Online Monitoring of Structural Change with Adjusted-Range Self-Normalization
Published:
This working paper connects two central themes in economic statistics: self-normalization and sequential change-point detection. Self-normalization provides tuning-free inference for dependent, heteroskedastic time series by avoiding long-run variance (LRV) estimation and its fragile bandwidth/kernel choices, while delivering pivotal limits under weak conditions.
An adjusted-range-based self-normalizer refines classical (Shao’s) self-normalization by using the partial-sum range rather than quadratic variation; it is less sensitive to mild contamination in the training window and grows more slowly under level shifts, thereby preserving monotonic power and robustness without extra tuning.
Sequential change-point detection is crucial in real time—when the operative question is whether today’s data remain consistent with yesterday’s model—so procedures must control false alarms while signaling quickly. By combining adjusted-range self-normalization with a CUSUM monitor, our method offers size-stable, tuning-free thresholds and improved detection efficiency, yielding higher power and shorter average run lengths (ARLs) in practice.
Summary and Contribution:
We develop an online change-point detector—RSMS, a CUSUM-based, adjusted-range self-normalized monitoring scheme—that avoids long-run variance estimation and all tuning choices (bandwidths, kernels, block lengths). We provide finite- and open-horizon asymptotics with ready-to-use critical values and practical guidance on a small early-detection weight.
Relative to quadratic (Shao’s) self-normalization, the adjusted range curbs normalizer inflation and is more robust to mild contamination in the training window. The procedure attains correct size under the null hypothesis and consistency under the alternative hypothesis.
Evidence:
Extensive simulations (VARs with homoskedastic/heteroskedastic errors and a PAR(1) count model) show that RSMS delivers more reliable size, higher power, and shorter ARLs than:
- The self-normalized scheme of Chan et al. (2021)
- Standard HAC–CUSUM monitors
In the appendix, we show that RSMS remains power-stable and continues to reduce ARLs even when the training sample is contaminated—a realistic setting because type II errors and rolling re-estimation can push shifted observations into the training window. An empirical study of functional USD/GBP data around the 2016 EU referendum and COVID-19 shows that RSMS flags major breaks promptly, often earlier than alternatives and frequently with the shortest ARL.
R Code and Availability:
You can access the R code at Zenodo. The manuscript is not hosted on this website due to copyright considerations.