Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2020 019

Inference of breakpoints in high-dimensional time series

Likai Chen
Weining Wang
Wei Biao Wu

Abstract:
For multiple change-points detection of high-dimensional time series, we provide
asymptotic theory concerning the consistency and the asymptotic distribution of
the breakpoint statistics and estimated break sizes. The theory backs up a
simple two- step procedure for detecting and estimating multiple change-points.
The proposed two-step procedure involves the maximum of a MOSUM (moving sum)
type statistics in the rst step and a CUSUM (cumulative sum) re nement step on
an aggregated time series in the second step. Thus, for a xed time-point, we
can capture both the biggest break across di erent coordinates and aggregating
simultaneous breaks over multiple coordinates. Extending the existing high-
dimensional Gaussian approxima- tion theorem to dependent data with jumps, the
theory allows us to characterize the size and power of our multiple change-point
test asymptotically. Moreover, we can make inferences on the breakpoints
estimates when the break sizes are small. Our theoretical setup incorporates
both weak temporal and strong or weak cross-sectional dependence and is suitable
for heavy-tailed innovations. A robust long-run covariance matrix estimation is
proposed, which can be of independent interest. An application on detecting
structural changes of the U.S. unemployment rate is considered to illus- trate
the usefulness of our method.

Keywords:
multiple change points detection; temporal and cross-sectional dependence;
Gaussian approximation; inference of break locations

JEL Classification:
C00