void cArch::ComputeHess(uint theDate, const cRegArchValue& theData, cRegArchGradient& theGradData, cRegArchHessien& theHessData, cAbstResiduals* theResiduals)
{
theHessData.mCurrentHessVar = 0.0L;
uint myp = mvArch.GetSize();
uint myBegIndex = theGradData.GetNMeanParam();
register uint i,j,k;
for (i = 0; i < MIN(myp, theDate); i++)
theHessData.mCurrentHessVar -= 2.*mvArch[i] * theData.mUt[theDate -i-1]* theHessData.mHessMt[i];
for (k = 0; k < MIN(myp, theDate); k++)
for (i = 0; i < theHessData.mCurrentHessVar.GetNRow(); i++)
for (j = 0; j < theHessData.mCurrentHessVar.GetNCol(); j++)
theHessData.mCurrentHessVar[i][j] += 2 * mvArch[k] * theGradData.mGradMt[k][i] * theGradData.mGradMt[k][j];
for (i = 0; i < MIN(myp, theDate); i++)
for (j = 0; j < theHessData.mCurrentHessVar.GetNCol(); j++)
theHessData.mCurrentHessVar[1+i][j] -= 2 * theData.mUt[theDate -i-1] * theGradData.mGradMt[i][j];
for (i = 0; i < theHessData.mCurrentHessVar.GetNCol(); i++)
for (j = 1; j <= MIN(myp, theDate); j++)
theHessData.mCurrentHessVar[i][1+j] -= 2 * theData.mUt[theDate - j] * theGradData.mGradMt[j][i];
}
void cArch::ComputeGrad(uint theDate, const cRegArchValue& theValue, cRegArchGradient& theGradData, cAbstResiduals* theResiduals)
{
uint myp = mvArch.GetSize() ;
theGradData.mCurrentGradVar = 0.0L ;
uint myBegIndex = theGradData.GetNMeanParam() ;
theGradData.mCurrentGradVar[myBegIndex] = 1.0 ;
register uint i ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
theGradData.mCurrentGradVar[myBegIndex+i] = theValue.mUt[theDate - i]*theValue.mUt[theDate - i] ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
theGradData.mCurrentGradVar -= 2.0 * mvArch[i-1] * theValue.mUt[theDate - i] * theGradData.mGradMt[i-1] ;
}
void cTarch::ComputeGrad(int theDate, const cRegArchValue& theValue, cRegArchGradient& theGradData, cAbstResiduals* theResiduals) const
{
int myp = (int)mvArchPos.GetSize() ;
theGradData.mCurrentGradVar = 0.0L ;
int myBegIndex = (int)theGradData.GetNMeanParam() ;
theGradData.mCurrentGradVar[myBegIndex] = 1.0 ;
register int i ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
if (theValue.mUt[theDate-i] > 0)
theGradData.mCurrentGradVar[myBegIndex+i] = theValue.mUt[theDate - i]*theValue.mUt[theDate - i] ;
else
theGradData.mCurrentGradVar[myBegIndex+myp+i] = theValue.mUt[theDate - i]*theValue.mUt[theDate - i] ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
if (theValue.mUt[theDate-i] > 0)
theGradData.mCurrentGradVar -= 2.0 * mvArchPos[i-1] * theValue.mUt[theDate - i] * theGradData.mGradMt[i-1] ;
else
theGradData.mCurrentGradVar -= 2.0 * mvArchNeg[i-1] * theValue.mUt[theDate - i] * theGradData.mGradMt[i-1] ;
}
void cConstCondVar::ComputeGrad(int theDate, const cRegArchValue& theValue, cRegArchGradient& theGradData, cAbstResiduals* theResids) const
{
theGradData.mCurrentGradVar[theGradData.GetNMeanParam()] = 1.0 ;
}
void cAparch::ComputeGrad(int theDate, const cRegArchValue& theValue, cRegArchGradient& theGradData, cAbstResiduals* theResiduals) const
{
int myp = (int)mvArch.GetSize(),
myq = (int)mvGarch.GetSize() ;
theGradData.mCurrentGradVar = 0.0L ;
int myBegIndex = (int)theGradData.GetNMeanParam() ;
double myDeltaDiv2 = mvDelta/2.0 ;
/* derivative with respect to the constant */
theGradData.mCurrentGradVar[myBegIndex++] = 1.0 ;
register int i ;
/* derivative with respect to Delta */
theGradData.mCurrentGradVar[myBegIndex] = 0.0 ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theValue.mUt[theDate-i]) - mvGamma[i-1]*theValue.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex] += mvArch[i-1]* log(myTemp1) * myTemp2 ;
}
for (i = 1 ; i <= MIN(myq, theDate) ; i++)
{
double myTemp1 = pow(theValue.mHt[theDate-i], myDeltaDiv2) ;
theGradData.mCurrentGradVar[myBegIndex] += mvGarch[i-1] * myTemp1 * log(theValue.mHt[theDate-i])/2.0 ;
}
/* derivative with respect to Arch */
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theValue.mUt[theDate-i]) - mvGamma[i-1]*theValue.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex+i] = myTemp2 ;
}
/* derivative with respect to Gamma */
myBegIndex += myp ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theValue.mUt[theDate-i]) - mvGamma[i-1]*theValue.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex+i] = -mvArch[i-1] * mvDelta * theValue.mUt[theDate-i] * myTemp2/myTemp1 ;
}
/* derivative with respect to Garch */
myBegIndex += myp ;
for (i = 1 ; i <= MIN(myq, theDate) ; i++)
theGradData.mCurrentGradVar[myBegIndex+i] = pow(theValue.mHt[theDate-i], myDeltaDiv2) ;
/* Need now to add the derivatives with respect to u(t-i) and h(t-j) */
for ( i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theValue.mUt[theDate-i])/theValue.mUt[theDate-i] - mvGamma[i-1],
myTemp2 = pow(myTemp1, mvDelta-1) ;
theGradData.mCurrentGradVar -= mvArch[i-1] * mvDelta * myTemp1 * theGradData.mGradMt[i-1] ;
}
for ( i = 1 ; i <= MIN(myq, theDate) ; i++)
{
double myTemp1 = mvGarch[i-1] * myDeltaDiv2 * pow(theValue.mHt[theDate-i], myDeltaDiv2 - 1.0) ;
theGradData.mCurrentGradVar += myTemp1 * theGradData.mGradHt[i-1] ;
}
/* we computed d(ht^Delta/2)/dTheta, we need to compute dht.dTheta */
myBegIndex = (int)theGradData.GetNMeanParam() + 1 ; // We get the index of Delta
double myAux = theGradData.mCurrentGradVar[myBegIndex] ;
/* Correct formula for all parameters except Delta */
double myTemp = pow(theValue.mHt[theDate], myDeltaDiv2-1) ;
theGradData.mCurrentGradVar /= myDeltaDiv2 * myTemp ;
/* For Delta */
theGradData.mCurrentGradVar[myBegIndex] = (myAux - 0.5*log(theValue.mHt[theDate]) * myTemp * theValue.mHt[theDate])/(myDeltaDiv2 * myTemp) ;
}
void cAparch::ComputeGrad(uint theDate, const cRegArchValue& theData, cRegArchGradient& theGradData, cAbstResiduals* theResiduals)
{
uint myp =mvArch.GetSize(),
myq = mvGarch.GetSize(),
myBegIndex = theGradData.GetNMeanParam() ;
theGradData.mCurrentGradVar = 0.0 ;
double myDeltaDiv2 = mvDelta/2.0 ;
/* dérivée par rapport à la constante */
theGradData.mCurrentGradVar[myBegIndex++] = 1.0 ;
register uint i ;
/* dérivée par rapport à Delta */
theGradData.mCurrentGradVar[myBegIndex] = 0.0 ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theData.mUt[theDate-i]) - mvGamma[i-1]*theData.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex] += mvArch[i-1]* log(myTemp1) * myTemp2 ;
}
for (i = 1 ; i <= MIN(myq, theDate) ; i++)
{
double myTemp1 = pow(theData.mHt[theDate-i], myDeltaDiv2) ;
theGradData.mCurrentGradVar[myBegIndex] += mvGarch[i-1] * myTemp1 * log(theData.mHt[theDate-i])/2.0 ;
}
/* d�riv�e par rapport � Arch */
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theData.mUt[theDate-i]) - mvGamma[i-1]*theData.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex+i] = myTemp2 ;
}
/* d�riv�e par rapport � Gamma */
myBegIndex += myp ;
for (i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theData.mUt[theDate-i]) - mvGamma[i-1]*theData.mUt[theDate-i],
myTemp2 = pow(myTemp1, mvDelta) ;
theGradData.mCurrentGradVar[myBegIndex+i] = -mvArch[i-1] * mvDelta * theData.mUt[theDate-i] * myTemp2/myTemp1 ;
}
/* d�riv�e par rapport � Garch */
myBegIndex += myp ;
for (i = 1 ; i <= MIN(myq, theDate) ; i++)
theGradData.mCurrentGradVar[myBegIndex+i] = pow(theData.mHt[theDate-i], myDeltaDiv2) ;
/* Il faut maintenant rajouter les d�riv�es par rapport aux u(t-i) et h(t-j) */
for ( i = 1 ; i <= MIN(myp, theDate) ; i++)
{
double myTemp1 = abs(theData.mUt[theDate-i])/theData.mUt[theDate-i] - mvGamma[i-1] ;
theGradData.mCurrentGradVar -= mvArch[i-1] * mvDelta * myTemp1 * theGradData.mGradMt[i-1] ;
}
for ( i = 1 ; i <= MIN(myq, theDate) ; i++)
{
double myTemp1 = mvGarch[i-1] * myDeltaDiv2 * pow(theData.mHt[theDate-i], myDeltaDiv2 - 1.0) ;
theGradData.mCurrentGradVar += myTemp1 * theGradData.mGradHt[i-1] ;
}
/* on a calcul� d(ht^Delta/2)/dTeta ... Il faut calculer dht/dTeta */
myBegIndex = (int)theGradData.GetNMeanParam() + 1 ; // On recup�re l'indice de Delta
double myAux = theGradData.mCurrentGradVar[myBegIndex] ;
/* Formule valable pour tous les param�tres sauf Delta */
double myTemp = pow(theData.mHt[theDate], myDeltaDiv2-1) ;
theGradData.mCurrentGradVar /= myDeltaDiv2 * myTemp ;
/* Et pour Delta */
theGradData.mCurrentGradVar[myBegIndex] = (myAux - 0.5*log(theData.mHt[theDate]) * myTemp * theData.mHt[theDate])/(myDeltaDiv2 * myTemp) ;
}
