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Abstract Details

Activity Number: 81
Type: Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #306391
Title: Tracking Beliefs: Accurate Methods for Approximate Bayesian Computation Filtering
Author(s): Laurent Calvet*+ and Veronika Czellar
Companies: HEC Paris and HEC Paris
Address: 1, rue de la Liberation, Jouy en Josas, International, 78351, France
Keywords: Bandwidth ; Kernel density estimation ; Likelihood estimation ; Model selection ; Particle filter ; State-space model
Abstract:

The Approximate Bayesian Computation (ABC) filter extends the particle filtering methodology to general state-space models in which the density of the observation conditional on the state is intractable. We provide an exact upper bound for the mean squared error of the ABC filter and show that under appropriate bandwidth and kernel specifications, ABC converges to the target distribution as the number of particles goes to infinity. The optimal convergence rate decreases with the dimension of the observation space but is invariant to the complexity of the state space. We also show that the usual adaptive bandwidth used in the ABC literature leads to an inconsistent filter. We develop a plug-in rule for the bandwidth and demonstrate the good accuracy of the resulting filter on a multifractal asset pricing model with investor learning.


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