["Oxford Bulletin of Economics and Statistics, Volume 88, Issue 4, Page 623-642, August 2026. ", "\nABSTRACT\nCointegrating rank selection is studied in a function space reduced rank regression where the data are time series of cross‐section curves. Consistent cointegrating rank estimation is developed using information criteria extended to curve time series environments. The asymptotic theory involves two‐parameter Gaussian processes that generalise the standard limit processes involved in cointegrating regressions. Simulations provide evidence of the effectiveness of consistent rank selection by the BIC criterion and the tendency of AIC to overestimate order as in standard lag order selection in autoregression, as well as in reduced rank regression with multiple time series.\n"]