  We provide the asymptotic minimax detection boundary for a bump, i.e. an
abrupt change, in the mean function of a stationary Gaussian process. This will
be characterized in terms of the asymptotic behavior of the bump length and
height as well as the dependency structure of the process. A major finding is
that the asymptotic minimax detection boundary is generically determined by the
value of its spectral density at zero. Finally, our asymptotic analysis is
complemented by non-asymptotic results for AR($p$) processes and confirmed to
serve as a good proxy for finite sample scenarios in a simulation study. Our
proofs are based on laws of large numbers for non-independent and
non-identically distributed arrays of random variables and the asymptotically
sharp analysis of the precision matrix of the process.
