  Detecting and localizing change points in sequential data is of interest in
many areas of application. Various notions of change points have been proposed,
such as changes in mean, variance, or the linear regression coefficient. In
this work, we consider settings in which a response variable $Y$ and a set of
covariates $X=(X^1,\ldots,X^{d+1})$ are observed over time and aim to find
changes in the causal mechanism generating $Y$ from $X$. More specifically, we
assume $Y$ depends linearly on a subset of the covariates and aim to determine
at what time points either the dependency on the subset or the subset itself
changes. We call these time points causal change points (CCPs) and show that
they form a subset of the commonly studied regression change points. We propose
general methodology to both detect and localize CCPs. Although motivated by
causality, we define CCPs without referencing an underlying causal model. The
proposed definition of CCPs exploits a notion of invariance, which is a purely
observational quantity but -- under additional assumptions -- has a causal
meaning. For CCP localization, we propose a loss function that can be combined
with existing multiple change point algorithms to localize multiple CCPs
efficiently. We evaluate and illustrate our methods on simulated datasets.
