Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.

We wish to test the null hypothesis that a collection of functional observations are independent and identically distributed. Our procedure is based on the sum of the L2 norms of the empirical correlation functions. The limit distribution of the proposed test statistic is established under the...

This paper investigates, in a particular parametric framework, the geometric meaning of joint unpredictability for a bivariate discrete process. In particular, the paper provides a characterization of the joint unpredictability in terms of distance between information sets in an Hilbert space.