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Gauss, Kalman and advances in recursive parameter estimation


  • Peter C. Young


The paper considers how the Kalman filter has influenced the development of recursive parameter estimation since the publication of Rudolf Kalman's seminal article in 1960. It will present a partial review of developments over the past half century and provide a tutorial introduction to the refined instrumental variable approach to the optimal recursive estimation of parameters in both discrete and continuous-time transfer function models. The paper concludes with a case study that shows how recursive parameter estimation and the Kalman filter can be combined in the design and development of a real‐time adaptive forecasting and data assimilation system for flow in river systems. Copyright (C) 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Peter C. Young, 2011. "Gauss, Kalman and advances in recursive parameter estimation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(1), pages 104-146, January.
  • Handle: RePEc:jof:jforec:v:30:y:2011:i:1:p:104-146

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    References listed on IDEAS

    1. Nieto, Fabio H. & Guerrero, Victor M., 1995. "Kalman filter for singular and conditional state-space models when the system state and the observational error are correlated," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 303-310, March.
    2. Víctor Guerrero & Fabio Nieto, 1999. "Temporal and contemporaneous disaggregation of multiple economic time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 459-489, December.
    3. repec:adr:anecst:y:1987:i:6-7:p:12 is not listed on IDEAS
    4. repec:adr:anecst:y:1987:i:6-7 is not listed on IDEAS
    5. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    6. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    7. F. Javier Fernandez Macho & Andrew C. Harvey & James H. Stock, 1987. "Forecasting and Interpolation Using Vector Autoregressions with Common Trends," Annals of Economics and Statistics, GENES, issue 6-7, pages 279-287.
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    1. repec:bla:jtsera:v:38:y:2017:i:3:p:417-457 is not listed on IDEAS
    2. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.


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