PARKED · estimator noise
Hypothesis
A positive largest Lyapunov exponent $\lambda_1$ means sensitive dependence (chaos, low short-term predictability); $\lambda_1\to0$ windows are more forecastable.
Math — largest Lyapunov exponent
Average exponential divergence of nearby trajectories in the embedded phase space:
$$ \lambda_1 = \lim_{t\to\infty}\frac{1}{t}\ln\frac{\|\delta \mathbf{x}(t)\|}{\|\delta \mathbf{x}(0)\|} $$
Method
Rosenstein algorithm on delay-embedded returns; gate forecasting models to low-$\lambda_1$ windows.
Conceptually appealing, but $\lambda_1$ estimates on short, noisy financial windows are statistically unstable (the embedding and noise floor dominate). Parked: cannot get an estimator we trust at tradeable window lengths.
Chaos-theory invariants need long, clean, low-noise series. Financial windows are short and noise-saturated — the estimator measures the noise.