Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper examines local influence assessment in generalized autoregressive conditional heteroscesdasticity models with Gaussian and Student-t errors, where influence is examined via the likelihood displacement. The analysis of local influence is discussed under three perturbation schemes: data perturbation, innovative model perturbation and additive model perturbation. For each case, expressions for slope and curvature diagnostics are derived. Monte Carlo experiments are presented to determine the threshold values for locating influential observations. The empirical study of daily returns of the New York Stock Exchange composite index shows that local influence analysis is a useful technique for detecting influential observations; most of the observations detected as influential are associated with historical shocks in the market. Finally, based on this empirical study and the analysis of simulated data, some advice is given on how to use the discussed methodology.821115711589Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Laboratorio EPIFISMAFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)