Testing for Changes in Multivariate Dependent Observations with an Application to Temperature Changes

We develop procedures for testing for changes in the mean of multivariatem-dependent stationary processes. Several test statistics are considered and corresponding limit theorems are derived. These include functional and Darling–Erdős type limit theorems. The tests are shown to be consistent under alternatives of abrupt and gradual changes in the mean. Finite sample performance is examined by means of a simulation study, and the procedures are applied to the analysis of the average monthly temperatures in Prague.