Semiparametric Cointegrating Rank Selection for Curved Cross Section Time Series

Cointegrating rank selection is studied in a function space reduced rank regression where the data are time series of cross section curves. A semiparametric approach to rank selection is employed using information criteria suitably modified to take account of the function space context, extending the linear cointegrating model to accommodate cross section data under general forms of dependence. A parametric formulation is employed analogous to recent work on cross section curve autoregression and cointegrating regression. Consistent cointegrating rank estimation is developed by the use of information criteria methods that are extended to the curve time series environment. The asymptotic theory involves two parameter Gaussian processes that generalize the standard limit processes involved in cointegrating regressions with conventional multiple time series. Simulations provide evidence of the effectiveness of consistent rank selection by the BIC criterion and the tendency of AIC to overestimate order as it does in standard lag order selection in autoregression as well as in reduced rank regression with multiple time series.