Conditional Heteroscedastic (GARCH) model modulated by a hidden Markov chain. The first stage involves the estimation of a hidden Markov chain using the Vitberi algorithm given the model parameters. The second stage uses the maximum likelihood method to estimate the model parameters given the estimated hidden Markov chain. Applications to financial risk management are discussed through simulated data.

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File URL: http://hdl.handle.net/10.1080/1350486X.2011.620396
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 19 (2012)
Issue (Month): 3 (August)
Pages: 219-231

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Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:219-231

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References

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  1. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  2. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  3. Peter Winker & Dietmar Maringer, 2009. "The convergence of estimators based on heuristics: theory and application to a GARCH model," Computational Statistics, Springer, vol. 24(3), pages 533-550, August.
  4. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
  5. Carl Chiarella & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 150, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. 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.
  7. Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
  8. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
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Cited by:
  1. Monica Billio & Roberto Casarin & Anthony Osuntuyi, 2012. "Efficient Gibbs Sampling for Markov Switching GARCH Models," Working Papers 2012:35, Department of Economics, University of Venice "Ca' Foscari".

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