  This paper concerns about the limiting distributions of change point
estimators, in a high-dimensional linear regression time series context, where
a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed
at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called
change points, the regression coefficients change, with the jump sizes measured
in $\ell_2$-norm. We provide limiting distributions of the change point
estimators in the regimes where the minimal jump size vanishes and where it
remains a constant. We allow for both the covariate and noise sequences to be
temporally dependent, in the functional dependence framework, which is the
first time seen in the change point inference literature. We show that a
block-type long-run variance estimator is consistent under the functional
dependence, which facilitates the practical implementation of our derived
limiting distributions. We also present a few important byproducts of our
analysis, which are of their own interest. These include a novel variant of the
dynamic programming algorithm to boost the computational efficiency, consistent
change point localisation rates under temporal dependence and a new Bernstein
inequality for data possessing functional dependence. Extensive numerical
results are provided to support our theoretical results. The proposed methods
are implemented in the R package \texttt{changepoints} \citep{changepoints_R}.
