  Tests for structural breaks in time series should ideally be sensitive to
breaks in the parameter of interest, while being robust to nuisance changes.
Statistical analysis thus needs to allow for some form of nonstationarity under
the null hypothesis of no change. In this paper, estimators for integrated
parameters of locally stationary time series are constructed and a
corresponding functional central limit theorem is established, enabling
change-point inference for a broad class of parameters under mild assumptions.
The proposed framework covers all parameters which may be expressed as
nonlinear functions of moments, for example kurtosis, autocorrelation, and
coefficients in a linear regression model. To perform feasible inference based
on the derived limit distribution, a bootstrap variant is proposed and its
consistency is established. The methodology is illustrated by means of a
simulation study and by an application to high-frequency asset prices.
