IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/52116.html
   My bibliography  Save this paper

On the stability of recursive least squares in the Gauss-Markov model

Author

Listed:
  • Salies, Evens

Abstract

In the Gauss-Markov regression model, one can always update the least square estimate of the slope vector, given new observations at the values of the explanatory variables. The updated estimate is often considered as a time-varying state of an auto-regressive system in Kalman filtering and recursive least squares theory. This note shows that the auto-regressive matrix of this dynamic system once centered has its largest eigenvalues equal to 1; the remaining eigenvalues are equal.

Suggested Citation

  • Salies, Evens, 2004. "On the stability of recursive least squares in the Gauss-Markov model," MPRA Paper 52116, University Library of Munich, Germany, revised 10 Dec 2013.
    • Handle: RePEc:pra:mprapa:52116
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/52116/1/MPRA_paper_52116.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/58036/1/MPRA_paper_52116.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrew C. Harvey, 1990. "The Econometric Analysis of Time Series, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rocha, Roberto de Rezende, 1991. "Inflation and stabilization in Yugoslavia," Policy Research Working Paper Series 752, The World Bank.
    2. Campos, Nauro & Nugent, Jeffrey B, 2000. "Investment and Instability," CEPR Discussion Papers 2609, C.E.P.R. Discussion Papers.
    3. Torstein Bye & Alexandra Katz, 1995. "Returns to Publicly Owned Transport Infrastructure Investment . A Cost Function/Cost Share Approach for Norway, 1971-1991," Discussion Papers 154, Statistics Norway, Research Department.
    4. John T. Cuddington & Leila Dagher, 2015. "Estimating Short and Long-Run Demand Elasticities: A Primer with Energy-Sector Applications," The Energy Journal, , vol. 36(1), pages 185-210, January.
    5. Steen, Frode & Sorgard, Lars, 1999. "Semicollusion in the Norwegian cement market," European Economic Review, Elsevier, vol. 43(9), pages 1775-1796, October.
    6. Seale, James L. & Solano, Alexis A., 2012. "The changing demand for energy in rich and poor countries over 25years," Energy Economics, Elsevier, vol. 34(6), pages 1834-1844.
    7. Jacques Mairesse & Bronwyn H. Hall & Benoît Mulkay, 1999. "Firm-Level Investment in France and the United States: An Exploration of What We Have Learned in Twenty Years," Annals of Economics and Statistics, GENES, issue 55-56, pages 27-67.
    8. Sassi, M., 2013. "Child Nutritional Status in the Malawian District of Salima: A Capability Approach," 2013 Second Congress, June 6-7, 2013, Parma, Italy 149892, Italian Association of Agricultural and Applied Economics (AIEAA).
    9. Guy V. G. Stevens, 1995. "On the inverse of the covariance matrix in portfolio analysis," International Finance Discussion Papers 528, Board of Governors of the Federal Reserve System (U.S.).
    10. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
    11. Beck, Guenter W. & Wieland, Volker, 2008. "Central bank misperceptions and the role of money in interest-rate rules," Journal of Monetary Economics, Elsevier, vol. 55(Supplemen), pages 1-17, October.
    12. Salvanes, Kjell G. & Steen, Frode & Sorgard, Lars, 2005. "Hotelling in the air? Flight departures in Norway," Regional Science and Urban Economics, Elsevier, vol. 35(2), pages 193-213, March.
    13. Jacobs, Jan & Sterken, Elmer, 1995. "The IBS-CCSO quarterly model of the Netherlands Specification, simulation and analysis," Economic Modelling, Elsevier, vol. 12(2), pages 111-163, April.
    14. Roberto Casarin & Andrea Piva & Loriana Pelizzon, 2008. "Italian Equity Funds: Efficiency and Performance Persistence," The IUP Journal of Financial Economics, IUP Publications, vol. 0(1), pages 7-28, March.
    15. Isabel Figuerola-Ferretti, 2005. "Prices and production cost in aluminium smelting in the short and the long run," Applied Economics, Taylor & Francis Journals, vol. 37(8), pages 917-928.
    16. LaFrance, Jeffrey T., 1999. "U.S. Food and Nutrient Demand and the Effects of Agricultural Policies," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt52h9v4dq, Department of Agricultural & Resource Economics, UC Berkeley.
    17. Ronald A. Babula & Fred J. Ruppel & David A. Bessler, 1995. "U.S. corn exports: the role of the exchange rate," Agricultural Economics, International Association of Agricultural Economists, vol. 13(2), pages 75-88, November.
    18. Chris Gardiner & John Henneberry, 1995. "Analysing the property-gilts yield differential," Applied Economics Letters, Taylor & Francis Journals, vol. 2(1), pages 12-15.
    19. Garsztka Przemysław & Hołubowicz Krzysztof, 2015. "The Application of Asymmetric Liquidity Risk Measure in Modelling the Risk of Investment," Folia Oeconomica Stetinensia, Sciendo, vol. 15(1), pages 83-100, June.
    20. Lauridsen, J. & Kosfeld, R., 2004. "A wald Test for Spatial Nonstationarity," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 1-12, Diciembre.

    More about this item

    Keywords

    Recursive Least Squares; Gauss-Markov model.;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:52116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.