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1.AIC只需两个inputs ( LLF , numParams)
2.BIC需要三个inputs (LLF , numParams , numObs)
3.aicbic.m在garch toolbox工具箱,AIC,BIC都容易计算,重点是求LLF.
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function [AIC , BIC] = aicbic(LLF , numParams , numObs)
%AICBIC Akaike and Bayesian information criteria for model order selection.
% Given optimized log-likelihood function (LLF) values obtained by fitting
% models of the conditional mean and variance to a univariate return series,
% compute the Akaike (AIC) and Bayesian (BIC) information criteria. Since
% information criteria penalize models with additional parameters, AIC and
% BIC are model order selection criteria based on parsimony. When using
% either AIC or BIC, models that minimize the criteria are preferred.
%
% [AIC , BIC] = aicbic(LLF , NumParams , NumObs)
%
% Optional Inputs: NumObs
%
% Inputs:
% LLF – Vector of optimized log-likelihood objective function (LLF)
% values associated with parameter estimates of various models. The LLF
% values are assumed to be obtained from the estimation function GARCHFIT,
% or the inference function GARCHINFER. Type “help garchfit” or “help
% garchinfer” for details.
%
% NumParams – Number of estimated parameters associated with each value
% in LLF. NumParams may be a scalar applied to all values in LLF, or a
% vector the same length as LLF. All elements of NumParams must be
% positive integers. NumParams may be obtained from the function
% GARCHCOUNT. Type “help garchcount” for details.
%
% Optional Input:
% NumObs – Sample sizes of the observed return series associated with each
% value of LLF. NumObs is required for computing BIC, but is not needed
% for AIC. NumObs may be a scalar applied to all values in LLF, or a
% vector the same length as LLF. All elements NumObs must be positive
% integers.
%
% Outputs:
% AIC – Vector of AIC statistics associated with each LLF objective
% function value. The AIC statistic is defined as:
%
% AIC = -2*LLF + 2*NumParams
%
% BIC – Vector of BIC statistics associated with each LLF objective
% function value. The BIC statistic is defined as:
%
% BIC = -2*LLF + NumParams*Log(NumObs)
%
%example
%garch.pdf page 8-2.
load garchdata
dem2gbp = price2ret(DEM2GBP);
[m,n]=size(dem2gbp); %[1974,1]
NumObs=m; %NumObs=1974
spec11 = garchset(‘P’,1,’Q’,1,’Display’,’off’);
[coeff11,errors11,LLF11] = garchfit(spec11,dem2gbp);
garchdisp(coeff11,errors11)
NumParams = garchcount(coeff11); %NumParams=4
format long
[AIC,BIC] = aicbic(LLF11,NumParams,NumObs);
[AIC,BIC]
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