El 01/05/11 23:07, Anutechia Asongu escribió: > Thanks Micheal, > In addition to the concern over what optimal lags to choose. When > observations are less than 60, the AIC and FPE best to optimise lags > that fit the model to the data structure. However, when observations are > above 60, the HQC is best. The SIC or BIC underestimate lags with > increase in degrees of freedom( See: Khim(2004): > http://ideas.repec.org/a/ebl/ecbull/v3y2004i33p1-9.html)
I am not sure this last sentence is correct (although I see it is correctly interpreted from the work of Khim). In fact HQC and BIC are criteria that obtain a consistent estimator for p (the order of the VAR). So, when T (or T-k) grows the probability of underestimate p should decrease. With respect to this question it is very detailed the explanation given in chapter 4 of "New Introduction to Multiple time Series" by Helmut Lütkepohl (Springer, 2005). Let me copy here some conclusions that may be appropiate given the debate that has emerged in this list: (page 151) "... It is worth emphasizing that the foregoing results do nor necessarily mean that AIC and FPE are inferior to HQ and SC [BIC]. Only if consistency is the yardstick for evaluating the criteria, the latter two are superior under conditions of the previous section. So far we have not considered the small sample properties of the estimators. In small samples, AIC and FPE may have better properties (chose the correct order more often) than HQ and SC. Also, the former two criteria are designed for minimizing the forecast error variance. Thus, in small as well as large samples, models based on AIC and FPE may produce superior forecasts although they may not estimate the orders correctly. In fact, Shibata(1980) derived asymptotic optimality properties of AIC and FPE for univariate processes. He showed that, under suitable conditions, they indeed minimize the 1-step ahead forecast MSE asymptotically". -- Ignacio Diaz-Emparanza DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA) UPV/EHU Avda. Lehendakari Aguirre, 83 | 48015 BILBAO T.: +34 946013732 | F.: +34 946013754 www.ea3.ehu.es
