Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods
In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macro-economic and financial data. However, many theoretically motivated models imply non-linear or non-Gaussian specifications – or both. Existing methods for estimating such models are computationally intensive, and often cannot be applied to models with more than a few states. Building upon recent developments in precision-based algorithms, we propose a general approach to estimating high-dimensional non-linear non-Gaussian state space models. The baseline algorithm approximates the conditional distribution of the states by a multivariate Gaussian or t density, which is then used for posterior simulation. We further develop this baseline algorithm to construct more sophisticated samplers with attractive properties: on based on the accept—reject Metropolis-Hastings (ARHM) algorithm, and another adaptive collapsed sampler inspired by the cross-entropy method. To illustrate the proposed approach, we investigate the effect of the zero lower bound of interest rate on monetary transmission mechanism.
|Date of creation:||Mar 2012|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +61 2 6125 4705
Fax: +61 2 6125 5448
Web page: http://cama.crawford.anu.edu.au
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sylvia Fr�Hwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
- Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
- Thomas Flury & Neil Shephard, 2008.
"Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models,"
OFRC Working Papers Series
2008fe32, Oxford Financial Research Centre.
- Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(05), pages 933-956, October.
- Neil Shephard & Thomas Flury, 2008. "Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models," Economics Series Working Papers 413, University of Oxford, Department of Economics.
- Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005.
"Estimating dynamic equilibrium economies: linear versus nonlinear likelihood,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
- Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez, 2004. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Working Paper 2004-3, Federal Reserve Bank of Atlanta.
- Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood," PIER Working Paper Archive 04-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996.
"Stochastic Volatility: Likelihood Inference And Comparison With Arch Models,"
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
- McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
- Siddhartha Chib & Ivan Jeliazkov, 2005. "Accept-reject Metropolis-Hastings sampling and marginal likelihood estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 30-44.
- Chris M. Strickland & Catherine S. Forbes & Gael M. Martin, 2003.
"Bayesian Analysis of the Stochastic Conditional Duration Model,"
Monash Econometrics and Business Statistics Working Papers
14/03, Monash University, Department of Econometrics and Business Statistics.
- Strickland, Chris M. & Forbes, Catherine S. & Martin, Gael M., 2006. "Bayesian analysis of the stochastic conditional duration model," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2247-2267, May.
- Iwata, Shigeru & Wu, Shu, 2006. "Estimating monetary policy effects when interest rates are close to zero," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1395-1408, October.
- David Reifschneider & John C. Williams, 2000.
"Three lessons for monetary policy in a low-inflation era,"
Conference Series ; [Proceedings],
Federal Reserve Bank of Boston, pages 936-978.
- David Reifschneider & John C. Williams, 1999. "Three lessons for monetary policy in a low inflation era," Finance and Economics Discussion Series 1999-44, Board of Governors of the Federal Reserve System (U.S.).
- J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
- McCAUSLAND, William, 2008.
"The Hessian Method (Highly Efficient State Smoothing, In a Nutshell),"
Cahiers de recherche
03-2008, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- McCAUSLAND, William, 2008. "The Hessian Method (Highly Efficient State Smoothing, In a Nutshell)," Cahiers de recherche 2008-03, Universite de Montreal, Departement de sciences economiques.
- Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2008. "On the Evolution of Monetary Policy," Working Paper Series 24-08, The Rimini Centre for Economic Analysis, revised Jan 2008.
- Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
- Reifschneider, David & Willams, John C, 2000. "Three Lessons for Monetary Policy in a Low-Inflation Era," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(4), pages 936-66, November.
- H�vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
When requesting a correction, please mention this item's handle: RePEc:een:camaaa:2012-13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Cama Admin)
If references are entirely missing, you can add them using this form.