Particle filters for continuous likelihood evaluation and maximisation
AbstractIn this paper, a method is introduced for approximating the likelihood for the unknown parameters of a state space model. The approximation converges to the true likelihood as the simulation size goes to infinity. In addition, the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions. The approach advocated is fast and robust, and it avoids many of the pitfalls associated with current techniques based upon importance sampling. We assess the performance of the method by considering a linear state space model, comparing the results with the Kalman filter, which delivers the true likelihood. We also apply the method to a non-Gaussian state space model, the stochastic volatility model, finding that the approach is efficient and effective. Applications to continuous time finance models and latent panel data models are considered. Two different multivariate approaches are proposed. The neoclassical growth model is considered as an application.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 165 (2011)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Importance sampling; Volatility; Filtering; Particle filter; Simulation; SIR; State space;
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
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- 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.
- Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(3), pages 527-552, June.
- Kleppe, Tore Selland & Liesenfeld, Roman, 2014. "Efficient importance sampling in mixture frameworks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 449-463.
- Bretó, Carles, 2014. "On idiosyncratic stochasticity of financial leverage effects," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 20-26.
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