Unit Roots in White Noise
AbstractWe show that the empirical distribution of the roots of the vector auto-regression of order n fitted to T observations of a general stationary or non-stationary process, converges to the uniform distribution over the unit circle on the complex plane, when both T and n tend to infinity so that (ln T ) /n → 0 and n^3/T → 0. In particular, even if the process is a white noise, the roots of the estimated vector auto-regression will converge by absolute value to unity.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 14057.
Date of creation: 08 Mar 2009
Date of revision:
unit roots; unit root; white noise; asymptotics; autoregression; Granger and Jeon; clustering of roots;
Other versions of this item:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-03-22 (All new papers)
- NEP-ECM-2009-03-22 (Econometrics)
- NEP-ETS-2009-03-22 (Econometric Time Series)
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,
Wiley Blackwell, vol. 24(6), pages 663-678, November.
- Soren JOHANSEN, 2001. "The Asymptotic Variance of the Estimated Roots in a Cointegrated Vector Autoregressive Model," Economics Working Papers ECO2001/01, European University Institute.
- Bent Nielsen & Heino Bohn Nielsen, 2008.
"Properties of Estimated Characteristic Roots,"
08-13, University of Copenhagen. Department of Economics.
- Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of etimated characteristic roots," Economics Papers 2008-W07, Economics Group, Nuffield College, University of Oxford.
- Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of estimated characteristic roots," Economics Series Working Papers 2008-WO7, University of Oxford, Department of Economics.
- Ulrich Mueller & Mark W. Watson, 2006.
"Testing Models of Low-Frequency Variability,"
NBER Working Papers
12671, National Bureau of Economic Research, Inc.
- Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
- Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
- Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
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