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Quantile Filtering and Learning

40 Pages Posted: 21 Nov 2009  

Michael S. Johannes

Columbia Business School - Finance and Economics

Nick Polson

University of Chicago - Booth School of Business

Seung M. Yae

University of Chicago - Booth School of Business

Date Written: November 19, 2009

Abstract

Quantile and least-absolute deviations (LAD) methods are popular robust statistical methods but have not generally been applied to state filtering and sequential parameter learning. This paper introduces robust state space models whose error structure coincides with quantile estimation criterion, with LAD a special case. We develop an efficient particle based method for sequential state and parameter inference. Existing approaches focus solely on the problem of state filtering, conditional on parameter values. Our approach allows for sequential hypothesis testing and model monitoring by computing marginal likelihoods and Bayes factors sequentially through time. We illustrate our approach with a number of applications with real and simulated data. In all cases we compare our results with existing algorithms where possible and document the efficiency of our methodology.

Keywords: Quantile, LAD, Particle Filtering, Particle Learning, Bayes Factor

JEL Classification: C1, C11, C15

Suggested Citation

Johannes, Michael S. and Polson, Nick and Yae, Seung M., Quantile Filtering and Learning (November 19, 2009). Available at SSRN: https://ssrn.com/abstract=1509808 or http://dx.doi.org/10.2139/ssrn.1509808

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)

Seung Min Yae

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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