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Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outliers

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Author Info

  • J. Q. Smith

    (Department of Statistics, University of Warwick)

  • António Santos

    ()
    (GEMF and Faculdade de Economia, Universidade de Coimbra)

Abstract

Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the log-likelihood. We argue in this paper that for series such as stock returns, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, an auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. To detach the issue of algorithm design from problems related to model misspecification and parameter estimation, we demonstrate the lack of robustness of the first order approximation and the feasibility of a specific second order approximation using simulated data.

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Bibliographic Info

Paper provided by GEMF - Faculdade de Economia, Universidade de Coimbra in its series GEMF Working Papers with number 2005-11.

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Length: 36 pages
Date of creation: 2005
Date of revision:
Publication status: Published in Journal of Business and Economic Statistics, 24(3): 329-337, 2006.
Handle: RePEc:gmf:wpaper:2005-11

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Related research

Keywords: Bayesian inference; Importance sampling; Particle filter; State space model; Stochastic volatility.;

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References

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  1. Francis X. Diebold & Andrew Hickman & Atsushi Inoue & Til Schuermann, 1997. "Converting 1-Day Volatility to h-Day Volatitlity: Scaling by Root-h is Worse Than You Think," Center for Financial Institutions Working Papers 97-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
  2. Yacine Ait-Sahalia, 1996. "Dynamic Equilibrium and Volatility in Financial Asset Markets," NBER Working Papers 5479, National Bureau of Economic Research, Inc.
  3. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
  4. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
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Cited by:
  1. David N. DeJong & Hariharan Dharmarajan & Roman Liesenfeld & Guilherme Moura & Jean-Francois Richard, 2007. "Efficient Likelihood Evaluation in State-Space Representations," Working Papers 374, University of Pittsburgh, Department of Economics, revised Dec 2008.
  2. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.

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