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Filtering and smoothing of state vector for diffuse state-space models


  • S. J. Koopman
  • J. Durbin


This paper presents exact recursions for calculating the mean and mean square error matrix of the state vector given the observations for the multi-variate linear Gaussian state-space model in the case where the initial state vector is (partially) diffuse. Copyright 2003 Blackwell Publishing Ltd.

Suggested Citation

  • S. J. Koopman & J. Durbin, 2003. "Filtering and smoothing of state vector for diffuse state-space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 85-98, January.
  • Handle: RePEc:bla:jtsera:v:24:y:2003:i:1:p:85-98

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    1. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
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    3. Pastorello, Sergio & Renault, Eric & Touzi, Nizar, 2000. "Statistical Inference for Random-Variance Option Pricing," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 358-367, July.
    4. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    5. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    7. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
    8. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    9. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    10. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Daniel Rees & David Lancaster & Richard Finlay, 2014. "A State-space Approach to Australian GDP Measurement," RBA Research Discussion Papers rdp2014-12, Reserve Bank of Australia.
    2. Fondeur, Y. & Karamé, F., 2013. "Can Google data help predict French youth unemployment?," Economic Modelling, Elsevier, vol. 30(C), pages 117-125.
    3. Maarten Dossche & Gerdie Everaert, 2005. "Measuring Inflation Persistence: A Structural Time Series Approach," Computing in Economics and Finance 2005 459, Society for Computational Economics.
    4. Siem Jan Koopman & Kai Ming Lee, 2009. "Seasonality with trend and cycle interactions in unobserved components models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 427-448.
    5. repec:fgv:epgrbe:v:68:n:2:a:4 is not listed on IDEAS
    6. Mesters, G. & Koopman, S.J., 2014. "Generalized dynamic panel data models with random effects for cross-section and time," Journal of Econometrics, Elsevier, vol. 180(2), pages 127-140.
    7. Adrian Pizzinga, 2010. "Constrained Kalman Filtering: Additional Results," International Statistical Review, International Statistical Institute, vol. 78(2), pages 189-208, August.
    8. Xiaoshan Chen & Terence Mills, 2012. "Measuring the Euro area output gap using a multivariate unobserved components model containing phase shifts," Empirical Economics, Springer, vol. 43(2), pages 671-692, October.
    9. Chen, Xiaoshan & MacDonald, Ronald, 2014. "Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model," Stirling Economics Discussion Papers 2014-12, University of Stirling, Division of Economics.
    10. Jungbacker, B. & Koopman, S.J. & van der Wel, M., 2011. "Maximum likelihood estimation for dynamic factor models with missing data," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1358-1368, August.
    11. Michal Franta & Branislav Saxa & Katerina Smidkova, 2007. "Inflation Persistence in New EU Member States: Is It Different Than in the Euro Area Members?," Working Papers 2007/10, Czech National Bank, Research Department.
    12. Machado, Vicente da Gama & Portugal, Marcelo Savino, 2014. "Measuring inflation persistence in Brazil using a multivariate model," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 68(2), June.
    13. T. Berger & G. Everaert, 2006. "Re-examining the Structural and the Persistence Approach to Unemployment," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/383, Ghent University, Faculty of Economics and Business Administration.
    14. Chen, Xiaoshan & MacDonald, Ronald, 2010. "Revisiting the Dollar-Euro Permanent Equilibrium Exchange Rate: Evidence from Multivariate Unobserved Components Models," SIRE Discussion Papers 2010-41, Scottish Institute for Research in Economics (SIRE).
    15. B. Jungbacker & S.J. Koopman & M. van der Wel, 2009. "Dynamic Factor Analysis in The Presence of Missing Data," Tinbergen Institute Discussion Papers 09-010/4, Tinbergen Institute, revised 11 Mar 2011.
    16. Chen, Xiaoshan & MacDonald, Ronald, 2014. "Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-05, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Prashant Srivastava & Dawei Han & Miguel Rico-Ramirez & Deleen Al-Shrafany & Tanvir Islam, 2013. "Data Fusion Techniques for Improving Soil Moisture Deficit Using SMOS Satellite and WRF-NOAH Land Surface Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(15), pages 5069-5087, December.
    18. Chen, Xiaoshan & MacDonald, Ronald, 2015. "Measuring the dollar–euro permanent equilibrium exchange rate using the unobserved components model," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 20-35.

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