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Correlation, Regression, and Cointegration of Nonstationary Economic Time Series

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  • Søren Johansen

    (Department of Economics, University of Copenhagen)

Abstract

Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were independent. This was later discussed by Granger and Newbold (1974), and Phillips (1986) found the limit distributions. We propose to distinguish between empirical and population correlation coefficients and show in a bivariate autoregressive model for nonstationary variables that the empirical correlation and regression coefficients do not converge to the relevant population values, due to the trending nature of the data. We conclude by giving a simple cointegration analysis of two interests. The analysis illustrates that much more insight can be gained about the dynamic behavior of the nonstationary variables then simply by calculating a correlation coefficient.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 07-25.

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Length: 9 pages
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:kud:kuiedp:0725

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  1. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  2. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  3. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
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Cited by:
  1. Ansgar Belke & Marcel Wiedmann, 2013. "Monetary Policy, Stock Prices and Central Banks - Cross-Country Comparisons of Cointegrated VAR Models," Ruhr Economic Papers 0435, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  2. Paul Alagidede & Theodore Panagiotidis & Xu Zhang, 2010. "Why a Diversified Portfolio Should Include African Assets," Koç University-TUSIAD Economic Research Forum Working Papers 1034, Koc University-TUSIAD Economic Research Forum.
  3. Ansgar Belke & Marcel Wiedmann, 2013. "Money, Stock Prices and Central Banks – Cross-Country Comparisons of Cointegrated VAR Models," ROME Working Papers 201308, ROME Network.

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