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Second-Order Filter Distribution Approximations for Financial Time Series With Extreme Outliers

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  • Smith, J.Q.
  • Santos, Antonio A.F.

Abstract

Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. The method 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 return, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, the auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. We demonstrate our results with a typical stock market series.
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Suggested Citation

  • Smith, J.Q. & Santos, Antonio A.F., 2006. "Second-Order Filter Distribution Approximations for Financial Time Series With Extreme Outliers," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 329-337, July.
  • Handle: RePEc:bes:jnlbes:v:24:y:2006:p:329-337
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    Cited by:

    1. Roman Liesenfeld & Guilherme V. Moura & Jean-François Richard & Hariharan Dharmarajan, 2013. "Efficient Likelihood Evaluation of State-Space Representations," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 538-567.
    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.
    3. António A. F. Santos, 2015. "On the Forecasting of Financial Volatility Using Ultra-High Frequency Data," GEMF Working Papers 2015-17, GEMF, Faculty of Economics, University of Coimbra.
    4. Patrick Leung & Catherine S. Forbes & Gael M. Martin & Brendan McCabe, 2016. "Data-driven particle Filters for particle Markov Chain Monte Carlo," Monash Econometrics and Business Statistics Working Papers 17/16, Monash University, Department of Econometrics and Business Statistics.

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