Class Garch11

java.lang.Object

com.quantfinlib.volatility.Garch11

public final class Garch11
extends Object

GARCH(1,1) volatility model (Bollerslev 1986, J. Econometrics 31, 307-327): h_t = ω + α r_{t-1}² + β h_{t-1} on demeaned returns.

Estimation is full maximum likelihood over (ω, α, β) and, for Innovation.STUDENT_T, the degrees of freedom ν. The admissible region ω > 0, α, β ≥ 0, α + β < 1 is mapped onto R³ by ω = e^{u₀}, α = p·s, β = p·(1−s) with p = logistic(u₁), s = logistic(u₂), and the negative log-likelihood is minimised by Nelder-Mead from three starting points. The recursion starts at h₀ = sample variance of the demeaned returns (the usual backcast). Standard errors come from the observed information (numerical Hessian); robust QMLE standard errors from the Bollerslev-Wooldridge (1992) sandwich, which stay valid when the innovation is not Gaussian. Both are NaN when the estimate sits on the boundary and the information matrix is singular.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Garch11.Fit	A fitted model with its uncertainty.
static final record	Garch11.Params

Method Summary

Modifier and Type	Method	Description
static double[]	conditionalVariances(double[] returns, Garch11.Params params)	Conditional variance series under the fitted parameters, seeded at the sample variance of the demeaned returns (the same backcast the fit uses).
static Garch11.Fit	estimate(double[] returns, Innovation innovation)	Maximum-likelihood fit with standard errors.
static Garch11.Params	fit(double[] returns)	Gaussian maximum-likelihood fit; see estimate(double[], Innovation).
static double	forecastVariance(double[] returns, Garch11.Params params, int horizon)	k-step-ahead variance forecast: h_{T+k} = σ̄² + (α+β)^{k-1} (h_{T+1} - σ̄²) — mean-reverts to the unconditional variance at the persistence rate.

Methods inherited from class Object

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

Method Details

fit

public static Garch11.Params fit(double[] returns)

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

estimate

public static Garch11.Fit estimate(double[] returns,
 Innovation innovation)

Maximum-likelihood fit with standard errors.

Parameters:

returns - at least 100 finite returns; the sample mean is removed

conditionalVariances

public static double[] conditionalVariances(double[] returns,
 Garch11.Params params)

Conditional variance series under the fitted parameters, seeded at the sample variance of the demeaned returns (the same backcast the fit uses).

forecastVariance

public static double forecastVariance(double[] returns,
 Garch11.Params params,
 int horizon)

k-step-ahead variance forecast: h_{T+k} = σ̄² + (α+β)^{k-1} (h_{T+1} - σ̄²) — mean-reverts to the unconditional variance at the persistence rate.