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Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series

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  • Stock, James H.

Abstract

This paper provides asymptotic confidence intervals for the largest autoregressive root of a time series when this root is close to one. The intervals are readily constructed either graphically or using tables in the Appendix. When applied to the Nelson-Plosser (1982) data set, the main conclusion is that the confidence intervals typically are wide. The conventional emphasis on testing for whether the largest root equals one fails to convey the substantial sampling variability associated with this measure of persistence.
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  • Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
  • Handle: RePEc:eee:moneco:v:28:y:1991:i:3:p:435-459
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    5. Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-163, January.
    6. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
    7. Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-680, August.
    8. Donald W.K. Andrews, 1991. "Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models," Cowles Foundation Discussion Papers 975, Cowles Foundation for Research in Economics, Yale University.
    9. Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(02), pages 241-255, August.
    10. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
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