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Prediction, Filtering and Smoothing in Non-linear and Non-normal Cases Using Monte Carlo Integration

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  • Tanizaki, Hisashi
  • Mariano, Roberto S

Abstract

A simulation-based non-linear filter is developed for prediction and smoothing in non-linear and/or non-normal structural time-series models. Recursive algorithms of weighting functions are derived by applying Monte Carlo integration. Through Monte Carlo experiments, it is shown that (1) for a small number of random draws (or nodes) our simulation-based density estimator using Monte Carlo integration (SDE) performs better than Kitagawa's numerical integration procedure (KNI), and (2) SDE and KNI give less biased parameter estimates than the extended Kalman filter (EKF). Finally, an estimation of per capita final consumption data is taken as an application to the non-linear filtering problem. Copyright 1994 by John Wiley & Sons, Ltd.

Suggested Citation

  • Tanizaki, Hisashi & Mariano, Roberto S, 1994. "Prediction, Filtering and Smoothing in Non-linear and Non-normal Cases Using Monte Carlo Integration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 163-179, April-Jun.
    • Handle: RePEc:jae:japmet:v:9:y:1994:i:2:p:163-79
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    Citations

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    Cited by:

    1. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
    2. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1059-1087.
    3. Tanizaki, Hisashi, 1997. "Nonlinear and nonnormal filters using Monte Carlo methods," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 417-439, September.
    4. Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    5. Heiss, Florian, 2006. "Nonlinear State-Space Models for Microeconometric Panel Data," Discussion Papers in Economics 1157, University of Munich, Department of Economics.
    6. Tanizaki, Hisashi & Mariano, Roberto S., 1998. "Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 263-290.
    7. Hermann Singer, 2003. "Simulated Maximum Likelihood in Nonlinear Continuous-Discrete State Space Models: Importance Sampling by Approximate Smoothing," Computational Statistics, Springer, vol. 18(1), pages 79-106, March.
    8. Panayotis G. Michaelides & Efthymios G. Tsionas & Angelos T. Vouldis & Konstantinos N. Konstantakis & Panagiotis Patrinos, 2018. "A Semi-Parametric Non-linear Neural Network Filter: Theory and Empirical Evidence," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 637-675, March.
    9. S. Borağan Aruoba, 2008. "Data Revisions Are Not Well Behaved," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(2‐3), pages 319-340, March.
    10. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.

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