{
  "seed": 20260921,
  "observations": 500,
  "units": "Synthetic level units; first differences, not percentage returns",
  "method": "Known constructions; no fitted hedge, p-value or seed search",
  "examples": [
    {
      "file": "assets/images/pairs-cointegration-without-correlation.svg",
      "construction": "A = X + u; B = X - u | X: random walk; u: independent white noise",
      "population_first_difference_correlation": 0.0,
      "sample_first_difference_correlation": -0.04742496319508465,
      "spread": "Stationary spread: A - B = 2u",
      "explanation": "Var(dX) = 1; Var(u) = 0.5. Cov(dA, dB) = 1 - 2(0.5) = 0."
    },
    {
      "file": "assets/images/pairs-correlation-without-cointegration.svg",
      "construction": "A = X + 0.2Y; B = X | X and Y: independent random walks",
      "population_first_difference_correlation": 0.9805806756909201,
      "sample_first_difference_correlation": 0.9797652609527159,
      "spread": "Nonstationary spread: A - B = 0.2Y",
      "explanation": "Var(dX) = Var(dY) = 1. Var(A - B) = 0.04t; no fixed hedge removes Y."
    }
  ]
}