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

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  • 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. 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.

Suggested Citation

  • J. Q. Smith & António Santos, 2003. "Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outlier," GEMF Working Papers 2003-03, GEMF, Faculty of Economics, University of Coimbra.
    • Handle: RePEc:gmf:wpaper:2003-03
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    References listed on IDEAS

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    Cited by:

    1. Antonio A. F. Santos, 2021. "Bayesian Estimation for High-Frequency Volatility Models in a Time Deformed Framework," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 455-479, February.
    2. Roman Liesenfeld & Guilherme V. Moura & Jean-François Richard & Hariharan Dharmarajan, 2013. "Efficient Likelihood Evaluation of State-Space Representations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 538-567.
    3. Patrick Leung & Catherine S. Forbes & Gael M Martin & Brendan McCabe, 2019. "Forecasting Observables with Particle Filters: Any Filter Will Do!," Monash Econometrics and Business Statistics Working Papers 22/19, Monash University, Department of Econometrics and Business Statistics.
    4. Shalini Sharma & Víctor Elvira & Emilie Chouzenoux & Angshul Majumdar, 2021. "Recurrent Dictionary Learning for State-Space Models with an Application in Stock Forecasting," Post-Print hal-03184841, HAL.
    5. 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.
    6. 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.
    7. 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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