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//! Forecastability fingerprint — compact summary of a series' predictive
//! structure.
//!
//! Mirrors the "information geometry" workflow from `dependence-forecastability`:
//! compute AMI + GCMI curves, test significance against phase surrogates,
//! and distill into a handful of interpretable summary statistics.
use super::ami::{ami_curve, gcmi_curve};
use super::surrogates::significance_bands;
/// Compact forecastability fingerprint.
#[derive(Debug, Clone)]
pub struct ForecastabilityFingerprint {
/// Mean AMI across lags where AMI exceeds the 3σ threshold.
/// Normalized by `max_lag` so values are comparable across different
/// lag settings. Range: typically 0–5 (0 = no signal).
pub information_mass: f64,
/// Last lag where AMI exceeds the 3σ threshold.
/// Higher = deeper temporal dependence.
pub information_horizon: usize,
/// Entropy of the significant AMI profile (normalized to [0, 1]).
/// Higher = more evenly distributed dependence across lags.
pub information_structure: f64,
/// `1 − (sum of significant GCMI) / (sum of significant AMI)`.
/// Higher = more nonlinear dependence (AMI captures it but GCMI doesn't).
pub nonlinear_share: f64,
/// Peak AMI / mean surrogate AMI at the same lag.
/// Higher = stronger signal relative to noise.
pub signal_to_noise: f64,
/// `AMI(1) / total_significant_ami` — how concentrated the dependence
/// is at the first lag vs spread across all lags.
pub directness_ratio: f64,
/// Which lag indices (1-based) have AMI exceeding the 3σ threshold.
pub informative_horizons: Vec<usize>,
/// The raw AMI curve.
pub ami: Vec<f64>,
/// The raw GCMI curve.
pub gcmi: Vec<f64>,
/// Surrogate 3σ threshold for AMI (`mean + 3 * std`).
pub surrogate_threshold: Vec<f64>,
/// Surrogate mean for AMI.
pub surrogate_mean: Vec<f64>,
/// Surrogate std for AMI.
pub surrogate_std: Vec<f64>,
}
impl ForecastabilityFingerprint {
/// Compute the forecastability fingerprint for a series.
///
/// # Arguments
/// * `series` — the time series to analyze
/// * `max_lag` — number of lags to probe (default: ~n/5 or 20)
/// * `n_surrogates` — number of phase surrogates for significance testing
/// (default: 100)
/// * `alpha` — significance level (default: 0.05)
/// * `seed` — optional RNG seed for reproducibility
pub fn compute(
series: &[f64],
max_lag: usize,
n_surrogates: usize,
alpha: f64,
seed: Option<u64>,
) -> Self {
let ami = ami_curve(series, max_lag);
let gcmi = gcmi_curve(series, max_lag);
// Compute surrogate significance bands for AMI.
let bands = significance_bands(series, ami_curve, max_lag, n_surrogates, alpha, seed);
// Identify informative horizons: where AMI > 3σ threshold.
// The 3σ parametric test (mean + 3*std) is more selective than the
// rank-based percentile upper band, matching the Python original.
let informative_horizons: Vec<usize> = (0..max_lag)
.filter(|&i| ami[i] > bands.threshold_3sigma[i])
.map(|i| i + 1) // 1-based
.collect();
// Information mass: mean significant AMI, normalized by max_lag.
// This makes the value comparable across different max_lag settings.
let total_significant_ami: f64 = informative_horizons.iter().map(|&h| ami[h - 1]).sum();
let information_mass = if max_lag > 0 {
total_significant_ami / max_lag as f64
} else {
0.0
};
// Information horizon: last significant lag.
let information_horizon = informative_horizons.last().copied().unwrap_or(0);
// Information structure: entropy of significant AMI profile.
let information_structure = if total_significant_ami > 1e-15 {
let probs: Vec<f64> = informative_horizons
.iter()
.map(|&h| ami[h - 1] / total_significant_ami)
.collect();
let k = probs.len() as f64;
if k <= 1.0 {
0.0
} else {
let h: f64 = probs
.iter()
.filter(|&&p| p > 1e-15)
.map(|&p| -p * p.ln())
.sum();
h / k.ln() // normalize to [0, 1]
}
} else {
0.0
};
// Nonlinear share: 1 − (sum significant GCMI) / (sum significant AMI).
let gcmi_mass: f64 = informative_horizons
.iter()
.map(|&h| gcmi[h - 1].max(0.0))
.sum();
let nonlinear_share = if total_significant_ami > 1e-15 {
(1.0 - gcmi_mass / total_significant_ami).clamp(0.0, 1.0)
} else {
0.0
};
// Signal-to-noise: peak AMI / mean surrogate AMI at the peak lag.
let (peak_idx, peak_ami) = ami
.iter()
.enumerate()
.max_by(|a, b| a.1.partial_cmp(b.1).unwrap())
.unwrap_or((0, &0.0));
let surr_mean_at_peak = bands.mean.get(peak_idx).copied().unwrap_or(1.0).max(1e-15);
let signal_to_noise = peak_ami / surr_mean_at_peak;
// Directness ratio.
let directness_ratio = if total_significant_ami > 1e-15 {
ami[0] / total_significant_ami
} else {
0.0
};
Self {
information_mass,
information_horizon,
information_structure,
nonlinear_share,
signal_to_noise,
directness_ratio,
informative_horizons,
ami,
gcmi,
surrogate_threshold: bands.threshold_3sigma,
surrogate_mean: bands.mean,
surrogate_std: bands.std,
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use rand::{Rng, SeedableRng};
fn make_ar1(n: usize, phi: f64, seed: u64) -> Vec<f64> {
let mut rng = rand::rngs::StdRng::seed_from_u64(seed);
let mut s = Vec::with_capacity(n);
s.push(0.0);
for _ in 1..n {
let noise = (rng.gen::<f64>() - 0.5) * 2.0;
s.push(phi * *s.last().unwrap() + noise);
}
s
}
#[test]
fn fingerprint_ar1_has_signal() {
let series = make_ar1(500, 0.8, 42);
let fp = ForecastabilityFingerprint::compute(&series, 10, 30, 0.05, Some(1));
assert!(
fp.information_mass > 0.0,
"AR(1) should have positive information mass"
);
assert!(
fp.information_horizon >= 1,
"AR(1) should have at least 1 informative horizon"
);
assert!(fp.signal_to_noise > 1.0, "SNR should exceed 1 for AR(1)");
}
#[test]
fn fingerprint_white_noise_has_little_signal() {
let mut rng = rand::rngs::StdRng::seed_from_u64(99);
let series: Vec<f64> = (0..500).map(|_| (rng.gen::<f64>() - 0.5) * 2.0).collect();
let fp = ForecastabilityFingerprint::compute(&series, 10, 50, 0.05, Some(2));
// White noise may still have 1-2 false positives at α=0.05.
assert!(
fp.informative_horizons.len() <= 3,
"white noise should have few informative horizons: {:?}",
fp.informative_horizons
);
}
}