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//! Rolling Pearson correlation of the period-over-period *returns* of two series.
use std::collections::VecDeque;
use crate::error::{Error, Result};
use crate::traits::Indicator;
/// Rolling correlation of the **returns** of two synchronised series.
///
/// Where [`crate::PearsonCorrelation`] correlates the raw *levels* `(x, y)`,
/// this indicator first differences each channel into a one-step return and
/// correlates those returns over the trailing window:
///
/// ```text
/// rxₜ = xₜ − xₜ₋₁ ryₜ = yₜ − yₜ₋₁
/// corr = cov(rx, ry) / √(var(rx) · var(ry))
/// ```
///
/// Return correlation is the quantity that matters for hedging and portfolio
/// risk: two assets can trend together (high level correlation) while their
/// day-to-day moves are nearly independent (low return correlation). The output
/// is in `[−1, +1]`; a flat return channel makes the ratio undefined and the
/// indicator reports `0` rather than `NaN`. The value is clamped to `[−1, +1]`
/// to absorb tiny floating-point overshoots near the boundaries.
///
/// Each `update` is O(1): the five running sums (`Σrx`, `Σry`, `Σrx²`, `Σry²`,
/// `Σrxry`) are maintained as the window of returns slides. The first level in
/// each channel produces no return, so a `period`-pair correlation needs
/// `period + 1` updates of warmup.
///
/// # Example
///
/// ```
/// use wickra_core::{Indicator, RollingCorrelation};
///
/// let mut rc = RollingCorrelation::new(10).unwrap();
/// let mut last = None;
/// for i in 0..40 {
/// // A varying path where y always moves with x ⇒ return correlation +1.
/// let x = (f64::from(i) * 0.5).sin() * 10.0;
/// last = rc.update((x, 2.0 * x));
/// }
/// assert!((last.unwrap() - 1.0).abs() < 1e-9);
/// ```
#[derive(Debug, Clone)]
pub struct RollingCorrelation {
period: usize,
prev: Option<(f64, f64)>,
window: VecDeque<(f64, f64)>,
sum_x: f64,
sum_y: f64,
sum_xx: f64,
sum_yy: f64,
sum_xy: f64,
}
impl RollingCorrelation {
/// Construct a new rolling return-correlation.
///
/// # Errors
/// Returns [`Error::InvalidPeriod`] if `period < 2` — correlation is
/// undefined for fewer than two return pairs.
pub fn new(period: usize) -> Result<Self> {
if period < 2 {
return Err(Error::InvalidPeriod {
message: "rolling correlation needs period >= 2",
});
}
Ok(Self {
period,
prev: None,
window: VecDeque::with_capacity(period),
sum_x: 0.0,
sum_y: 0.0,
sum_xx: 0.0,
sum_yy: 0.0,
sum_xy: 0.0,
})
}
/// Configured window of returns.
pub const fn period(&self) -> usize {
self.period
}
}
impl Indicator for RollingCorrelation {
type Input = (f64, f64);
type Output = f64;
fn update(&mut self, input: (f64, f64)) -> Option<f64> {
let (x, y) = input;
let Some((px, py)) = self.prev else {
// First level in each channel: store it, no return yet.
self.prev = Some((x, y));
return None;
};
self.prev = Some((x, y));
let (rx, ry) = (x - px, y - py);
if self.window.len() == self.period {
let (ox, oy) = self.window.pop_front().expect("non-empty");
self.sum_x -= ox;
self.sum_y -= oy;
self.sum_xx -= ox * ox;
self.sum_yy -= oy * oy;
self.sum_xy -= ox * oy;
}
self.window.push_back((rx, ry));
self.sum_x += rx;
self.sum_y += ry;
self.sum_xx += rx * rx;
self.sum_yy += ry * ry;
self.sum_xy += rx * ry;
if self.window.len() < self.period {
return None;
}
let n = self.period as f64;
let mean_x = self.sum_x / n;
let mean_y = self.sum_y / n;
let var_x = (self.sum_xx / n - mean_x * mean_x).max(0.0);
let var_y = (self.sum_yy / n - mean_y * mean_y).max(0.0);
let cov = self.sum_xy / n - mean_x * mean_y;
let denom = (var_x * var_y).sqrt();
if denom == 0.0 {
// At least one return channel is flat: correlation is undefined.
return Some(0.0);
}
Some((cov / denom).clamp(-1.0, 1.0))
}
fn reset(&mut self) {
self.prev = None;
self.window.clear();
self.sum_x = 0.0;
self.sum_y = 0.0;
self.sum_xx = 0.0;
self.sum_yy = 0.0;
self.sum_xy = 0.0;
}
fn warmup_period(&self) -> usize {
self.period + 1
}
fn is_ready(&self) -> bool {
self.window.len() == self.period
}
fn name(&self) -> &'static str {
"RollingCorrelation"
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::traits::BatchExt;
use approx::assert_relative_eq;
#[test]
fn rejects_period_below_two() {
assert!(RollingCorrelation::new(0).is_err());
assert!(RollingCorrelation::new(1).is_err());
assert!(RollingCorrelation::new(2).is_ok());
}
#[test]
fn accessors_and_metadata() {
let rc = RollingCorrelation::new(14).unwrap();
assert_eq!(rc.period(), 14);
assert_eq!(rc.warmup_period(), 15);
assert_eq!(rc.name(), "RollingCorrelation");
assert!(!rc.is_ready());
}
#[test]
fn warmup_needs_period_plus_one() {
let mut rc = RollingCorrelation::new(3).unwrap();
// First update only seeds the previous level ⇒ None.
assert_eq!(rc.update((1.0, 1.0)), None);
assert_eq!(rc.update((2.0, 3.0)), None); // 1 return
assert_eq!(rc.update((3.0, 5.0)), None); // 2 returns
assert!(rc.update((4.0, 7.0)).is_some()); // 3 returns ⇒ ready
assert!(rc.is_ready());
}
#[test]
fn comoving_returns_are_plus_one() {
// y always moves by 2x x's move ⇒ perfectly correlated returns.
let pairs: Vec<(f64, f64)> = (0..20)
.map(|i| {
let x = (f64::from(i) * 0.5).sin() * 10.0;
(x, 2.0 * x + 100.0)
})
.collect();
let last = RollingCorrelation::new(8)
.unwrap()
.batch(&pairs)
.into_iter()
.flatten()
.last()
.unwrap();
assert_relative_eq!(last, 1.0, epsilon = 1e-9);
}
#[test]
fn opposing_returns_are_minus_one() {
let pairs: Vec<(f64, f64)> = (0..20)
.map(|i| {
let x = (f64::from(i) * 0.5).sin() * 10.0;
(x, -1.5 * x + 50.0)
})
.collect();
let last = RollingCorrelation::new(8)
.unwrap()
.batch(&pairs)
.into_iter()
.flatten()
.last()
.unwrap();
assert_relative_eq!(last, -1.0, epsilon = 1e-9);
}
#[test]
fn flat_return_channel_yields_zero() {
// y is constant ⇒ its returns are all zero ⇒ undefined ⇒ 0.
let pairs: Vec<(f64, f64)> = (0..20).map(|i| (f64::from(i), 7.0)).collect();
let last = RollingCorrelation::new(6)
.unwrap()
.batch(&pairs)
.into_iter()
.flatten()
.last()
.unwrap();
assert_relative_eq!(last, 0.0, epsilon = 1e-12);
}
#[test]
fn output_in_range() {
let pairs: Vec<(f64, f64)> = (0..80)
.map(|i| {
let t = f64::from(i);
(100.0 + t.sin() * 5.0, 50.0 + (t * 0.3).cos() * 3.0)
})
.collect();
let mut rc = RollingCorrelation::new(20).unwrap();
for v in rc.batch(&pairs).into_iter().flatten() {
assert!((-1.0..=1.0).contains(&v));
}
}
#[test]
fn reset_clears_state() {
let mut rc = RollingCorrelation::new(4).unwrap();
rc.batch(&[(1.0, 2.0), (2.0, 4.0), (3.0, 6.0), (4.0, 8.0), (5.0, 10.0)]);
assert!(rc.is_ready());
rc.reset();
assert!(!rc.is_ready());
assert_eq!(rc.update((1.0, 1.0)), None);
}
#[test]
fn batch_equals_streaming() {
let pairs: Vec<(f64, f64)> = (0..60)
.map(|i| {
let t = f64::from(i);
(t.sin(), (t * 0.5).cos())
})
.collect();
let batch = RollingCorrelation::new(14).unwrap().batch(&pairs);
let mut rc = RollingCorrelation::new(14).unwrap();
let streamed: Vec<_> = pairs.iter().map(|p| rc.update(*p)).collect();
assert_eq!(batch, streamed);
}
}