fattailed_garchlikelihood.m

经济类的实用的时间序列分析软件包

function [LLF, h, likelihoods] = fattailed_garchlikelihood(parameters , data , p , q, errortype, stdEstimate, T)
% PURPOSE:
%     Likelihood for fattailed garch estimation
% 
% USAGE:
%     [LLF, h, likelihoods] = fattailed_garchlikelihood(parameters , data , p , q, errortype, stdEstimate, T)
% 
% INPUTS:
%     parameters:   A vector of GARCH process aprams of the form [constant, arch, garch]
%     data:         A set of zero mean residuals
%     p:            The lag order length for ARCH
%     q:            The lag order length for GARCH
%     m:            The max of p and q
%     error:        The type of error being assumed, valid types are:
%                   1 if 'NORMAL'
%                   2 if 'STUDENTST' 
%                   3 if 'GED' 
%     stdEstimate:  The std deviation of the data
%     T:             Length of data
% 
% OUTPUTS:
%     LLF:          Minus 1 times the log likelihood
%     h:            Time series of conditional volatilities
%     likelihoods   Time series of likelihoods
% 
% COMMENTS:
%     This is a helper function for garchinmean
% 
% 
% Author: Kevin Sheppard
% [e-mail]
% Revision: 2    Date: 12/31/2001
% 



[r,c]=size(parameters);
if c>r
    parameters=parameters';
end


parameters(find(parameters <= 0)) = realmin;

constp=parameters(1);
archp=parameters(2:p+1);
garchp=parameters(p+2:p+q+1);
if errortype ~=1;
    nu = parameters(p+q+2);
    parameters = parameters(1:p+q+1);
end



if isempty(q)
    m=p;
else
    m  =  max(p,q);   
end

h=garchcore(data,parameters,stdEstimate^2,p,q,m,T);
Tau = T-m;
LLF = 0;
t = (m + 1):T;
if errortype == 1
    LLF  =  sum(log(h(t))) + sum((data(t).^2)./h(t));
    LLF  =  0.5 * (LLF  +  (T - m)*log(2*pi));
elseif errortype == 2
    LLF = Tau*gammaln(0.5*(nu+1)) - Tau*gammaln(nu/2) - Tau/2*log(pi*(nu-2));
    LLF = LLF - 0.5*sum(log(h(t))) - ((nu+1)/2)*sum(log(1 + (data(t).^2)./(h(t)*(nu-2)) ));
    LLF = -LLF;
else
    Beta = (2^(-2/nu) * gamma(1/nu)/gamma(3/nu))^(0.5);
    LLF = (Tau * log(nu)) - (Tau*log(Beta)) - (Tau*gammaln(1/nu)) - Tau*(1+1/nu)*log(2);
    LLF = LLF - 0.5 * sum(log(h(t))) - 0.5 * sum((abs(data(t)./(sqrt(h(t))*Beta))).^nu);
    LLF = -LLF;
end


if nargout >1
    if nargout > 2
        likelihoods=zeros(size(T));
        if errortype == 1
            likelihoods = 0.5 * ((log(h(t))) + ((data(t).^2)./h(t)) + log(2*pi));
            likelihoods = -likelihoods;
        elseif errortype == 2
            likelihoods = gammaln(0.5*(nu+1)) - gammaln(nu/2) - 1/2*log(pi*(nu-2))...
                - 0.5*(log(h(t))) - ((nu+1)/2)*(log(1 + (data(t).^2)./(h(t)*(nu-2)) ));
            likelihoods = -likelihoods;
        else
            Beta = (2^(-2/nu) * gamma(1/nu)/gamma(3/nu))^(0.5);
            likelihoods = (log(nu)/(Beta*(2^(1+1/nu))*gamma(1/nu))) - 0.5 * (log(h(t))) ...
                - 0.5 * ((abs(data(t)./(sqrt(h(t))*Beta))).^nu);
            likelihoods = -likelihoods;
        end
    end
    h=h(t);
end