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

Author

Listed:
  • Joshua Chan
  • Rodney Strachan
Abstract
In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macroeconomic 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: one based on the accept-reject Metropolis-Hastings (ARMH) 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.

Suggested Citation

  • Joshua Chan & Rodney Strachan, 2012. "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods," CAMA Working Papers 2012-13, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2012-13
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    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2021-06/13_chan_strachan_2012.pdf
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Joshua C. C. Chan & Gary Koop & Simon M. Potter, 2016. "A Bounded Model of Time Variation in Trend Inflation, Nairu and the Phillips Curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 551-565, April.
    2. Andreza A Palma, 2016. "Natural interest rate in Brazil: further evidence frThe main objective of this study is to estimate the natural interest rate for Brazil using a parsimonious AR-trend-bound model proposed by Chan, Koo," Economics Bulletin, AccessEcon, vol. 36(3), pages 1306-1314.
    3. Eric Eisenstat & Joshua C. C. Chan & Rodney W. Strachan, 2016. "Stochastic Model Specification Search for Time-Varying Parameter VARs," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1638-1665, December.
    4. Joshua C.C. Chan & Rodney W. Strachan, 2023. "Bayesian State Space Models In Macroeconometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 58-75, February.
    5. Abhishek K. Umrawal & Joshua C. C. Chan, 2021. "On Parameter Estimation in Unobserved Components Models subject to Linear Inequality Constraints," Papers 2110.12149, arXiv.org, revised Feb 2023.
    6. Phillip, Andrew & Chan, Jennifer & Peiris, Shelton, 2020. "On generalized bivariate student-t Gegenbauer long memory stochastic volatility models with leverage: Bayesian forecasting of cryptocurrencies with a focus on Bitcoin," Econometrics and Statistics, Elsevier, vol. 16(C), pages 69-90.
    7. Dany-Knedlik, Geraldine & Holtemöller, Oliver, 2017. "Inflation dynamics during the financial crisis in Europe: Cross-sectional identification of long-run inflation expectations," IWH Discussion Papers 10/2017, Halle Institute for Economic Research (IWH).
    8. Joshua C. C. Chan & Gary Koop & Simon M. Potter, 2013. "A New Model of Trend Inflation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 94-106, January.
    9. Eric Eisenstat & Joshua C.C. Chan & Rodney W. Strachan, 2018. "Reducing Dimensions in a Large TVP-VAR," Working Paper Series 43, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    10. Eric Eisenstat & Rodney W. Strachan, 2016. "Modelling Inflation Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(5), pages 805-820, August.
    11. István Barra & Lennart Hoogerheide & Siem Jan Koopman & André Lucas, 2017. "Joint Bayesian Analysis of Parameters and States in Nonlinear non‐Gaussian State Space Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(5), pages 1003-1026, August.

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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