Elsevier

Journal of Econometrics

Volume 33, Issue 3, December 1986, Pages 311-340
Journal of Econometrics

Understanding spurious regressions in econometrics

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Abstract

This paper provides an analytical study of linear regressions involving the levels of economic time series. An asymptotic theory is developed for regressions that relate quite general integrated random processes. This includes the spurious regressions of Granger and Newbold (1974) and the recent cointegrating regressions of Granger and Engle (1985). An asymptotic theory is developed for the regression coefficients and for conventional significance tests. It is shown that the usual t- and F-ratio test statistics do not possess limiting distributions in this context but actually diverge as the sample size T ↑ ∞. The limiting behavior of regression diagnostics such as the Durbin–Watson statistic, the coefficient of determination and the Box–Pierce statistic is also analyzed. The theoretical results that we present explain many of the earlier simulation findings of Granger and Newbold, 1974, Granger and Newbold, 1977.

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My thanks, as always, go to Glena Ames for her skill and effort in typing the manuscript of this paper. The research reported here was undertaken during the author's tenure of a John Simon Guggenheim Fellowship. My thanks go to the Guggenheim Foundation for their financial support during 1984/85. Thanks are also due to the NSF for support under Grant No. SES 8218792.