When to Refresh a Functional Representation: Online Monitoring of Structural Change in Functional Time Series
Published:
This working paper asks when a functional representation estimated in an earlier regime should be refreshed as new functional observations arrive. The motivating examples include yield curves, volatility profiles, option-implied surfaces, and high-frequency return curves, where the economically relevant signal may lie in shape, slope, curvature, or intraday timing rather than in a single scalar summary.
Authors:
Jiajing Sun, Meiting Zhu, Wolfgang Karl Härdle, Oliver Linton, and Zhuo Lin.
Summary and Contribution:
The paper studies online monitoring of structural change in functional time series after training-anchored FPCA compression. An initial stable training sample is used to estimate the curve representation, which is then held fixed while incoming curves are monitored sequentially. A monitoring alarm is interpreted as a model-maintenance signal: the old representation should be refreshed before inference or decision rules drift too far from the current regime.
The paper compares:
- HAC-based monitoring
- Shao-type quadratic self-normalization
- adjusted-range self-normalization
for both KS-type and weighted Cramer-von Mises monitoring rules.
Evidence:
The simulations and empirical analysis suggest that adjusted-range self-normalization offers a favorable calibration-detection trade-off. In an application to 1-minute S&P 500 return curves, the main monitoring horizon signals on February 27, 2020, while a comparable HAC benchmark signals later, around April 1-2, 2020.