Online Monitoring of Structural Change with Adjusted-Range Self-Normalization
Published:
Status: Working paper.
Authors:
Meiting Zhu, Yongmiao Hong, Jiajing Sun, and Oliver Linton.
This working paper connects two central themes in economic statistics: self-normalization and online structural-change monitoring. The goal is to detect, in real time, when incoming time-series observations no longer conform to the training-sample regime.
The paper proposes an adjusted-range self-normalized monitoring scheme (RSMS) for online detection of structural change. Unlike CUSUM procedures based on heteroskedasticity- and autocorrelation-consistent long-run variance estimation, RSMS requires no kernel, bandwidth, or block-length choice.
Summary and Contribution:
The central methodological idea is to replace the quadratic training-window self-normalizer used in standard online self-normalized monitoring with the range of centered training partial sums. With a clean training sample, the distinction mainly changes the limiting constants. With contaminated training observations, however, drift can inflate the quadratic normalizer and compress the monitoring statistic; the adjusted-range normalizer is designed to be more resilient in this setting.
The paper derives finite- and open-horizon null limits, fixed-alternative consistency, local-power limits, post-break delay implications, and contaminated-training results. It also studies when clean-training critical values remain valid under mild training-sample contamination.
Evidence:
Simulations show that RSMS has higher post-break detection probabilities than standard self-normalized monitoring in many designs, while delivering size-adjusted performance that is competitive with HAC-CUSUM monitoring.
An empirical application to high-frequency USD/GBP exchange-rate data around the 2016 UK referendum and the 2020 COVID-19 turmoil gives economically interpretable alarms and illustrates how adjusted-range self-normalization can improve online monitoring in financial time series.
Keywords:
Conditional average detection delay; cumulative sum monitoring; empirical processes; high-frequency data; long-run variance.
R Code and Availability:
Replication code for the revised manuscript is available at Zenodo. The deposit contains the R package for critical-value calculations, finite-horizon and open-end monitoring boundaries, simulation studies, robustness checks, and empirical application scripts. The manuscript is not hosted on this website due to copyright considerations.