Class GjrGarch11

java.lang.Object

com.quantfinlib.volatility.GjrGarch11

public final class GjrGarch11
extends Object

GJR-GARCH(1,1,1) — GARCH with the leverage term equity markets demand:

  h_t = ω + (α + γ·1{r<0}) r_{t-1}² + β h_{t-1}

A down move raises tomorrow's variance by α + γ; an equal up move by only α. That asymmetry (Glosten-Jagannathan-Runkle, 1993) is not a refinement — on equity indices γ is typically larger than α, i.e. most of the ARCH effect is the leverage effect, and a symmetric Garch11 systematically underestimates post-selloff volatility. Fitting a GJR and finding γ ≈ 0 is itself information: the series has no asymmetry and the simpler model suffices (FX pairs often land there; equity indices rarely do).

Estimation is full maximum likelihood over (ω, α, γ, β) and, for Innovation.STUDENT_T, ν, with the same machinery as Garch11: the region ω > 0, α, γ, β ≥ 0, α + γ/2 + β < 1 is mapped onto R⁴ by ω = e^{u₀}, persistence p = logistic(u₁) split into α, γ/2, β by a softmax of (u₂, u₃, 0); Nelder-Mead from several starts; observed-information and Bollerslev-Wooldridge robust standard errors. The persistence α + γ/2 + β assumes a symmetric innovation (P(z < 0) = ½). Same 100-return minimum, conditional-variance and mean-reverting forecast accessors. Research lane.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	GjrGarch11.Fit
static final record	GjrGarch11.Params

Method Summary

Modifier and Type	Method	Description
static double[]	conditionalVariances(double[] returns, GjrGarch11.Params params)	Conditional variance series under the fitted parameters (seeded at sample variance).
static GjrGarch11.Fit	estimate(double[] returns, Innovation innovation)	Maximum-likelihood fit with standard errors (at least 100 finite returns).
static GjrGarch11.Params	fit(double[] returns)	Gaussian maximum-likelihood fit; see estimate(double[], Innovation).
static double	forecastVariance(double[] returns, GjrGarch11.Params params, int horizon)	k-step-ahead variance forecast — mean-reverts to the unconditional variance at the persistence rate, exactly as Garch11 but with the asymmetric first step.

Methods inherited from class Object

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

Method Details

fit

public static GjrGarch11.Params fit(double[] returns)

Gaussian maximum-likelihood fit; see estimate(double[], Innovation).

estimate

public static GjrGarch11.Fit estimate(double[] returns,
 Innovation innovation)

Maximum-likelihood fit with standard errors (at least 100 finite returns).

conditionalVariances

public static double[] conditionalVariances(double[] returns,
 GjrGarch11.Params params)

Conditional variance series under the fitted parameters (seeded at sample variance).

forecastVariance

public static double forecastVariance(double[] returns,
 GjrGarch11.Params params,
 int horizon)

k-step-ahead variance forecast — mean-reverts to the unconditional variance at the persistence rate, exactly as Garch11 but with the asymmetric first step.