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A Switching ARCH Model for the German DAX Index

Author

Listed:
  • Kaufmann Sylvia

    (Oesterreichische Nationalbank)

  • Scheicher Martin

    (European Central Bank)

Abstract

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.

Suggested Citation

  • Kaufmann Sylvia & Scheicher Martin, 2006. "A Switching ARCH Model for the German DAX Index," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-37, December.
    • Handle: RePEc:bpj:sndecm:v:10:y:2006:i:4:n:3
    DOI: 10.2202/1558-3708.1290
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    References listed on IDEAS

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    Cited by:

    1. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    2. Colavecchio, Roberta & Funke, Michael, 2009. "Volatility dependence across Asia-Pacific onshore and offshore currency forwards markets," Journal of Asian Economics, Elsevier, vol. 20(2), pages 174-196, March.
    3. Carlos Alberto Gonçalves da Silva, 2020. "Impacts of Covid-19 Pandemic and Persistence of Volatility in the Returns of the Brazilian Stock Exchange: An Application of the Markov Regime Switching GARCH (MRS-GARCH) Model," International Journal of Applied Economics, Finance and Accounting, Online Academic Press, vol. 8(2), pages 62-72.
    4. David Ardia & Lennart F. Hoogerheide, 2010. "Efficient Bayesian Estimation and Combination of GARCH-Type Models," Tinbergen Institute Discussion Papers 10-046/4, Tinbergen Institute.
    5. Abounoori, Esmaiel & Elmi, Zahra (Mila) & Nademi, Younes, 2016. "Forecasting Tehran stock exchange volatility; Markov switching GARCH approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 264-282.

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