Jiajing Sun

Jiajing Sun

PhD, CFA, FIMA, Member of the London Mathematical Society. Associate Professor and the Deputy Director of the Department of Statistics and Data Science, School of Economics and Management, University of the Chinese Academy of Sciences.

Online Monitoring of Loading-Space Instability in Large Factor Models via Self-Normalized DFT Spectral Scores

Published:

This working paper studies real-time detection of factor loading instability in large approximate factor models. The motivating question is practical: after estimating a factor model on a clean Phase I training window, when do incoming data stop being consistent with the trained loading space? If the loading space drifts, PCA-based factor extraction can become contaminated and silently degrade forecasting/nowcasting and monitoring systems.

Our approach converts each new panel observation into a DFT spectral score curve by projecting it onto the frozen (Phase I) loading space. We then map the curve to a fixed-dimensional real score vector using either low-frequency grid vectorization or frequency-domain functional PCA, and run a CUSUM-style sequential monitor on these scores.

A key contribution is to make sequential calibration tuning-lean and robust by using self-normalization—avoiding bandwidth-sensitive long-run variance estimation and bootstrap calibration that can be fragile at short monitoring horizons.

Summary and Contribution:

We propose two self-normalized Fourier spectral score monitors for online change-point detection in factor loading spaces:

  1. SSMS: a Shao-type quadratic self-normalized sequential statistic.
  2. RSMS: an adjusted-range self-normalized sequential statistic that uses a partial-sum range normalizer and is more resilient to mild training-window contamination.

For both monitors, we develop:

  • KS-type (Kolmogorov–Smirnov) and CvM-type (Cramér–von Mises) stopping rules,
  • pivotal null limits and power properties,
  • ready-to-use critical values obtained by simulating the limiting Brownian-motion functionals.

Evidence:

Monte Carlo experiments under abrupt, smooth, heterogeneous, and staggered loading changes show that self-normalization yields substantially more stable false-alarm control than HAC-style studentization, which can be severely oversized at short horizons. Within the self-normalized family:

  • For KS-type rules, RSMS improves late-break detection and shortens conditional detection delays.
  • For CvM-type rules, SSMS paired with a late-emphasis weight offers a favorable size–power compromise.

Additional experiments indicate that adjusted-range self-normalization remains more resilient when the Phase I training window is mildly contaminated.

An empirical illustration using the FHFA metro house price index panel signals an alarm at 2005Q1, and the post-alarm analysis reveals heterogeneous metro-level shifts in factor exposures.

Availability:

The manuscript is not hosted on this website due to copyright considerations.