In this paper, we analyze the adequacy of using GARCH as the data-generating process to model conditional volatility of stock market index rates-of-return series. Using the Hinich portmanteau bicorrelation test, we find that a GARCH formulation or any of its variants fail to provide an adequate characterization for the underlying process of the main Latin American stock market indices. Policymakers need to be careful when using autoregressive models for policy analysis and forecast because the inadequacy of GARCH models has strong implications for the pricing of stock index options, portfolio selection, and risk management. In particular, measures of spillover effects and output volatility may not be correct when GARCH-type models are used to evaluate economic policy.