We use the Box-Jenkins approach to fit an autoregressive integrated moving average (ARIMA) model to dengue incidence in Rio de Janeiro, Brazil, from 1997 to 2004. We find that the number of dengue cases in a month can be estimated by the number of dengue cases occurring one, two, and twelve months prior. We use our fitted model to predict dengue incidence for the year 2005 when two alternative approaches are used: 12-steps ahead versus 1-step ahead. Our calculations show that the 1-step ahead approach for predicting dengue incidence provides significantly more accurate predictions (P value=0.002, Wilcoxon signed-ranks test) than the 12-steps ahead approach. We also explore the predictive power of alternative ARIMA models incorporating climate variables as external regressors. Our findings indicate that ARIMA models are useful tools for monitoring dengue incidence in Rio de Janeiro. Furthermore, these models can be applied to surveillance data for predicting trends in dengue incidence.