This study assesses two alternative approaches for investigating linear and nonlinear lagged associations in environmental time series data, comparing through simulations simple methods based on moving average summaries with more flexible distributed lag linear and nonlinear models. Results indicate that the latter provide estimates with no or low bias and close-to-nominal confidence intervals, even for long-lagged associations and in the presence of strong seasonal trends. Moving average models represent a viable alternative only in the presence of relatively short lag periods, and when the lag interval is correctly specified. In contrast, the use of moving averages to roughly approximate long and complex lag patterns, or the specification of an interval different than the actual lag period, can result in substantial biases. More flexible approaches based on distributed lag linear or nonlinear models provide noteworthy advantages, in particular when complex lagged associations are assumed.