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Particle filters and Bayesian inference in financial econometrics
Author(s) -
Lopes Hedibert F.,
Tsay Ruey S.
Publication year - 2011
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1195
Subject(s) - particle filter , kalman filter , ensemble kalman filter , algorithm , monte carlo method , computer science , auxiliary particle filter , filter (signal processing) , bayesian inference , state space , bayesian probability , econometrics , mathematics , artificial intelligence , extended kalman filter , statistics , computer vision
In this paper we review sequential Monte Carlo (SMC) methods, or particle filters (PF), with special emphasis on its potential applications in financial time series analysis and econometrics. We start with the well‐known normal dynamic linear model, also known as the normal linear state space model, for which sequential state learning is available in closed form via standard Kalman filter and Kalman smoother recursions. Particle filters are then introduced as a set of Monte Carlo schemes that enable Kalman‐type recursions when normality or linearity or both are abandoned. The seminal bootstrap filter (BF) of Gordon, Salmond and Smith (1993) is used to introduce the SMC jargon, potentials and limitations. We also review the literature on parameter learning, an area that started to attract much attention from the particle filter community in recent years. We give particular attention to the Liu–West filter (2001), Storvik filter (2002) and particle learning (PL) of Carvalho, Johannes, Lopes and Polson (2010). We argue that the BF and the auxiliary particle filter (APF) of Pitt and Shephard (1999) define two fundamentally distinct directions within the particle filter literature. We also show that the distinction is more pronounced with parameter learning and argue that PL, which follows the APF direction, is an attractive extension. One of our contributions is to sort out the research from BF to APF (during the 1990s), from APF to now (the 2000s) and from Liu–West filter to Storvik filter to PL. To this end, we provide code in R for all the examples of the paper. Readers are invited to find their own way into this dynamic and active research arena. Copyright © 2010 John Wiley & Sons, Ltd.