Approximate inference for observation-driven time series models with intractable likelihoods

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Title: Approximate inference for observation-driven time series models with intractable likelihoods
Authors: Jasra, A
Kantas, N
Ehrlich, E
Item Type: Journal Article
Abstract: In this article, we consider approximate Bayesian parameter inference for observation-driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This article considers the scenario where the likelihood function cannot be evaluated pointwise; in such cases, one cannot perform exact statistical inference, including parameter estimation, which often requires advanced computational algorithms, such as Markov Chain Monte Carlo (MCMC). We introduce a new approximation based upon Approximate Bayesian Computation (ABC). Under some conditions, we show that as n → ∞, with n the length of the time series, the ABC posterior has, almost surely, a Maximum A Posteriori (MAP) estimator of the parameters that is often different from the true parameter. However, a noisy ABC MAP, which perturbs the original data, asymptotically converges to the true parameter, almost surely. In order to draw statistical inference, for the ABC approximation adopted, standard MCMC algorithms can have acceptance probabilities that fall at an exponential rate in n and slightly more advanced algorithms can mix poorly. We develop a new and improved MCMC kernel, which is based upon an exact approximation of a marginal algorithm, whose cost per iteration is random, but the expected cost, for good performance, is shown to be O(n2) per iteration. We implement our new MCMC kernel for parameter inference from models in econometrics.
Issue Date: 1-May-2014
Date of Acceptance: 1-Nov-2013
URI: http://hdl.handle.net/10044/1/40829
DOI: https://dx.doi.org/10.1145/2592254
ISSN: 1558-1195
Publisher: Association for Computing Machinery (ACM)
Journal / Book Title: ACM Transactions on Modeling and Computer Simulation
Volume: 24
Issue: 3
Copyright Statement: © 2014 ACM. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Modeling and Computer Simulation (TOMACS), Vol. 24, 3, (2014). http://doi.acm.org/10.1145/10.1145/2592254.
Keywords: Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Mathematics, Applied
Computer Science
Mathematics
Observation-driven time series models
approximate Bayesian computation
asymptotic consistency
Markov chain Monte Carlo
Distributions
Operations Research
Computation Theory And Mathematics
Information Systems
Publication Status: Published
Article Number: ARTN 13
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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