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l1-Penalized Likelihood Smoothing of Volatility Processes allowing for Abrupt Changes

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  • David Neto
  • Sylvain Sardy
  • Paul Tseng
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    Abstract

    We consider the problem of estimating the volatility of a financial asset from a time series record of length T. We believe the underlying volatility process is smooth, possibly stationary, and with potential abrupt changes due to market news. By drawing parallels between time series and regression models, in particular between stochastic volatility models and Markov random fields smoothers, we propose a semiparametric estimator of volatility. Our Bayesian posterior mode estimate is the solution to an l1-penalized likelihood optimization that we solve with an interior point algorithm that is efficient since its complexity is bounded by O(T^3/2). We apply our volatility estimator to real financial data, diagnose the model and perform back-testing to investigate to forecasting power of the method by comparison to (I)GARCH.

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    Bibliographic Info

    Paper provided by Institut d'Economie et Econométrie, Université de Genève in its series Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva with number 2009.05.

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    Length: 27 pages
    Date of creation: Apr 2009
    Date of revision:
    Handle: RePEc:gen:geneem:2009.05

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    Related research

    Keywords: l1 penalty; Markov random field; stochastic volatility model; smoothing; wavelet; extreme value theory; forecasting; GARCH.;

    References

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    1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    2. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    3. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    4. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 1999. "A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation," CIRANO Working Papers 99s-48, CIRANO.
    5. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-89, July.
    6. Catalin Starica, 2004. "Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?," Econometrics 0411015, EconWPA.
    7. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
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