Properties of Estimated Characteristic Roots

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Properties of Estimated Characteristic Roots

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Bent Nielsen (Department of Economics, University of Oxford)
Heino Bohn Nielsen (Department of Economics, University of Copenhagen)

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Bent Nielsen

Abstract

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the δ-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots.

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Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 08-13.

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Length: 13 pages
Date of creation: May 2008
Date of revision:
Handle: RePEc:kud:kuiedp:0813

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Paper
- Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of etimated characteristic roots," Economics Papers 2008-W07, Economics Group, Nuffield College, University of Oxford. [Downloadable!]

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-06-13 (All new papers)
NEP-ETS-2008-06-13 (Econometric Time Series)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Søren Johansen, 2003. "The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model," Journal of Time Series Analysis, Blackwell Publishing, vol. 24(6), pages 663-678, November. [Downloadable!] (restricted)
Other versions:
- Soren JOHANSEN, 2001. "The Asymptotic Variance of the Estimated Roots in a Cointegrated Vector Autoregressive Model," Economics Working Papers ECO2001/01, European University Institute. [Downloadable!]
Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-77, May. [Downloadable!] (restricted)
Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(3), pages 347-365, 05. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Onatski, Alexei & Uhlig, Harald, 2009. "Unit Roots in White Noise," MPRA Paper 14057, University Library of Munich, Germany. [Downloadable!]

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