Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2019 013

Inference of Break-Points in High-Dimensional Time Series

Likai Chen
Weining Wang
Wei Biao Wu

We consider a new procedure for detecting structural breaks in mean for high-
dimensional time series. We target breaks happening at unknown time points and
locations. In particular, at a fixed time point our method is concerned with
either the biggest break in one location or aggregating simultaneous breaks over
multiple locations. We allow for both big or small sized breaks, so that we can
1), stamp the dates and the locations of the breaks, 2), estimate the break
sizes and 3), make inference on the break sizes as well as the break dates. Our
theoretical setup incorporates both temporal and crosssectional dependence, and
is suitable for heavy-tailed innovations. We derive the asymptotic distribution
for the sizes of the breaks by extending the existing powerful theory on local
linear kernel estimation and high dimensional Gaussian approximation to allow
for trend stationary time series with jumps. A robust long-run covariance matrix
estimation is proposed, which can be of independent interest. An application on
detecting structural changes of the US unemployment rate is considered to
illustrate the usefulness of our method.

high-dimensional time series, multiple change-points, Gaussian approximation,
nonparametric estimation, heavy tailed, long-run covariance matrix

JEL Classification: