Polyphonic Stationarity

A way of measuring stationarity by treating a time series as a musical fugue. Decompose via FFT into four voices at target frequencies (252, 126, 63, 31 trading days). Score how.

stationarity regime-detection frequency-decomposition financial-markets heuristic-algebra
concept Updated 2026-04-10

Polyphonic Stationarity

A way of measuring stationarity by treating a time series as a musical fugue. Decompose via FFT into four voices at target frequencies (252, 126, 63, 31 trading days). Score how well the voices stay in tune. When they go out of tune — regime shift.

The metric

Polyphonic Drift Score (PDS), 0–1. Aggregates:

  • Amplitude stability across voices
  • Phase-locking between voices
  • Inter-voice coupling
  • Consonance ratios mapped to musical intervals (unison = 1.0, tritone = low)

PDS ≥ 0.75 = stationary. Sharp drop = drift detected.

Three findings

  1. Stationarity is per-voice, not aggregate (SFF1). Global tests like ADF mask frequency-specific breaks.
  2. The keynote is invariant (SFF2). Longest-horizon pair (126–252) maintains 100% consonance.
  3. Breaks start in the middle (SFF3). Mid-range frequencies (63–126) are the fragile zone.

The central result

Stationarity breaks are not forecastable from market data. Three tests — orbital (internal topology), tuning (autocorrelation), spiderweb (cross-market coupling) — all falsified predictability. Consonance is a strictly local property of each market’s internal frequency spectrum. Price coupling (41.2% hit rate via FIIJ) outperforms consonance coupling (~0%).

The value of the metric is detection, not prediction. It tells you which voice broke, how late you detected it, and when to stop trusting a scaffold built on the old regime.

Tools

  • Lag Sum Estimator — total detection lag = statistical + fidelity + cognitive tax
  • Atomic Fragility Flip — triggers on independence collapse
  • Conservation Triple Audit — theory/measurement/bias check per LJ6
  • Drift-Decay Parallel Plot — lockstep confirmation

Relationship to other work

Built on heuristic-algebra operators (⊕ha, ⊕inn, ¬, π). Research governed by lucid-judgment — LJ4 crossed the thinking-acting threshold after the spiderweb test, retiring prediction-seeking in favor of detection-lag minimization. Directly relevant to the-silk-report, which operates on the same interconnected markets.

See Also