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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. 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.
  2. 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 gd08-038, Institute of Economic Research, Hitotsubashi University.
  3. 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.
  4. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2009. "Macroeconomic Forecasting and Structural Change," Working Papers ECARES 2009_020, ULB -- Universite Libre de Bruxelles.
  6. Neil Shephard & Gabriele Fiorentini Enrique Sentana, 2002. "Likelihood-based estimation of latent generalised ARCH structures," Economics Series Working Papers 2002-W19, University of Oxford, Department of Economics.
  7. 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.
  8. 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.
  9. 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.
  10. Koopman S.J. & Bos C.S., 2004. "State Space Models With a Common Stochastic Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 346-357, July.
  11. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  12. Charles S. Bos & Neil Shephard, 2004. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space form," Tinbergen Institute Discussion Papers 04-015/4, Tinbergen Institute.
  13. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  14. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  15. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.
  16. Dario Caldara & Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Yao Wen, 2012. "Computing DSGE models with recursive preferences and stochastic volatility," Finance and Economics Discussion Series 2012-04, Board of Governors of the Federal Reserve System (U.S.).
  17. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
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