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If there is an unknown trend status, or the information that a trend exists is used, then SIC and AIC always perform better than the two simulated hypothesis testing strategies.
The most popular are the Akaike Information Criteria (AIC), Schwartz Information Criteria (SIC) and Hannan and Quinn (HQ) Information Criteria.
Therefore, other information criteria can be considered such as HQ or SIC criteria.
The SIC criterion firstly introduced by Schwartz (1978) can be written in the form:
The test of criterions performed by Lütkepohl (1985) shows that in general, SIC outperforms HQ for any T, if , AIC outperforms SIC, however, if HQ tends to be the most
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