Testing for a change in covariance operator

•A test for comparison of covariance operators of two samples and a change point analogue are presented.•Behavior of the suggested test under the null hypothesis and the alternative are studied.•Applications to civil engineering and climatology are presented.

The paper considers a problem of equality of two covariance operators. Using functional principal component analysis, a method for testing equality of K largest eigenvalues and the corresponding eigenfunctions, together with its generalization to a corresponding change point problem is suggested. Asymptotic distributions of the test statistics are presented.