How to interpret the result of AIC-BIC test?

Hi all,

I wanted to set the value of p,q or p,d,q for an ARIMA model using following code, even though I don't know how to interpret the obtained results, so any help would be highly appreciated.

LOGL = zeros(4,4);

PQ = zeros(4,4);

for p = 0:3

for q = 0:3

mod = arima(p,1,q);

[fit,~,logL] = estimate(mod,z,'print',false);

LOGL(p,q) = logL;

PQ(p,q) = p+q;

end

end

LOGL = reshape(LOGL,16,1);

PQ = reshape(PQ,16,1);

[aic,bic] = aicbic(LOGL,PQ+1,100);

mAIC=reshape(aic,4,4)

mBIC=reshape(bic,4,4)

output:

mAIC =

1.0e+04 *

-1.4059 -1.6748 -1.9129 -2.0337

-3.2659 -3.0362 -3.0430 -3.0458

-1.4044 -3.0381 -3.0379 -3.0377

-1.4042 -3.0379 -2.7176 -2.7174

mBIC =

1.0e+04 *

-1.4057 -1.6743 -1.9121 -2.0326

-3.2654 -3.0354 -3.0419 -3.0445

-1.4036 -3.0370 -3.0366 -3.0361

-1.4032 -3.0366 -2.7160 -2.7155

Answer 1

[Karanjot]

Hi Hamed,

I understand that you want to learn about interpreting results of AIC-BIC test.

Information criteria rank models using measures that balance goodness of fit with parameter parsimony. For a particular criterion, models with lower values are preferred. Akaike's Information Criterion (AIC) provides a measure of model quality obtained by simulating the situation where the model is tested on a different data set. After computing several different models, you can compare them using this criterion.

The mAIC matrix represents the AIC values for different combinations of p and q, while the mBIC matrix represents the BIC values.

The AIC and BIC are used as model selection criteria in statistics. Lower values indicate better-fitting models. In this case, you can compare the AIC and BIC values within each matrix to identify the combination of p and q that provides the best fit for your ARIMA model.

To learn more about this, please refer to the pages below, especially the ‘More About’ section:

https://www.mathworks.com/help/econ/aicbic.html#btvzzrv-5

https://www.mathworks.com/help/ident/ref/idmodel.aic.html#buy66ft-5

https://stats.stackexchange.com/questions/35010/aic-bic-number-interpretation

I hope this helps!