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This article makes a comparison of the non-Gaussian state space models (NGSSM) family and APARCH models. The NGSSM is a subclass of state space models, where it is possible to compute the exact likelihood. The results showed that NGSSM has a better performance than APARCH models for estimating the volatility for several important financial indexes, as S&P 500, DAX, Nikkei 225, among others.