Useful spurious correlations

This paper presents useful application of spurious canonical correlations when N time series observed for T time periods and generated by cointegrated processes integrated of order 1, with a fixed number s of common trends. The limit distributions of eigenvalues and eigenvectors associated with Canonical Correlations Analysis (CCA) are discussed, where the CCA involves the N observed variables and two alternative sets of spurious explanatory variables, namely either K simulated independent random walks or the first K elements of a basis of L 2 [0, 1] associated with the Karhunen-Loève representation of specific Wiener diffusions. It is shown how these CCA, while spurious, deliver useful inferential tools, including estimators of the number of common trends and of a basis of the common trends loadings space. (Super-)consistency as well as the asymptotic distributions of estimators are first derived for diverging T and K fixed, and then for diverging (T, K) with K/T = o(1) (amend condition?), possibly followed by diverging N . The properties of the estimators are compared with alternatives both theoretically and via a Monte Carlo simulation study.