  Motivated by an example from remote sensing of gas emission sources, we
derive two novel change point procedures for multivariate time series where, in
contrast to classical change point literature, the changes are not required to
be aligned in the different components of the time series. Instead the change
points are described by a functional relationship where the precise shape
depends on unknown parameters of interest such as the source of the gas
emission in the above example. Two different types of tests and the
corresponding estimators for the unknown parameters describing the change
locations are proposed. We derive the null asymptotics for both tests under
weak assumptions on the error time series and show asymptotic consistency under
alternatives. Furthermore, we prove consistency for the corresponding
estimators of the parameters of interest. The small sample behavior of the
methodology is assessed by means of a simulation study and the above remote
sensing example analyzed in detail.
