## The Annals of Applied Statistics

### Identifying multiple changes for a functional data sequence with application to freeway traffic segmentation

#### Abstract

Motivated by the study of road segmentation partitioned by shifts in traffic conditions along a freeway, we introduce a two-stage procedure, Dynamic Segmentation and Backward Elimination (DSBE), for identifying multiple changes in the mean functions for a sequence of functional data. The Dynamic Segmentation procedure searches for all possible changepoints using the derived global optimality criterion coupled with the local strategy of at-most-one-changepoint by dividing the entire sequence into individual subsequences that are recursively adjusted until convergence. Then, the Backward Elimination procedure verifies these changepoints by iteratively testing the unlikely changes to ensure their significance until no more changepoints can be removed. By combining the local strategy with the global optimal changepoint criterion, the DSBE algorithm is conceptually simple and easy to implement and performs better than the binary segmentation-based approach at detecting small multiple changes. The consistency property of the changepoint estimators and the convergence of the algorithm are proved. We apply DSBE to detect changes in traffic streams through real freeway traffic data. The practical performance of DSBE is also investigated through intensive simulation studies for various scenarios.

#### Article information

Source
Ann. Appl. Stat., Volume 13, Number 3 (2019), 1430-1463.

Dates
Received: May 2018
Revised: October 2018
First available in Project Euclid: 17 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1571277759

Digital Object Identifier
doi:10.1214/19-AOAS1242

Mathematical Reviews number (MathSciNet)
MR4019145

#### Citation

Chiou, Jeng-Min; Chen, Yu-Ting; Hsing, Tailen. Identifying multiple changes for a functional data sequence with application to freeway traffic segmentation. Ann. Appl. Stat. 13 (2019), no. 3, 1430--1463. doi:10.1214/19-AOAS1242. https://projecteuclid.org/euclid.aoas/1571277759

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#### Supplemental materials

• Additional simulation results. We provide additional simulation results of Section 5.4 for DSBE, BScust and CBSec with the sample size $N=100$ in comparison with those with $N=200$.