This paper presents and compares several time-series models for returns of broad-based stock indices. These models nest a nonlinear asymetric GARCH (NGARCH) model as a special case. Some of these models are empirically motivated ad-hoc specifications others are derived from a representative investor economy with HARA-utility and some are behavioral, i.e. are based on recent findings in behavioral finance. To compare these models we use the inflation adjusted MSCI total return indices of 5 large economies, USA, United Kingdom, Germany, France and Japan. The empirical results show that although the pure NGARCH model performs well, the estimation for two indices could be significantly improved by an extension which follows from the representative investor model with HARA-utility.
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