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Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods

  • Joshua Chan

    ()

  • Rodney Strachan

    ()

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.

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File URL: http://cama.crawford.anu.edu.au/pdf/working-papers/2012/132012.pdf
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Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2012-13.

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Length: 39 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:een:camaaa:2012-13
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  13. 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.
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  15. 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.
  16. 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.
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