Spectral Regime Detection: Change-Point Identification via Eigenmode Drift

We introduce spectral regime detection: a method to identify structural breaks in time series and panel data by monitoring the drift of spectral coefficients over sliding windows. The key insight is that a regime change is a jump in the spectral representation of the data-generating process — the coefficient vector \(A = (A_1, \ldots, A_K)\) moves discontinuously when the underlying regression relationship changes.

The method requires a shared eigenbasis across windows, computed once from a reference period. Each window's data is projected onto this basis, yielding comparable coefficient vectors. The drift \(d_t = \|A_t - A_{t-1}\|\) between consecutive windows is monitored. Under a stable regime, drift is \(O(\sigma/\sqrt{n_{window}})\); at a regime change, drift spikes to \(O(\|\beta_{new} - \beta_{old}\|)\).

On synthetic data with known regime changes at \(t = 500\) and \(t = 800\) (structural break in regression coefficients), the detector identifies both changes with 20–40 sample lag and 6–10x drift spike relative to within-regime fluctuation. The method requires no distributional assumptions, works with any number of features, and naturally adapts to the signal-to-noise ratio through the spectral shrinkage filter.