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Asymptotic properties of particle filter-based maximum likelihood estimators for state space models

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  • Olsson, Jimmy
  • Rydén, Tobias

Abstract

We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly, running possibly dependent particle filters on a fixed grid in the parameter space, yielding a pointwise approximation of the log-likelihood function. Secondly, extensions of this approximation to the whole parameter space are formed by means of piecewise constant functions or B-spline interpolation, and approximate maximum likelihood estimates are obtained through maximization of the resulting functions. In this setting we formulate criteria for how to increase the number of particles and the resolution of the grid in order to produce estimates that are consistent and asymptotically normal.

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  • Olsson, Jimmy & Rydén, Tobias, 2008. "Asymptotic properties of particle filter-based maximum likelihood estimators for state space models," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 649-680, April.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:4:p:649-680
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Olivier Cappé & Randal Douc & Eric Moulines & Christian Robert, 2002. "On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 615-635, December.
    3. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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    Cited by:

    1. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    2. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    3. Hanming Fang & Edward Kung, 2021. "Why do life insurance policyholders lapse? The roles of income, health, and bequest motive shocks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 937-970, December.
    4. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.
    5. Jiawen Xu & Pierre Perron, 2023. "Forecasting in the presence of in-sample and out-of-sample breaks," Empirical Economics, Springer, vol. 64(6), pages 3001-3035, June.
    6. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    7. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    8. van Handel, Ramon, 2009. "Uniform time average consistency of Monte Carlo particle filters," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3835-3861, November.

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