Module net.finmath.lib

Package net.finmath.timeseries.models.parametric

Class GARCH

java.lang.Object

net.finmath.timeseries.models.parametric.GARCH

All Implemented Interfaces:

HistoricalSimulationModel

public class GARCH
extends Object
implements HistoricalSimulationModel

Log-normal process with GARCH(1,1) volatility. This class estimate the process \[ \mathrm{d} \log(X) = \sigma(t) \mathrm{d}W(t) \] where \( \sigma \) is given by a GARCH(1,1) process from time discrete realizations \( X_{i} \). That is, given a time series of values \( X_{i} \) the GARCH(1,1) volatility of the log-returns \( \log(X_{i+1}/X_{i}) \) is estimated.

Version:

1.0

Author:

Christian Fries

Constructor Summary

Constructors

Constructor	Description
GARCH(double[] values)	Create GARCH model estimated form the given time series of values.
GARCH(double[] values, int windowIndexStart, int windowIndexEnd)	Create GARCH model estimated form the given time series of values.

Method Summary

Modifier and Type	Method	Description
Map<String,Object>	getBestParameters()	Returns the parameters estimated for the given time series.
Map<String,Object>	getBestParameters(Map<String,Object> guess)	Returns the parameters estimated for the given time series, using a parameter guess.
GARCH	getCloneWithWindow(int windowIndexStart, int windowIndexEnd)	Create a new model, using only a window of the times series.
double	getLastResidualForParameters(double omega, double alpha, double beta)	Returns the last estimate of the time series volatility.
double	getLogLikelihoodForParameters(double omega, double alpha, double beta)	Get log likelihood of the sample time series for given model parameters.
double[]	getQuantilPredictionsForParameters(double omega, double alpha, double beta, double[] quantiles)
double[]	getSzenarios(double omega, double alpha, double beta)

Methods inherited from class java.lang.Object

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

Constructor Detail

GARCH

public GARCH(double[] values)

Create GARCH model estimated form the given time series of values.

Parameters:

values - Given set of values.

GARCH

public GARCH(double[] values,
             int windowIndexStart,
             int windowIndexEnd)

Create GARCH model estimated form the given time series of values.

Parameters:

values - Given set of values.

windowIndexStart - First index to consider in the given set of values.

windowIndexEnd - Last index to consider in the given set of values.

Method Detail

getCloneWithWindow

public GARCH getCloneWithWindow(int windowIndexStart,
                                int windowIndexEnd)

Description copied from interface: HistoricalSimulationModel

Create a new model, using only a window of the times series.

Specified by:

getCloneWithWindow in interface HistoricalSimulationModel

Parameters:

windowIndexStart - Index of the first element to be part of the new time series.

windowIndexEnd - Index of the last element to be part of the new time series.

Returns:

A new historical simulation using a different data window.

getLogLikelihoodForParameters

public double getLogLikelihoodForParameters(double omega,
                                            double alpha,
                                            double beta)

Get log likelihood of the sample time series for given model parameters.

Parameters:

omega - The parameter ω of the GARCH model.

alpha - The parameter α of the GARCH model.

beta - The parameter β of the GARCH model.

Returns:

The log likelihood of the times series under the specified GARCH model.

getLastResidualForParameters

public double getLastResidualForParameters(double omega,
                                           double alpha,
                                           double beta)

Returns the last estimate of the time series volatility.

Parameters:

omega - The parameter ω of the GARCH model.

alpha - The parameter α of the GARCH model.

beta - The parameter β of the GARCH model.

Returns:

Last residual, i.e., σ

getSzenarios

public double[] getSzenarios(double omega,
                             double alpha,
                             double beta)

getQuantilPredictionsForParameters

public double[] getQuantilPredictionsForParameters(double omega,
                                                   double alpha,
                                                   double beta,
                                                   double[] quantiles)

getBestParameters

public Map<String,Object> getBestParameters()

Description copied from interface: HistoricalSimulationModel

Returns the parameters estimated for the given time series.

Specified by:

getBestParameters in interface HistoricalSimulationModel

Returns:

The parameters estimated for the given time series.

getBestParameters

public Map<String,Object> getBestParameters(Map<String,Object> guess)

Description copied from interface: HistoricalSimulationModel

Returns the parameters estimated for the given time series, using a parameter guess.

Specified by:

getBestParameters in interface HistoricalSimulationModel

Parameters:

guess - A parameter guess.

Returns:

The parameters estimated for the given time series.