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Martingale unobserved component models

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  • Neil Shephard

Abstract

I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a time-varying signal/noise ratio. I call thisa martingale component model. This makes the rate of discounting of data local. I show how to handle such models effectively using an auxiliary particle filter which deploys M Kalman filters run in parallel competing against one another. Here one thinks of M as being 1,000 or more. The model is applied to inflation forecasting. The model generalises to unobserved component models where Gaussian shocks are replaced by martingale difference sequences.

Suggested Citation

  • Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:644
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    References listed on IDEAS

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    1. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
    2. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, September.
    3. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    4. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    6. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    7. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    8. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    9. 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, June.
    10. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    11. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2013. "Macroeconomic forecasting and structural change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 82-101, January.
    12. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    13. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    14. Dario Caldara & Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Wen Yao, 2012. "Computing DSGE Models with Recursive Preferences and Stochastic Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 188-206, April.
    15. 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.
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    Citations

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    Cited by:

    1. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    2. James M. Nason & Gregor W. Smith, 2021. "Measuring the slowly evolving trend in US inflation with professional forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 1-17, January.
    3. Hernández, Juan R., 2020. "Covered Interest Parity: A Stochastic Volatility Approach to Estimate the Neutral Band," MPRA Paper 100744, University Library of Munich, Germany.
    4. Elmar Mertens & James M. Nason, 2020. "Inflation and professional forecast dynamics: An evaluation of stickiness, persistence, and volatility," Quantitative Economics, Econometric Society, vol. 11(4), pages 1485-1520, November.
    5. Timothy Cogley & Thomas J. Sargent, 2014. "Measuring Price-Level Uncertainty and Instability in the U.S., 1850-2012," Working Papers 2014-33, Economic Research Institute, Bank of Korea.
    6. Frank Schorfheide & Dongho Song & Amir Yaron, 2018. "Identifying Long‐Run Risks: A Bayesian Mixed‐Frequency Approach," Econometrica, Econometric Society, vol. 86(2), pages 617-654, March.
    7. Cogley, Timothy & Sargent, Thomas J. & Surico, Paolo, 2015. "Price-level uncertainty and instability in the United Kingdom," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 1-16.

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    More about this item

    Keywords

    Auxiliary particle filter; EM algorithm; EWMA; forecasting; Kalman filter; likelihood; martingale unobserved component model; particle filter; stochastic volatility;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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