Unit Roots in White Noise
We 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 â†’ 0 and n3/T â†’ 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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- Litterman, Robert B, 1986.
"Forecasting with Bayesian Vector Autoregressions-Five Years of Experience,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 4(1), pages 25-38, January.
- Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
- Soren JOHANSEN, 2001.
"The Asymptotic Variance of the Estimated Roots in a Cointegrated Vector Autoregressive Model,"
Economics Working Papers
ECO2001/01, European University Institute.
- 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.
- Bent Nielsen & Heino Bohn Nielsen, 2008.
"Properties of etimated characteristic roots,"
2008-W07, Economics Group, Nuffield College, University of Oxford.
- 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.
- Ulrich Mueller & Mark W. Watson, 2006.
"Testing Models of Low-Frequency Variability,"
NBER Working Papers
12671, National Bureau of Economic Research, Inc.
- 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.
- Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
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