Monitoring Structural Change

TLDR

Contemporary structural‑change tests detect one‑shot breaks, but the law of the iterated logarithm prevents them from monitoring out‑of‑sample stability without generating false positives. We propose and analyze two real‑time monitoring procedures—fluctuation and CUSUM—with asymptotically controlled size. Our approach extends an invariance principle from sequential testing to derive these monitoring results. Simulations confirm the procedures maintain asymptotic size, and detection timing varies with the magnitude of the parameter change, the signal‑to‑noise ratio, and the break point’s location.

Abstract

Contemporary tests for structural change deal with detections of the one-shot type: given an historical data set of fixed size, these tests are designed to detect a structural break within the data set. Due to the law of the iterated logarithm, one-shot tests cannot be applied to monitor out-of-sample stability each time new data arrive without signalling a nonexistent break with probability one. We propose and analyze two real-time monitoring procedures with controlled size asymptotically: the fluctuation and CUSUM monitoring procedures. We extend an invariance principle in the sequential testing literature to obtain our results. Simulation results show that the proposed monitoring procedures indeed have controlled asymptotic size. Detection timing depends on the magnitude of parameter change, the signal to noise ratio, and the location of the out-of-sample break point.