What question did this study set out to answer?

The study aims to differentiate deterministic chaotic dynamics from periodic behaviors and stochastic noise in univariate time series using a novel statistical method.

February 26, 2026Open Access

Seeking Structural Patterns in Time Series with Diophantine Approximations

Puntos clave

The study aims to differentiate deterministic chaotic dynamics from periodic behaviors and stochastic noise in univariate time series using a novel statistical method.
Introduced the Diophantine Dynamical Boundary Method (DDBM) for analysis.
Implemented rank-normalization and two-level residualization.
Applied lattice quantization and cubic Diophantine phase extraction.
Employed Kolmogorov–Smirnov statistics for testing phase non-uniformity.
Successfully distinguishes between chaotic dynamics, periodic behavior, and noise in time series.
Demonstrates effectiveness even with moderate sample sizes.
Eliminates the need for hyperparameter tuning and training data.

Resumen

We introduce the Diophantine Dynamical Boundary Method (DDBM), a lattice‑based statistical procedure for distinguishing deterministic chaotic dynamics from periodic behavior and stochastic noise in univariate time series. DDBM applies rank‑normalization, two‑level residualization, lattice quantization, and cubic Diophantine phase extraction, then tests for phase non‑uniformity via Kolmogorov–Smirnov statistics with multiple‑testing correction. The method operates directly on scalar observables without phase‑space reconstruction, hyperparameter tuning, or training data, and remains effective for moderate sample sizes.

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