The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Kalman and particle filtering

  • Jesús Fernández-Villaverde
Reference work entry


The Kalman and Particle filters are algorithms that recursively update an estimate of the state and find the innovations driving a stochastic process given a sequence of observations. The Kalman filter accomplishes this goal by linear projections, while the Particle filter does so by a sequential Monte Carlo method. With the state estimates, we can forecast and smooth the stochastic process. With the innovations, we can estimate the parameters of the model. The article discusses how to set a dynamic model in a state-space form, derives the Kalman and Particle filters, and explains how to use them for estimation.


dynamic stochastic general equilibrium models extended Kalman filter Gaussian sum approximations Kalman filter Kalman gain law of large numbers maximum likelihood Monte Carlo methods Particle filter sequential sampling state space models statistical inference 

JEL classifications

D4 D10 C22 C32 C51 
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Jesús Fernández-Villaverde
    • 1
  1. 1.