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Understanding unit rooters: a helicopter tour

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  • Christopher A. Sims
  • Harald Uhlig

Abstract

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels as if they were Bayesian posterior probabilities are calculated. They are shown to depend sensitively on the estimated coefficient and to put substantial probability on values of the coefficient above one. Copyright 1991 by The Econometric Society.
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Suggested Citation

  • Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmem:4
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    References listed on IDEAS

    as
    1. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
    2. Kohn, Robert, 1982. "When is an aggregate of a time series efficiently forecast by its past?," Journal of Econometrics, Elsevier, vol. 18(3), pages 337-349, April.
    3. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    4. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
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    Keywords

    Econometrics;

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