Nonsense Regressions in Econometrics, I(1) with drift vs. Trend Stationary

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In this paper we consider the spurious or nonsense regression phenomenon where the DGPs of the regressor and the regressand are I(1) with drift vs. trend stationary and I(0) vs. I(1) with drift, and all of these patterns have first order autoregressive errors. We derive the asymptotic distributions or probability limits of the OLS estimator, the conventional significance t test, R2 and DW statistics. In these cases it is found that the spurious or nonsense regression phenomenon occurs and we examine the effect of drifts and AR(1) coefficients of the errors of regressor or regressand to the asymptotic distributions of the OLS estimator and the associated test statistics.

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