One does not simply correct for serial dependence

Serial dependence is present in most time series data sets collected in psychological research. This paper investigates the implications of various approaches for handling such serial dependence, when one is interested in the linear effect of a time-varying covariate on the time-varying criterion. Specifically, the serial dependence is either neglected, corrected for by specifying autocorrelated residuals, or modeled by including a lagged version of the criterion as an additional predictor. Using both empirical and simulated data, we showcase that the obtained results depend considerably on which approach is selected. We discuss how these differences can be explained by understanding the restrictions imposed under the various approaches. Based on the insight that all three approaches are restricted versions of an autoregressive distributed lag model, we demonstrate that accessible statistical tools, such as information criteria and likelihood ratio tests can be used to justify a chosen approach empirically.