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A Switching ARCH Model for the German DAX Index

Listed author(s):
  • Kaufmann Sylvia

    ()

    (Oesterreichische Nationalbank)

  • Scheicher Martin

    ()

    (European Central Bank)

This paper estimates a switching autoregressive conditional heteroskedastic time series model for returns on the daily German stock market index. Volatility clustering is captured by persistent periods of different volatility levels and by the dependence on past innovations. We introduce a leverage term to model the asymmetric response of volatility to shocks. Model specification and estimation is performed within a Bayesian framework using Markov Chain Monte Carlo simulation methods. Model diagnostics document a good fit of the switching ARCH model. The persistence of shocks in volatility coming from the autoregressive conditional part of the variance is considerably lower than that obtained using a GARCH(1,1) model. Our volatility estimate closely follows market implied volatility. When we compare the forecasting performance, switching ARCH turns out to be an unbiased estimator of realized volatility. Nevertheless, over all forecast horizons, model-based volatility forecasts do not add information about future volatility. Up to a 7-day horizon, market implied volatility already contains nearly all information.

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File URL: https://www.degruyter.com/view/j/snde.2006.10.4/snde.2006.10.4.1290/snde.2006.10.4.1290.xml?format=INT
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Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 10 (2006)
Issue (Month): 4 (December)
Pages: 1-37

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Handle: RePEc:bpj:sndecm:v:10:y:2006:i:4:n:3
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References listed on IDEAS
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  1. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  2. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
  3. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
  4. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  5. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
  6. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  7. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
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