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Methodology Papers

Research

Original research and methodology documentation behind the FractalCycles pipeline. Each paper is grounded in primary sources and worked examples on real OHLCV data.

The Statistical Validation Problem in Financial Cycle Detection

14 pages

Apparent cycles emerge in any sufficiently long financial price series, including pure random walks. This paper surveys the statistical validation problem at the heart of cycle detection and reviews three canonical tools imported into finance from older disciplines: Goertzel narrowband DFT, Bartels significance testing, and the Hurst exponent. We argue that detection without a strict null model is curve-fitting, and consolidate primary-source references to inform future cycle claims.

cycle detectionspectral analysisrandom walk nullHurst exponentBartels test
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Published April 30, 2026

Research papers describe methodology and observable structure. They are not predictions, price targets, or trading recommendations.Learn how we interpret cycles