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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 this�a 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.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 644.

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Date of creation: 10 Feb 2013
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Handle: RePEc:oxf:wpaper:644

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Keywords: Auxiliary particle filter; EM algorithm; EWMA; forecasting; Kalman filter; likelihood; martingale unobserved component model; particle filter; stochastic volatility;

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  1. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2002. "Likelihood-based estimation of latent generalised ARCH structures," Economics Papers 2002-W19, Economics Group, Nuffield College, University of Oxford.
  2. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  3. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  4. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 3(1), pages 84-107.
  5. 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.
  6. Gambetti, Luca & D’Agostino, Antonello & Giannone, Domenico, 2010. "Macroeconomic forecasting and structural change," Working Paper Series, European Central Bank 1167, European Central Bank.
  7. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramírez & Martin Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," PIER Working Paper Archive 09-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Thomas Flury & Neil Shephard, 2008. "Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models," OFRC Working Papers Series, Oxford Financial Research Centre 2008fe32, Oxford Financial Research Centre.
  9. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series, Oxford Financial Research Centre 2006fe05, Oxford Financial Research Centre.
  10. Koopman S.J. & Bos C.S., 2004. "State Space Models With a Common Stochastic Variance," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 22, pages 346-357, July.
  11. Ole E. Barndorff-Nielsen & 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.
  12. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics, EconWPA 9610002, EconWPA.
  13. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
  14. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  15. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.
  16. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 129-157.
  17. Drew Creal & Siem Jan Koopman & Andre Lucas, 2009. "A General Framework for Observation Driven Time-Varying Parameter Models," Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University gd08-038, Institute of Economic Research, Hitotsubashi University.
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