Class Dependence

java.lang.Object
com.quantfinlib.risk.Dependence
public final class Dependence extends Object
Rank-based dependence measures — what Pearson correlation misses. Pearson (in RiskMetrics.correlation) measures LINEAR co-movement and is wrecked by a single outlier or a nonlinear (but monotone) relationship; risk work needs the rank alternatives:
  • Spearman's ρ — Pearson on the RANKS: "do they move in the same order?", robust to outliers and any monotone transform. Also the correlation FRTB's P&L attribution test is defined on (PnlAttribution);
  • Kendall's τ — the probability a random pair is concordant minus discordant. Slower to compute (O(n²) here — fine at risk sample sizes) but with the property copula work leans on: for elliptical copulas, ρ_pearson = sin(πτ/2) inverts τ into the copula correlation without distributional damage.

Ties get midranks (Spearman) / count as neither concordant nor discordant (Kendall τ-a — adequate for continuous return data, where exact ties are measure-zero; heavy-tie categorical data wants τ-b, out of scope and said so). Static, deterministic, research lane.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    kendallTau(double[] a, double[] b)
    Kendall's τ (tau-a) in [-1, 1]; O(n²).
    static double
    pearsonFromKendall(double tau)
    The elliptical-copula bridge: Pearson ρ implied by a Kendall τ.
    static double[]
    ranks(double[] values)
    Midranks (average rank for ties), 1-based.
    static double
    spearman(double[] a, double[] b)
    Spearman rank correlation in [-1, 1].

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • spearman

      public static double spearman(double[] a, double[] b)
      Spearman rank correlation in [-1, 1].

    • kendallTau

      public static double kendallTau(double[] a, double[] b)
      Kendall's τ (tau-a) in [-1, 1]; O(n²).

    • pearsonFromKendall

      public static double pearsonFromKendall(double tau)
      The elliptical-copula bridge: Pearson ρ implied by a Kendall τ.

    • ranks

      public static double[] ranks(double[] values)
      Midranks (average rank for ties), 1-based.