Detecting relevant changes in the spatiotemporal mean function

Abstract

For a spatiotemporal process {X j (s, t)| s ∈ S , t ∈ T } j=1,...,n , where S denotes the set of spatial locations and T the time domain, we consider the problem of testing for a change in the sequence of mean functions. In contrast to most of the literature we are not interested in arbitrarily small changes, but only in changes with a norm exceeding a given threshold. Asymptotically distribution free tests are proposed, which do not require the estimation of the long-run spatiotemporal covariance structure. In particular we consider a fully functional approach and a test based on the cumulative sum paradigm, investigate the large sample properties of the corresponding test statistics and study their finite sample properties by means of simulation study.