COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 757 "Understanding Spurious Regressions in Econometrics" Peter C.B. Phillips July 1985 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). |
