Particle Filtering and Parameter Learning

39 Pages Posted: 2 May 2007  

Michael S. Johannes

Columbia Business School - Finance and Economics

Nick Polson

University of Chicago - Booth School of Business

Date Written: March 2007

Abstract

In this paper, we provide an exact particle filtering and parameter learning algorithm. Our approach exactly samples from a particle approximation to the joint posterior distribution of both parameters and latent states, thus avoiding the use of and the degeneracies inherent to sequential importance sampling. Exact particle filtering algorithms for pure state filtering are also provided. We illustrate the efficiency of our approach by sequentially learning parameters and filtering states in two models. First, we analyze a robust linear state space model with t-distributed errors in both the observation and state equation. Second, we analyze a log-stochastic volatility model. Using both simulated and actual stock index return data, we find that algorithm efficiently learns all of the parameters and states in both models.

Keywords: Sequential learning, filtering, stochastic volatility, Kalman filter

Suggested Citation

Johannes, Michael S. and Polson, Nick, Particle Filtering and Parameter Learning (March 2007). Available at SSRN: https://ssrn.com/abstract=983646 or http://dx.doi.org/10.2139/ssrn.983646

Michael Slater Johannes

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States

Nick Polson (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

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