Testing for lack of dependence in the functions linear model

The authors consider the linear model Y-n = Psi X-n + epsilon(n) relating a functional response with explanatory variables. They propose a simple test of the nullity of Psi based on the principal component decomposition. The limiting distribution of their test statistic is chi-squared, but this distribution is also an excellent approximation in finite samples. The authors illustrate their method using data from terrestrial magnetic observatories.