Correlation, Regression, and Cointegration of Nonstationary Economic Time Series

CREATES Research Paper No. 2007-35

11 Pages Posted: 24 Jun 2008

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Date Written: November 6, 2007


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 indpendent. 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.

JEL Classification: C22

Suggested Citation

Johansen, Soren, Correlation, Regression, and Cointegration of Nonstationary Economic Time Series (November 6, 2007). CREATES Research Paper No. 2007-35, Available at SSRN: or

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000

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