On the Finite Sample Bhaviour of the Durbin-Watson Test in the Presence of Nonsense Regressions.

It is a well-known fact that in linear regressions involving the levels of nonstationary fractionally integrated process spuriously related, the Durbin-Watson statistic converges in probability to zero. In this paper, however, we prove using Monte-Carlo experiments that the behaviour of this statistic in finite samples could be completely different from the expected one in large samples. In particular, we show that in the mean reverting case, i.e., when the memory parameters of the underlying series are less than one, this statistic converges to two if the innovations driving the series have moderate moving average parameters, and even to four when these parameters are large.