Quick definitions you can scan.

If $x_t,y_t$ are both $I(1)$ but $y_t-\beta x_t\sim I(0)$, the pair is cointegrated. That stationary spread is what we trade.

Reject the unit-root null when the t-statistic on $y_{t-1}$ in the augmented regression is more negative than the MacKinnon critical value at the chosen level.

Estimate $y=\alpha +\beta x+u$ by OLS, then run an ADF test on the residuals using cointegration-specific MacKinnon CVs.

Fit on training window; record performance on held-out test window; roll forward. The Lab uses rolling estimation as a lighter equivalent.

η = T⁻² Σ S_t² / σ̂²_∞. Critical value 0.463 at 5% (level case). Pair worth trading: ADF rejects AND KPSS fails to reject.

VR(q) = Var(q-period sum) / (q · Var(1-period)). VR < 1 ⇒ mean reverting; VR > 1 ⇒ momentum.

H ≈ 0.5 random walk, H < 0.5 mean reverting, H > 0.5 trending. Tradable pairs typically show H in [0.30, 0.45].

Cumulative recursive residuals; under H0 it's a Brownian motion. Crossing ±a√T means the relationship has shifted.

Trace and max-eigenvalue stats from the rank of Π in the VECM ΔY = ΠY₋₁ + Σ Γ_iΔY_−i + ε. Correct generalisation of Engle-Granger to k ≥ 3 variables.

Geometric block lengths preserve serial dependence so Sharpe / total-return CIs are honest under autocorrelation.

$\hat{\beta }$ minimises the variance of $y_t-\hat{\beta }{x}_t$. Estimated via static OLS, rolling OLS, or a Kalman filter that lets β drift over time.

For an OU process with mean reversion speed $\theta$: $t_{1/2}=\ln 2/\theta$. Long half-lives die on transaction costs.

Once cointegration is detected, the VECM gives loadings α: how fast each leg adjusts back toward equilibrium. Tells you which leg leads the spread.

Normalise prices, compute SSD over a formation window, trade on ±2σ divergences in the trading window. No β, no ADF, fully empirical.

s = (X − μ_OU) / σ_OU using OU-fitted parameters rather than rolling moments. Trade when |s| ≥ 1.25, close at ≤ 0.5.

Bertram (2010) maximises (2aσ − cost) / E[T(a)] for an OU spread with fixed cost. The Pair Lab plots the surface.

A complementary view to Sharpe: how much CAGR you got per unit of pain.

Solves $w_i(\Sigma w{)}_i=c\forall i$. Reduces to inverse-vol when strategies are uncorrelated.

CVaR is the coherent risk measure VaR isn't. The Risk Lab reports both at 95% and 99%.

√(mean(DD_t²)). Captures depth and duration of drawdowns; smoother than max DD.

Smoother Calmar; correlates better with subjective discomfort than the more common single-DD ratios.

Average of yearly drawdowns rather than the global max — robust to a single bad year skewing the headline number.

Goodwin (1998). When benchmark = market, this is the right metric for evaluating sector-neutral pairs against passive long-only.

Simple, but does not hedge market β if the legs have different market exposures.

Size short leg as $\beta$ dollars per dollar long. Dollar exposure may be asymmetric, but the book is market-neutral in expectation.

Bigger orders, thinner books, faster moves all increase slippage. The Backtest Studio measures it in bps.

If mean reversion has not happened by your model's expected timeline, the relationship has likely shifted; cap the lossy tail.

Conservative proxy used in Portfolio: 1% of mean dollar volume on the worse leg. Real-money sizing should use Almgren-Chriss square-root impact.