/*##############################################################################
#                                                                              #
#        Information Criterion by Breno de Andrade Pinheiro Néri               #
#                                                                              #
#            brenoneri@gmail.com       www.fgv.br/aluno/bneri                  #
#                                                                              #
#                                                 Septembre, 2005 - Version 1  #
#                                                                              #
################################################################################
#                                                                              #
# This code estimates the coefficients for twelve models of volatility with    #
# two different distributions: Normal and Skewed Student-t, namely:            #
# ARCH(1)                                                                      #
# ARCH(2)                                                                      #
# GARCH(1,1)                                                                   #
# GARCH(2,1)                                                                   #
# GARCH(1,2)                                                                   #
# GARCH(2,2)                                                                   #
# APARCH(1,0)                                                                  #
# APARCH(2,0)                                                                  #
# APARCH(1,1)                                                                  #
# APARCH(2,1)                                                                  #
# APARCH(1,2)                                                                  #
# APARCH(2,2)                                                                  #
#                                                                              #
# For each model and for each distribution, four information criterions are    #
# provided: Akaike, Schwarz (Bayesian), Shibata and Hannan-Quinn.              #
#                                                                              #
# You enter a time series vector (vY) in a file called vY.mat, with the        #
# observations in one single column. The models for volatility are estimated   #
# using the residuals of the ols regression of vY in its lag (with intercept). #
#                                                                              #
# Due to the nonlinear optimizations, this code is computational intensive!    #
#                                                                              #
################################################################################
#                                                                              #
# You may use this code only if you accept the conditions:                     #
# (1) I am not liable for any problem caused by this code (i.e. you use it at  #
# your own risk);                                                              #
# (2) You must give me credit in your papers where this code has been used.    #
#                                                                              #
##############################################################################*/

#import<packages/Garch40/garch> // Set the path of the Garch40 package of your computer!

static decl s_vE, s_obj;

// ARCH(1)
arch1(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    for(i=0; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2;
    return(vSigma2);
}

// ARCH(2)
arch2(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    vSigma2 |= vP[0] +  vP[1]*s_vE[0]^2;
    for(i=1; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2 + vP[2]*s_vE[i-1]^2;
    return(vSigma2);
}

// GARCH(1,1)
garch11(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    for(i=0; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2 + vP[2]*vSigma2[i];
    return(vSigma2);
}

// GARCH(2,1)
garch21(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    vSigma2 |= vP[0] +  vP[1]*s_vE[0]^2 + vP[3]*vSigma2[0];
    for(i=1; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2 + vP[2]*s_vE[i-1]^2 + vP[3]*vSigma2[i];
    return(vSigma2);
}

// GARCH(1,2)
garch12(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    vSigma2 |= vP[0] +  vP[1]*s_vE[0]^2 + vP[2]*vSigma2[0];
    for(i=1; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2 + vP[2]*vSigma2[i] + vP[3]*vSigma2[i-1];
    return(vSigma2);
}

// GARCH(2,2)
garch22(const vP)
{
    decl vSigma2=s_vE[0]^2, i;

    vSigma2 |= vP[0] +  vP[1]*s_vE[0]^2 + vP[3]*vSigma2[0];
    for(i=1; i<rows(s_vE); ++i) vSigma2 |= vP[0] + vP[1]*s_vE[i]^2 + vP[2]*s_vE[i-1]^2 + vP[3]*vSigma2[i] + vP[4]*vSigma2[i-1];
    return(vSigma2);
}

// APARCH(1,0)
aparch10(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[3], i;

    for(i=0; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[3];
    return(sigmad.^(2/vP[3]));
}

// APARCH(2,0)
aparch20(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[5], i;

    sigmad |= vP[0] + vP[1]*(fabs(s_vE[0])-vP[2]*s_vE[0])^vP[5];
    for(i=1; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[5] + vP[3]*(fabs(s_vE[i-1])-vP[4]*s_vE[i-1])^vP[5];
    return(sigmad.^(2/vP[5]));
}

// APARCH(1,1)
aparch11(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[4], i;

    for(i=0; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[4] + vP[3]*sigmad[i];
    return(sigmad.^(2/vP[4]));
}

// APARCH(2,1)
aparch21(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[6], i;

    sigmad |= vP[0] + vP[1]*(fabs(s_vE[0])-vP[2]*s_vE[0])^vP[6] + vP[5]*sigmad[0];
    for(i=1; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[6] + vP[3]*(fabs(s_vE[i-1])-vP[4]*s_vE[i-1])^vP[6] + vP[5]*sigmad[i];
    return(sigmad.^(2/vP[6]));
}

// APARCH(1,2)
aparch12(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[5], i;

    sigmad |= vP[0] + vP[1]*(fabs(s_vE[0])-vP[2]*s_vE[0])^vP[5] + vP[3]*sigmad[0];
    for(i=1; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[5] + vP[3]*sigmad[i] + vP[4]*sigmad[i-1];
    return(sigmad.^(2/vP[5]));
}

// APARCH(2,2)
aparch22(const vP)
{
    decl sigmad=fabs(s_vE[0])^vP[7], i;

    sigmad |= vP[0] + vP[1]*(fabs(s_vE[0])-vP[2]*s_vE[0])^vP[7] + vP[5]*sigmad[0];
    for(i=1; i<rows(s_vE); ++i) sigmad |= vP[0] + vP[1]*(fabs(s_vE[i])-vP[2]*s_vE[i])^vP[7] + vP[3]*(fabs(s_vE[i-1])-vP[4]*s_vE[i-1])^vP[7] + vP[5]*sigmad[i] + vP[6]*sigmad[i-1];
    return(sigmad.^(2/vP[7]));
}

// Joint Likelihoods
LNA1(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, arch1(vP)[:rows(s_vE)-1])));}
LNA2(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, arch2(vP)[:rows(s_vE)-1])));}
LNG11(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, garch11(vP)[:rows(s_vE)-1])));}
LNG21(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, garch21(vP)[:rows(s_vE)-1])));}
LNG12(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, garch12(vP)[:rows(s_vE)-1])));}
LNG22(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, garch22(vP)[:rows(s_vE)-1])));}
LNAP10(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch10(vP)[:rows(s_vE)-1])));}
LNAP20(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch20(vP)[:rows(s_vE)-1])));}
LNAP11(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch11(vP)[:rows(s_vE)-1])));}
LNAP21(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch21(vP)[:rows(s_vE)-1])));}
LNAP12(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch12(vP)[:rows(s_vE)-1])));}
LNAP22(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.GaussLik(s_vE, aparch22(vP)[:rows(s_vE)-1])));}
LSTA1(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, arch1(vP[:1])[:rows(s_vE)-1], log(vP[3]), vP[2])));}
LSTA2(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, arch2(vP[:2])[:rows(s_vE)-1], log(vP[4]), vP[3])));}
LSTG11(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, garch11(vP[:2])[:rows(s_vE)-1], log(vP[4]), vP[3])));}
LSTG21(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, garch21(vP[:3])[:rows(s_vE)-1], log(vP[5]), vP[4])));}
LSTG12(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, garch12(vP[:3])[:rows(s_vE)-1], log(vP[5]), vP[4])));}
LSTG22(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, garch22(vP[:4])[:rows(s_vE)-1], log(vP[6]), vP[5])));}
LSTAP10(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch10(vP[:3])[:rows(s_vE)-1], log(vP[5]), vP[4])));}
LSTAP20(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch20(vP[:5])[:rows(s_vE)-1], log(vP[7]), vP[6])));}
LSTAP11(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch11(vP[:4])[:rows(s_vE)-1], log(vP[6]), vP[5])));}
LSTAP21(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch21(vP[:6])[:rows(s_vE)-1], log(vP[8]), vP[7])));}
LSTAP12(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch12(vP[:5])[:rows(s_vE)-1], log(vP[7]), vP[6])));}
LSTAP22(const vP, const dP, const vScore, const mHessian) {return(dP[0]=sumc(s_obj.SkStudentLik(s_vE, aparch22(vP[:7])[:rows(s_vE)-1], log(vP[9]), vP[8])));}

main()
{
    decl vY=loadmat("vY.mat", 1), vYlag=vY[:rows(vY)-2], vOls, vPna1=<1;0>, vPna2=<1;0;0>, vPng11=<1;0;0>, vPng21=<1;0;0;0>, vPng12=<1;0;0;0>, vPng22=<1;0;0;0;0>, vPnap10=<1;0;0;2>, vPnap20=<1;0;0;0;0;2>, vPnap11=<1;0;0;0;2>, vPnap21=<1;0;0;0;0;0;2>, vPnap12=<1;0;0;0;0;2>, vPnap22=<1;0;0;0;0;0;0;2>, vPsta1=<1;0;10;1>, vPsta2=<1;0;0;10;1>, vPstg11=<1;0;0;10;1>, vPstg21=<1;0;0;0;10;1>, vPstg12=<1;0;0;0;10;1>, vPstg22=<1;0;0;0;0;10;1>, vPstap10=<1;0;0;2;10;1>, vPstap20=<1;0;0;0;0;2;10;1>, vPstap11=<1;0;0;0;2;10;1>, vPstap21=<1;0;0;0;0;0;2;10;1>, vPstap12=<1;0;0;0;0;2;10;1>, vPstap22=<1;0;0;0;0;0;0;2;10;1>, dP;

    // OLS Regression (You can use more lags, if you want!)
    s_obj=new Garch();
    vY = vY[1:];
    olsc(vY, 1~vYlag, &vOls);
    s_vE = vY-(1~vYlag)*vOls;

    // Optimizations
    MaxBFGS(LNA1, &vPna1, &dP, 0, 1);
    MaxBFGS(LNA2, &vPna2, &dP, 0, 1);
    MaxBFGS(LNG11, &vPng11, &dP, 0, 1);
    MaxBFGS(LNG21, &vPng21, &dP, 0, 1);
    MaxBFGS(LNG12, &vPng12, &dP, 0, 1);
    MaxBFGS(LNG22, &vPng22, &dP, 0, 1);
    MaxBFGS(LNAP10, &vPnap10, &dP, 0, 1);
    MaxBFGS(LNAP20, &vPnap20, &dP, 0, 1);
    MaxBFGS(LNAP11, &vPnap11, &dP, 0, 1);
    MaxBFGS(LNAP21, &vPnap21, &dP, 0, 1);
    MaxBFGS(LNAP12, &vPnap12, &dP, 0, 1);
    MaxBFGS(LNAP22, &vPnap22, &dP, 0, 1);
    MaxBFGS(LSTA1, &vPsta1, &dP, 0, 1);
    MaxBFGS(LSTA2, &vPsta2, &dP, 0, 1);
    MaxBFGS(LSTG11, &vPstg11, &dP, 0, 1);
    MaxBFGS(LSTG21, &vPstg21, &dP, 0, 1);
    MaxBFGS(LSTG12, &vPstg12, &dP, 0, 1);
    MaxBFGS(LSTG22, &vPstg22, &dP, 0, 1);
    MaxBFGS(LSTAP10, &vPstap10, &dP, 0, 1);
    MaxBFGS(LSTAP20, &vPstap20, &dP, 0, 1);
    MaxBFGS(LSTAP11, &vPstap11, &dP, 0, 1);
    MaxBFGS(LSTAP21, &vPstap21, &dP, 0, 1);
    MaxBFGS(LSTAP12, &vPstap12, &dP, 0, 1);
    MaxBFGS(LSTAP22, &vPstap22, &dP, 0, 1);

    // Reporting Results
    println("Normal ARCH(1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:"}, vPna1);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, arch1(vPna1)[:rows(s_vE)-1])), rows(s_vE)-1, 2));
    println("Normal ARCH(2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:"}, vPna2);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, arch2(vPna2)[:rows(s_vE)-1])), rows(s_vE)-1, 3));
    println("Normal GARCH(1,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "beta1:"}, vPng11);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, garch11(vPng11)[:rows(s_vE)-1])), rows(s_vE)-1, 3));
    println("Normal GARCH(2,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:", "beta1:"}, vPng21);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, garch21(vPng21)[:rows(s_vE)-1])), rows(s_vE)-1, 4));
    println("Normal GARCH(1,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "beta1:", "beta2:"}, vPng12);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, garch12(vPng12)[:rows(s_vE)-1])), rows(s_vE)-1, 4));
    println("Normal GARCH(2,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:", "beta1:", "beta2:"}, vPng22);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, garch22(vPng22)[:rows(s_vE)-1])), rows(s_vE)-1, 5));
    println("Normal APARCH(1,0) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "delta:"}, vPnap10);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch10(vPnap10)[:rows(s_vE)-1])), rows(s_vE)-1, 4));
    println("Normal APARCH(2,0) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "delta:"}, vPnap20);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch20(vPnap20)[:rows(s_vE)-1])), rows(s_vE)-1, 6));
    println("Normal APARCH(1,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "beta1:", "delta:"}, vPnap11);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch11(vPnap11)[:rows(s_vE)-1])), rows(s_vE)-1, 5));
    println("Normal APARCH(2,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "beta1:", "delta:"}, vPnap21);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch21(vPnap21)[:rows(s_vE)-1])), rows(s_vE)-1, 7));
    println("Normal APARCH(1,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "beta1:", "beta2:", "delta:"}, vPnap12);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch12(vPnap12)[:rows(s_vE)-1])), rows(s_vE)-1, 6));
    println("Normal APARCH(2,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "beta1:", "beta2:", "delta:"}, vPnap22);
    println(s_obj.ICriterion(sumc(s_obj.GaussLik(s_vE, aparch22(vPnap22)[:rows(s_vE)-1])), rows(s_vE)-1, 8));
    println("Skewed Student-t ARCH(1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "nu:", "xi:"}, vPsta1);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, arch1(vPsta1[:1])[:rows(s_vE)-1], log(vPsta1[3]), vPsta1[2])), rows(s_vE)-1, 4));
    println("Skewed Student-t ARCH(2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:", "nu:", "xi:"}, vPsta2);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, arch2(vPsta2[:2])[:rows(s_vE)-1], log(vPsta2[4]), vPsta2[3])), rows(s_vE)-1, 5));
    println("Skewed Student-t GARCH(1,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "beta1:", "nu:", "xi:"}, vPstg11);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, garch11(vPstg11[:2])[:rows(s_vE)-1], log(vPstg11[4]), vPstg11[3])), rows(s_vE)-1, 5));
    println("Skewed Student-t GARCH(2,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:", "beta1:", "nu:", "xi:"}, vPstg21);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, garch21(vPstg21[:3])[:rows(s_vE)-1], log(vPstg21[5]), vPstg21[4])), rows(s_vE)-1, 6));
    println("Skewed Student-t GARCH(1,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "beta1:", "beta2:", "nu:", "xi:"}, vPstg12);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, garch12(vPstg12[:3])[:rows(s_vE)-1], log(vPstg12[5]), vPstg12[4])), rows(s_vE)-1, 6));
    println("Skewed Student-t GARCH(2,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "alpha2:", "beta1:", "beta2:", "nu:", "xi:"}, vPstg22);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, garch22(vPstg22[:4])[:rows(s_vE)-1], log(vPstg22[6]), vPstg22[5])), rows(s_vE)-1, 7));
    println("Skewed Student-t APARCH(1,0) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "delta:", "nu:", "xi:"}, vPstap10);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch10(vPstap10[:3])[:rows(s_vE)-1], log(vPstap10[5]), vPstap10[4])), rows(s_vE)-1, 6));
    println("Skewed Student-t APARCH(2,0) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "delta:", "nu:", "xi:"}, vPstap20);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch20(vPstap20[:5])[:rows(s_vE)-1], log(vPstap20[7]), vPstap20[6])), rows(s_vE)-1, 7));
    println("Skewed Student-t APARCH(1,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "beta1:", "delta:", "nu:", "xi:"}, vPstap11);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch11(vPstap11[:4])[:rows(s_vE)-1], log(vPstap11[6]), vPstap11[5])), rows(s_vE)-1, 8));
    println("Skewed Student-t APARCH(2,1) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "beta1:", "delta:", "nu:", "xi:"}, vPstap21);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch21(vPstap21[:6])[:rows(s_vE)-1], log(vPstap21[8]), vPstap21[7])), rows(s_vE)-1, 9));
    println("Skewed Student-t APARCH(1,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "beta1:", "beta2:", "delta:", "nu:", "xi:"}, vPstap12);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch12(vPstap12[:5])[:rows(s_vE)-1], log(vPstap12[7]), vPstap12[6])), rows(s_vE)-1, 8));
    println("Skewed Student-t APARCH(2,2) estimated coefficients and Information Criterions: ", "%r", {"omega:", "alpha1:", "gamma1:", "alpha2:", "gamma2:", "beta1:", "beta2:", "delta:", "nu:", "xi:"}, vPstap22);
    println(s_obj.ICriterion(sumc(s_obj.SkStudentLik(s_vE, aparch22(vPstap22[:7])[:rows(s_vE)-1], log(vPstap22[9]), vPstap22[8])), rows(s_vE)-1, 10));
}