Semiparametric cointegrating rank selection

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a non-parametric 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 Cn → ∞ and Cn/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 co-integration analysis. Some simulation results on the finite sample performance of the criteria are reported.