Estimating the number of common trends in large T and N factor models via canonical correlations analysis

Asymptotic results for canonical correlations are derived when the analysis is performed between levels and cumulated levels of N time series of length T, generated by a fac- tor model with s common stochastic trends. For T → ∞ and fixed N and s, the largest s squared canonical correlations are shown to converge to a non-degenerate limit distribu- tion while the remaining N − s converge in probability to 0. Furthermore, if s grows at most linearly in N, the largest s squared canonical correlations are shown to converge in prob- ability to 1 as (T, N)seq → ∞. This feature allows one to estimate the number of common trends as the integer with largest decrease in adjacent squared canonical correlations. The maximal gap equals 1 in the limit and this criterion is shown to be consistent. A Monte Carlo simulation study illustrates the findings.