Spurious Regressions With Time-Series data: Further Asymptotic Results
A “spurious regression” is one in which the time-series variables are non-stationary and independent. It is well-known that in this context the OLS parameter estimates and the R2 converge to functionals of Brownian motions; the “t-ratios” diverge in distribution; and the Durbin-Watson statistic converges in probability to zero. We derive corresponding results for some common tests for the Normality and homoskedasticity of the errors in a spurious regression.
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