Detecting relevant changes in the spatiotemporal mean function

For a spatiotemporal process {Xj(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 {μj(s,t)∣s∈S,t∈T}j=1,…,n. 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.