Pitfalls in the Use of Time as an Explanatory Variable in Regression

41 Pages Posted: 21 Jun 2001 Last revised: 3 Aug 2010

See all articles by Charles R. Nelson

Charles R. Nelson

Dept of Economics

Heejoon Kang

Indiana University - Kelley School of Business - Department of Business Economics & Public Policy

Date Written: November 1983

Abstract

Regression of a trendless random walk on time produces R-squared values around .44 regardless of sample length. The residuals from the regression exhibit only about 14 percent as much variation as the original series even though the underlying process has no functional dependence on time. The autocorrelation structure of these "detrended" random walks is pseudo-cyclical and purely artifactual. Conventional tests for trend are strongly biased towards finding a trend when none is present, and this effect is only partially mitigated by Cochrane-Orcutt correction for autocorrelation. The results are extended to show that pairs of detrended random walks exhibit spurious correlation.

Suggested Citation

Nelson, Charles R. and Kang, Heejoon, Pitfalls in the Use of Time as an Explanatory Variable in Regression (November 1983). NBER Working Paper No. t0030, Available at SSRN: https://ssrn.com/abstract=274544

Charles R. Nelson (Contact Author)

Dept of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

Heejoon Kang

Indiana University - Kelley School of Business - Department of Business Economics & Public Policy ( email )

Bloomington, IN 47405
United States

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