Detecting relevant changes in the spatiotemporal mean function

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