com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.garch
Class Garch

java.lang.Object
  com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.garch.Garch

public class Garch
extends java.lang.Object

This class does fitting for the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model.

This implementation does the fitting by maximizing the likelihood function, using the gradient information.

See Also:

"Bollerslev, Tim. Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, Issue 3, Vol. 31. 1986."

Constructor Summary

Garch(TimeSeries xt, int p, int q)
Fit the GARCH(p, q) model to the time series.

Garch(TimeSeries xt, int p, int q, int maxIterations)
Fit the GARCH(p, q) model to the time series.

Method Summary

RealVectorFunction	dLogLikelihood(double[] e_t2, int p, int q) the gradient of the log-likelihood function for a set of observations The gradient log-likelihood takes θ as the inputs.
RealScalarFunction	logLikelihood(double[] e_t2, int p, int q) the log-likelihood function for a set of observations The log-likelihood takes θ as the inputs.
GarchModel	model() Get the fitted GARCH model.

Methods inherited from class java.lang.Object

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

Constructor Detail

Garch

public Garch(TimeSeries xt,
             int p,
             int q,
             int maxIterations)

Fit the GARCH(p, q) model to the time series.

Parameters:

xt - a time series of the observations

q - the ARCH order

p - the GARCH part order

maxIterations - the maximum number of iterations in the numerical optimization algorithm

Garch

public Garch(TimeSeries xt,
             int p,
             int q)

Fit the GARCH(p, q) model to the time series.

Parameters:

xt - a time series of the observations

q - the ARCH order

p - the GARCH part order

Method Detail

model

public GarchModel model()

Get the fitted GARCH model.

Returns:

the fitted GARCH model, the estimators.

logLikelihood

public RealScalarFunction logLikelihood(double[] e_t2,
                                        int p,
                                        int q)

the log-likelihood function for a set of observations

The log-likelihood takes θ as the inputs.

Parameters:

e_t2 - squared observations

q - the ARCH order

p - the GARCH part order

Returns:

log-likelihood function for a set of observations

See Also:

"Bollerslev, Tim. "Eq. 18. Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Issue 3, Vol. 31. 1986."

dLogLikelihood

public final RealVectorFunction dLogLikelihood(double[] e_t2,
                                               int p,
                                               int q)

the gradient of the log-likelihood function for a set of observations

The gradient log-likelihood takes θ as the inputs.

Parameters:

e_t2 - the squared observations

p - the number of AR terms

q - the number of MA terms

Returns:

the gradient of the log-likelihood function

See Also:

"Bollerslev, Tim. "Eqs. 19, 21. Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Issue 3, Vol. 31. 1986."