Struct SpreadAr1Coefficient 

pub struct SpreadAr1Coefficient { /* private fields */ }

First-order autoregression coefficient ρ of the spread a − b.

Each update takes one (a, b) price pair and forms the spread sₜ = aₜ − bₜ. Over the trailing window of period spreads the indicator fits the discrete AR(1) model by ordinary least squares of the level on its own lag:

sₜ = ρ · sₜ₋₁ + c + εₜ
ρ  = cov(sₜ₋₁, sₜ) / var(sₜ₋₁)

ρ is the direct measure of cointegration / mean-reversion strength of the pair:

• ρ near 0 — the spread snaps back to its mean almost instantly (very strong mean reversion).
• ρ near 1 — the spread behaves like a random walk (a unit root: no reliable reversion, the pair is not cointegrated).
• ρ > 1 — the spread is explosive (diverging).

This is the complement of OuHalfLife: the OU half-life is −ln(2) / ln(ρ) for 0 < ρ < 1, but ρ itself is the raw, unbounded stationarity statistic many pairs-trading screens threshold on directly (e.g. “trade only pairs with ρ < 0.9”). When the spread is flat over the window (var(sₜ₋₁) = 0) the regression slope is undefined and the indicator returns 0.

Each update is O(period): the OLS slope is recomputed from the window’s running geometry.

Example

use wickra_core::{Indicator, SpreadAr1Coefficient};

let mut ar1 = SpreadAr1Coefficient::new(40).unwrap();
let mut last = None;
for t in 0..120 {
    let b = 100.0 + f64::from(t);
    // `a` hugs `b` with a fast mean-reverting wobble ⇒ ρ well below 1.
    let a = b + 2.0 * (f64::from(t) * 0.9).sin();
    last = ar1.update((a, b));
}
let rho = last.unwrap();
assert!(rho > 0.0 && rho < 1.0);

Implementations

impl SpreadAr1Coefficient

pub fn new(period: usize) -> Result<Self>

Construct a new AR(1) spread-coefficient estimator.

Errors

Returns Error::InvalidPeriod if period < 3 — the AR(1) regression needs at least two (level, next) observations (a slope and an intercept).

pub const fn period(&self) -> usize

Configured look-back window of spreads.

Trait Implementations

impl Clone for SpreadAr1Coefficient

fn clone(&self) -> SpreadAr1Coefficient

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SpreadAr1Coefficient

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Indicator for SpreadAr1Coefficient

type Input = (f64, f64)

Type of one input data point (typically f64 for a price, or Candle / Tick).

type Output = f64

Type of one output value.

fn update(&mut self, input: (f64, f64)) -> Option<f64>

Feed one new data point into the indicator and return the freshly computed output, or None if the indicator is still warming up.

fn reset(&mut self)

Reset all internal state, leaving the indicator equivalent to a freshly constructed instance with the same parameters.

fn warmup_period(&self) -> usize

Number of inputs required before the first non-None output can be produced.

fn is_ready(&self) -> bool

Whether the indicator has emitted at least one value since the last reset.

fn name(&self) -> &'static str

Stable, human-readable indicator name. Used by chaining and diagnostics.