  This paper studies multivariate nonparametric change point localization and
inference problems. The data consists of a multivariate time series with
potentially short range dependence. The distribution of this data is assumed to
be piecewise constant with densities in a H\"{o}lder class. The change points,
or times at which the distribution changes, are unknown. We derive the limiting
distributions of the change point estimators when the minimal jump size
vanishes or remains constant, a first in the literature on change point
settings. We are introducing two new features: a consistent estimator that can
detect when a change is happening in data with short-term dependence, and a
consistent block-type long-run variance estimator. Numerical evidence is
provided to back up our theoretical results.
