Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a nonparametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coeﬀicient C n → ∞ and C n /n → 0 as n → ∞. The limit distribution of the AIC criterion, which is inconsistent, is also obtained. The analysis provides a general limit theory for semiparametric reduced rank regression under weakly dependent errors. The method does not require the speciﬁcation of a full model, is convenient for practical implementation in empirical work, and is sympathetic with semiparametric estimation approaches to cointegration analysis. Some simulations results on ﬁnite sample performance of the criterion are reported.
Cheng, Xu and Phillips, Peter C.B., "Semiparametric Cointegrating Rank Selection" (2008). Cowles Foundation Discussion Papers. 1962.