A note on spurious significance in regressions involving I(0) and I(1) variables

Stewart, Chris (2011) A note on spurious significance in regressions involving I(0) and I(1) variables. Empirical Economics, 41(3), pp. 565-571. ISSN (print) 0377-7332

Official URL: http://dx.doi.org/10.1007/s00181-010-0404-5

Abstract

We demonstrate that t ratios (the F statistic) for I(1) regressors in a model with an I(0) dependent variable will generally be oversized. This indicates that spurious significance occurs in a situation where it was not previously identified. We also compare the asymptotic rejection rates of t ratios for various combinations of I(1) and I(0) variables in the two-variable linear regression model. These rejection rates systematically increase with the degree of autocorrelation, yielding spurious significance, when both variables are either positively or negatively autocorrelated. In contrast, when one variable is negatively autocorrelated and the other is positively autocorrelated the rejection rates systematically fall and are undersized.

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