Approximate Bayesian Computation in State Space Models

Gael Martin, Brendan McCabe, Worapree Maneesoonthorn () and Christian Robert ()

No 20/14, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency yielded by the MLE is replicated by the score. In multiple parameter settings a separate treatment of scalar parameters, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality. Some attention is given to a structure in which the state variable is driven by a continuous time process, with exact inference typically infeasible in this case as a result of intractable transitions. The ABC method is demonstrated using the unscented Kalman filter as a fast and simple way of producing an approximation in this setting, with a stochastic volatility model for financial returns used for illustration.

Keywords: Likelihood-free methods; latent diffusion models; linear Gaussian state space models; asymptotic sufficiency; unscented Kalman filter; stochastic volatility. (search for similar items in EconPapers)
JEL-codes: C11 C22 C58 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://business.monash.edu/econometrics-and-busine ... ions/ebs/wp20-14.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp20-14.pdf [301 Moved Permanently]--> https://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp20-14.pdf [301 Moved Permanently]--> https://www.monash.edu/business/econometrics-and-business-statistics/research/publications/ebs/wp20-14.pdf [301 Moved Permanently]--> https://www.monash.edu/business/econometrics-and-business-statistics-new/research/publications/ebs/wp20-14.pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:msh:ebswps:2014-20

Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics

Access Statistics for this paper

More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Professor Xibin Zhang ().