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

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  • 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
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    References listed on IDEAS

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    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, December.
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    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

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