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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.

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  • 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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    Cited by:

    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
    2. Tanizaki, Hisashi, 1997. "Nonlinear and nonnormal filters using Monte Carlo methods," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 417-439, September.
    3. repec:sbe:breart:v:23:y:2003:i:2:a:2724 is not listed on IDEAS
    4. Heiss, Florian, 2006. "Nonlinear State-Space Models for Microeconometric Panel Data," Discussion Papers in Economics 1157, University of Munich, Department of Economics.
    5. 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.
    6. Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.

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