Correlation, regression, and cointegration of nonstationary economic time series
AbstractYule (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 inde- pendent. 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 coe¢ cients 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 InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-35.
Date of creation: 06 Nov 2007
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Other versions of this item:
- Søren Johansen, 2007. "Correlation, Regression, and Cointegration of Nonstationary Economic Time Series," Discussion Papers 07-25, University of Copenhagen. Department of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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