Regime / Hurst

estimate_hurst_exponent fits a power-law slope to wavelet-leader scaling and returns a typed HurstResult with the Hurst exponent and a confidence interval. Track it over a rolling window for a regime classifier that needs no labelled training data.

When to use it

• You want an unsupervised regime signal: $H \approx 0.5$ is martingale (Brownian), $H < 0.5$ mean-reverts, $H > 0.5$ trends.
• You want a confidence interval on the estimate, not just a point value, before switching a strategy.
• You want a guard against feeding integrated inputs (prices) that would saturate the estimator.

Example

use ferro_wave::{Daubechies, DaubechiesType};
use ferro_wave::analysis::multifractal::{
    estimate_hurst_exponent, HurstResult, MultifractalConfig};
 
let wavelet = Daubechies::new(DaubechiesType::Db4);
let config  = MultifractalConfig::for_hurst_only();
 
let h: HurstResult = estimate_hurst_exponent(
    &log_returns, &wavelet, Some(config))?;
 
if h.saturated {
    // integrated input (prices, log-prices) — not a regime signal
    skip_regime_switch();
} else {
    match h.hurst_exponent {
        x if x < 0.45 => switch_to_mean_revert(),
        x if x > 0.55 => switch_to_trend_follow(),
        _ => keep_neutral(),
    }
}
// h.confidence_interval — half-width at config.confidence_level
// h.r_squared           — log-log fit quality
# Ok::<(), ferro_wave::WaveletError>(())

Notes

• Feed log-returns, not prices. An integrated input pins the estimator at the boundary and sets saturated = true rather than silently returning $H \approx 1.0$.
• The full multifractal spectrum H(q) is available via the same wavelet-leader estimator when you need intermittency, not just a single Hurst exponent.