# Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series

arXiv: https://arxiv.org/abs/2304.07003 · HTML: https://mlsanity.com/paper/2304.07003/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 14 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Multiple-change-point detection for high dimensional time series via sparsified binary segmentation](https://mlsanity.com/paper/1611.08639/) (2016)
- [High-dimensional changepoint estimation via sparse projection](https://mlsanity.com/paper/1606.06246/) (2016)
- [Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models](https://mlsanity.com/paper/1711.07357/) (2017)
- [Power Enhancement in High Dimensional Cross-Sectional Tests](https://mlsanity.com/paper/1310.3899/) (2013)
- [Simultaneous multiple change-point and factor analysis for high-dimensional time series](https://mlsanity.com/paper/1612.06928/) (2016)
- [Clustering and Forecasting Multiple Functional Time Series](https://mlsanity.com/paper/2201.01024/) (2022)
- [Detecting and dating structural breaks in functional data without dimension reduction](https://mlsanity.com/paper/1511.04020/) (2015)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Functional Neural Networks](https://mlsanity.com/paper/2503.21585/) (2025)

## Abstract (arXiv)

In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution theory comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where the proposed test has power, and results in stable power performance when breaks are sparse in the alternative hypothesis. Furthermore, we impose a latent group structure on the subjects with heterogeneous break points and introduce an easy-to-implement clustering algorithm with an information criterion to consistently estimate the unknown group number and membership. The estimated group structure can subsequently improve the convergence property of the post-clustering break point estimate. Monte-Carlo simulation studies and empirical applications show that the proposed estimation and testing techniques have satisfactory performance in finite samples.