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Parametric estimation of hidden stochastic model by contrast minimization and deconvolution

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  • Salima El Kolei

Abstract

We study a new parametric approach for particular hidden stochastic models. This method is based on contrast minimization and deconvolution and can be applied, for example, for ecological and financial state space models. After proving consistency and asymptotic normality of the estimation leading to asymptotic confidence intervals, we provide a thorough numerical study, which compares most of the classical methods that are used in practice (Quasi-Maximum Likelihood estimator, Simulated Expectation Maximization Likelihood estimator and Bayesian estimators) to estimate the Stochastic Volatility model. We prove that our estimator clearly outperforms the Maximum Likelihood Estimator in term of computing time, but also most of the other methods. We also show that this contrast method is the most robust with respect to non Gaussianity of the error and also does not need any tuning parameter. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:8:p:1031-1081
    DOI: 10.1007/s00184-013-0430-3
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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
    3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    4. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    7. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    9. Ronald J. Mahieu & Peter C. Schotman, 1998. "An empirical application of stochastic volatility models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 333-360.
    10. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    11. Hansen, Bruce E. & Horowitz, Joel L., 1997. "Handbook of Econometrics, vol. 4Robert F. Engle and Daniel L. McFadden, Editors Elsevier Science B. V., 1994," Econometric Theory, Cambridge University Press, vol. 13(1), pages 119-132, February.
    12. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    13. repec:dau:papers:123456789/7305 is not listed on IDEAS
    14. Newey, Whitney K., 1987. "Advanced Econometrics ByTakeshi Amemiya, Harvard University Press, 1986," Econometric Theory, Cambridge University Press, vol. 3(1), pages 153-158, February.
    15. Comte, F. & Lacour, C. & Rozenholc, Y., 2010. "Adaptive estimation of the dynamics of a discrete time stochastic volatility model," Journal of Econometrics, Elsevier, vol. 154(1), pages 59-73, January.
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    Cited by:

    1. Christophe Chesneau & Salima El Kolei & Fabien Navarro, 2017. "Parametric estimation of hidden Markov models by least squares type estimation and deconvolution," Working Papers 2017-66, Center for Research in Economics and Statistics.
    2. Christophe Chesneau & Salima El Kolei & Fabien Navarro, 2022. "Parametric estimation of hidden Markov models by least squares type estimation and deconvolution," Statistical Papers, Springer, vol. 63(5), pages 1615-1648, October.
    3. El Kolei, Salima & Pelgrin, Florian, 2017. "Parametric inference of autoregressive heteroscedastic models with errors in variables," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 63-70.

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