Hi @TrevorR
You can try using this command [aic, bic] = aicbic(). For more info, please check:
help aicbic
AICBIC Information criteria
Syntax:
aic = aicbic(logL,numParam)
[aic,bic] = aicbic(logL,numParam,numObs)
[aic,bic] = aicbic(logL,numParam,numObs,'Normalize',true)
[aic,bic,ic] = aicbic(logL,numParam,numObs)
[aic,bic,ic] = aicbic(logL,numParam,numObs,'Normalize',true)
Description:
Given loglikelihood values logL obtained by fitting a model to data,
compute information criteria to assess model adequacy. Information
criteria rank models using measures that balance goodness of fit with
parameter parsimony. Models with lower criteria values are preferred.
Input Arguments:
logL - Loglikelihoods associated with parameter estimates of different
models, specified as a vector of numeric values.
numParam - Number of estimated parameters in the models, specified as a
positive integer applied to all elements in logL, or a vector of
positive integers having the same length as logL.
Optional Input Argument:
numObs - Sample sizes used in estimation, specified as a positive
integer applied to all elements in logL, or a vector of positive
integers having the same length as logL. AICBIC requires numObs
for all criteria except the Akaike information criterion, or if
'Normalize' is true.
Optional Input Parameter Name/Value Arguments:
NAME VALUE
'Normalize' Flag to normalize results by numObs, specified as a
logical value. When true, all output arguments are
divided by numObs. The default is false.
Output Arguments:
aic - Vector of Akaike information criteria corresponding to elements
of logL.
bic - Vector of Bayesian (Schwarz) information criteria corresponding
to elements of logL.
ic - Structure array with fields:
aic Akaike information criteria (AIC)
bic Bayesian (Schwarz) information criteria (BIC)
aicc Corrected Akaike information criteria (AICc)
caic Consistent Akaike information criteria (CAIC)
hqc Hannan-Quinn criteria (HQC)
ic.aic and ic.bic are the same values returned in aic and bic.
AICBIC computes unnormalized criteria as follows:
o AIC = -2*logL + 2*numParam
o BIC = -2*logL + log(numObs)*numParam
o AICC = AIC + [2*numParam*(numParam+1)]/(numObs-numParam-1)
o CAIC = -2*logL + (log(numObs)+1)*numParam
o HQC = -2*logL + 2*log(log(numObs))*numParam
Notes:
o Misspecification tests LMTEST, LRATIOTEST, and WALDTEST compare the
loglikelihoods of two competing nested models. By contrast, AICBIC
accepts the loglikelihoods of individual model fits and returns
approximate measures of "information loss" with respect to the data-
generating process. Information criteria provide relative rankings of
any number of competing models, including non-nested models.
o In small samples, AIC tends to overfit. To address overfitting, AICc
adds a size-dependent correction term that increases the penalty on
the number of parameters. AICc approaches AIC asymptotically.
Analysis in [3] suggests using AICc when numObs/numParam < 40.
o When econometricians compare models with different numbers of
autoregressive lags or different orders of differencing, they often
scale information criteria by the number of observations [5]. To do
this, set numObs to the effective sample size of each estimate, and
set 'Normalize' to true.
Example:
% Simulate DGP
T = 100;
DGP = arima('Constant',1,'AR',[0.2,-0.4],'Variance',1);
y = simulate(DGP,T);
% Competing models
Mdl1 = arima('ARLags',1);
Mdl2 = arima('ARLags',1:2);
Mdl3 = arima('ARLags',1:3);
% Compute log-likelihoods
logL = zeros(3,1);
[~,~,logL(1)] = estimate(Mdl1,y,'Display','off');
[~,~,logL(2)] = estimate(Mdl2,y,'Display','off');
[~,~,logL(3)] = estimate(Mdl3,y,'Display','off');
% Compute and compare information criteria
numParam = [3;4;5];
numObs = T*ones(3,1);
[~,~,ic] = aicbic(logL,numParam,numObs)
References:
[1] Akaike, H. "Information Theory and an Extension of the Maximum
Likelihood Principle." In: Petrov B., Csaki F., editors. Second
International Symposium on Information Theory. Budapest: Akademiai
Kiado, 1973, pp. 267-281.
[2] Akaike, H. "A New Look at the Statistical Model Identification."
IEEE Transactions on Automatic Control. Vol. 19, No, 6, 1974,
pp. 716-723.
[3] Burnham, K. and D. Anderson. Model Selection and Multimodel
Inference: A Practical Information-Theoretic Approach, 2nd Ed.
New York: Springer, 2003.
[4] Hannan, E. and B. Quinn. "The Determination of the Order of an
Autoregression." Journal of the Royal Statistical Society, Series
B. Vol. 41, 1979, pp. 190-195.
[5] Lutkepohl, H. and M. Kratzig. Applied Time Series Econometrics.
Cambridge: Cambridge University Press, 2004.
[6] Schwarz, G. "Estimating the Dimension of a Model." The Annals of
Statistics. Vol. 6, No. 2, 1978, pp. 461-464.
See also LMTEST, LRATIOTEST, WALDTEST.
Documentation for aicbic
doc aicbic
Also read about Akaike's Information Criterion (AIC) here:
