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Recursive Estimation in Econometrics


  • Stephen Pollock

    (Queen Mary, University of London)


An account is given of recursive regression and of Kalman filtering which gathers the important results and the ideas that lie behind them within a small compass. It emphasises the areas in which econometricians have made contributions, which include the methods for handling the initial-value problem associated with nonstationary processes and the algorithms of fixed-interval smoothing.

Suggested Citation

  • Stephen Pollock, 2002. "Recursive Estimation in Econometrics," Working Papers 462, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp462

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    References listed on IDEAS

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    4. Merkus, H R & Pollock, D S G & de Vos, A F, 1993. "A Synopsis of the Smoothing Formulae Associated with the Kalman Filter," Computational Economics, Springer;Society for Computational Economics, vol. 6(3-4), pages 177-200, November.
    5. Harvey, Andrew C. & Collier, Patrick, 1977. "Testing for functional misspecification in regression analysis," Journal of Econometrics, Elsevier, vol. 6(1), pages 103-119, July.
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    7. Diebold, Francis X., 1986. "Exact maximum-likelihood estimation of autoregressive models via the Kalman filter," Economics Letters, Elsevier, vol. 22(2-3), pages 197-201.
    8. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    9. Dufour, Jean-Marie, 1982. "Recursive stability analysis of linear regression relationships: An exploratory methodology," Journal of Econometrics, Elsevier, vol. 19(1), pages 31-76, May.
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    14. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
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    24. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Godolphin, E.J. & Triantafyllopoulos, Kostas, 2006. "Decomposition of time series models in state-space form," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2232-2246, May.
    2. repec:ejw:journl:v:15:y:2018:i:1:p:51-66 is not listed on IDEAS
    3. Mazzocchi, Mario, 2006. "Time patterns in UK demand for alcohol and tobacco: an application of the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2191-2205, May.
    4. Mewael F. Tesfaselassie & Eric Schaling & Sylvester Eijffinger, 2011. "Learning about the Term Structure and Optimal Rules for Inflation Targeting," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(8), pages 1685-1706, December.
    5. Izquierdo, Segismundo S. & Hernández, Cesáreo & del Hoyo, Juan, 2006. "Forecasting VARMA processes using VAR models and subspace-based state space models," MPRA Paper 4235, University Library of Munich, Germany.
    6. Bujosa, Marcos & Garcia-Ferrer, Antonio & Young, Peter C., 2007. "Linear dynamic harmonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 999-1024, October.
    7. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    8. Heidorn, Thomas & Van Huellen, Sophie & Ruehl, C. & Woebbeking, F., 2017. "The long- and short-run impact of oil price changes on major global economies," Frankfurt School - Working Paper Series 225, Frankfurt School of Finance and Management.
    9. Giorgio Calzolari & Laura Neri, 2010. "The Method of Simulated Scores for Estimating Multinormal Regression Models with Missing Values," Econometrics Working Papers Archive wp2010_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    10. Tesfaselassie, M.F., 2005. "Communication, learning and optimal monetary policy," Other publications TiSEM 33c69063-eed7-4938-9f51-e, Tilburg University, School of Economics and Management.
    11. K. Triantafyllopoulos, 2007. "Covariance estimation for multivariate conditionally Gaussian dynamic linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 551-569.
    12. Freitas, Paulo S.A. & Rodrigues, Antonio J.L., 2006. "Model combination in neural-based forecasting," European Journal of Operational Research, Elsevier, vol. 173(3), pages 801-814, September.
    13. Pollock, D.S.G., 2006. "Introduction to the special issue on statistical signal extraction and filtering," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2137-2145, May.
    14. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    15. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    16. Lee, Woojoo & Lim, Johan & Lee, Youngjo & del Castillo, Joan, 2011. "The hierarchical-likelihood approach to autoregressive stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 248-260, January.

    More about this item


    Recursive regression; Kalman filtering; Fixed-interval smoothing; The initial-value problem;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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