TY - JOUR

T1 - Approximate inference for observation-driven time series models with intractable likelihoods

AU - Jasra, Ajay

AU - Kantas, Nikolas

AU - Ehrlich, Elena

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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. © 2014 ACM.

AB - 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. © 2014 ACM.

UR - http://dl.acm.org/citation.cfm?doid=2616590.2592254

UR - http://www.scopus.com/inward/record.url?scp=84904957897&partnerID=8YFLogxK

U2 - 10.1145/2592254

DO - 10.1145/2592254

M3 - Article

VL - 24

JO - ACM Transactions on Modeling and Computer Simulation

JF - ACM Transactions on Modeling and Computer Simulation

SN - 1049-3301

IS - 3

ER -