Understanding Spurious Regressions in Econometrics
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This paper provides an analytical study of spurious regressions involving the levels of economic time series. As asymptotic theory is developed for regressions that relate independent random walks. It is shown that the usual t ratio signiﬁcance tests do not possess limiting distributions but actually diverge as the sample size T approaches inﬁnity. The Durbin-Watson statistic, on the other hand, converges in probability to zero. An alternative asymptotic theory is also analyzed. An alternative asymptotic theory is developed based on the concept of continuous data recording. This theory together with the large sample asymptotics that we present go a long way towards explaining the experimental results of Granger and Newbold (1974, 1977).
Phillips, Peter C.B., "Understanding Spurious Regressions in Econometrics" (1985). Cowles Foundation Discussion Papers. 997.