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Accurate Methods for Approximate Bayesian Computation Filtering


  • Laurent E. Calvet
  • Veronika Czellar


The Approximate Bayesian Computation (ABC) filter extends the particle filtering methodology to general state-space models in which the density of the observation conditional on the state is intractable. We provide an exact upper bound for the mean squared error of the ABC filter, and derive sufficient conditions on the bandwidth and kernel under which the ABC filter converges to the target distribution as the number of particles goes to infinity. The optimal convergence rate decreases with the dimension of the observation space but is invariant to the complexity of the state space. We show that the adaptive bandwidth commonly used in the ABC literature can lead to an inconsistent filter. We develop a plug-in bandwidth guaranteeing convergence at the optimal rate, and demonstrate the powerful estimation, model selection, and forecasting performance of the resulting filter in a variety of examples.

Suggested Citation

  • Laurent E. Calvet & Veronika Czellar, 2015. "Accurate Methods for Approximate Bayesian Computation Filtering," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(4), pages 798-838.
  • Handle: RePEc:oup:jfinec:v:13:y:2015:i:4:p:798-838.

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    References listed on IDEAS

    1. Laurent-Emmanuel Calvet & Veronika Czellar, 2011. "State-Observation Sampling and the Econometrics of Learning Models," Working Papers hal-00625500, HAL.
    2. Laurent Calvet & Adlai Fisher, 2008. "Multifractal Volatility: Theory, Forecasting and Pricing," Post-Print hal-00671877, HAL.
    3. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    Cited by:

    1. Forneron, Jean-Jacques & Ng, Serena, 2018. "The ABC of simulation estimation with auxiliary statistics," Journal of Econometrics, Elsevier, vol. 205(1), pages 112-139.
    2. Gael M. Martin & Brendan P.M. McCabe & David T. Frazier & Worapree Maneesoonthorn & Christian P. Robert, 2016. "Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 09/16, Monash University, Department of Econometrics and Business Statistics.
    3. Ajay Jasra, 2015. "Approximate Bayesian Computation for a Class of Time Series Models," International Statistical Review, International Statistical Institute, vol. 83(3), pages 405-435, December.

    More about this item


    bandwidth; kernel density estimation; likelihood estimation; model selection; particle filter; state-space model; value-at-risk forecasts;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation


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