In all ARMA models we must decided th number of the AR and MA terms. For this
reason some criterias such as, AIC, BSC, FPE, HQ developed by the
econometricians. AIC and BSC cirterias are widely used by the researchers. But
some resreachers prefer the BSC criteria than AIC. The question is why do reseachers
prefer BSC to AIC criteria. The answer of this question is originated form the
AIC and BSC formula. Let us investigate the AIC and BSC formula respectively.
Our
main purpose is that, select the order p (numer of p)which is minimize the AIC
or BIC criterias. The first part of the right side is same in both criteria,
however the second part is differenced each other. The second part in both criterias are
relative with the penalty for order p. AIC criteria consider only the number of
p, but BIC consider both the number of p and
observations. BIC criteria also consider number of observation and lead to more penalty for the function. So
this reason, BIC is smaller than AIC and it is more reliable[1].
[1]
For the detatiled informations: Jianqing Fan and Qiwei Yao-Nonlinear Time
Series. Parametric and Non-parametric Methods p-99-104.
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