Class Egarch11

java.lang.Object
com.quantfinlib.volatility.Egarch11
public final class Egarch11 extends Object
EGARCH(1,1) — Nelson's exponential GARCH, the log-variance dynamics the plain family cannot express: 
  ln h_t = ω + β·ln h_{t-1} + α(|z_{t-1}| − √(2/π)) + γ·z_{t-1}
with standardized shocks z = r/√h. Two things the log form buys. First, no positivity constraints at all: any parameter signs give a valid variance, because the exp does the work Garch11's ω,α,β ≥ 0 constraints do. Second, leverage as a sign: γ < 0 means a down move raises tomorrow's volatility more than an equal up move, and the magnitude reads directly. Stationarity is |β| < 1, nothing else.

Estimation is full maximum likelihood over (ω, α, γ, β) and, for Innovation.STUDENT_T, ν, with ω, α, γ free and β = tanh(u) so that |β| < 1. Nelder-Mead from several starts, observed- information and Bollerslev-Wooldridge robust standard errors, recursion started at ln h₀ = ln σ̂² (Nelson 1991, Econometrica 59, 347-370). The centring constant is √(2/π) for both innovations, so Egarch11.Params drives the same recursion either way; under Student-t the difference to the t value of E|z| is absorbed in ω. One-step-ahead nextVariance(double[], Egarch11.Params) is exact; multi- step forecasts are not offered: iterating the log recursion gives the median variance, not the mean (Garch11/GjrGarch11 forecast multi-step; use them when you need horizons). Research lane.

  • Method Details

    • fit

      public static Egarch11.Params fit(double[] returns)
      Gaussian maximum-likelihood fit; see estimate(double[], Innovation).

    • estimate

      public static Egarch11.Fit estimate(double[] returns, Innovation innovation)
      Maximum-likelihood fit with standard errors (at least 100 finite returns).

    • conditionalVariances

      public static double[] conditionalVariances(double[] returns, Egarch11.Params p)
      Conditional variance series under the fitted parameters.

    • nextVariance

      public static double nextVariance(double[] returns, Egarch11.Params p)
      One-step-ahead variance — exact (tomorrow's ln h is deterministic today).