The use of multilevel VAR(1) models to unravel within-individual process dynamics is gaining momentum in psychological research. These models accommodate the structure of intensive longitudinal datasets in which repeated measurements are nested within individuals. They estimate within-individual auto- and cross-regressive relationships by incorporating and using information about the distributions of these effects across individuals. An important quality feature of the obtained estimates pertains to how well they generalize to unseen data. Bulteel and colleagues (2018a) showed that this feature can be assessed through a cross-validation approach, yielding a predictive accuracy measure. In this article, we follow up on their results, by performing three simulation studies that allow to systematically study five factors that likely affect the predictive accuracy of multilevel VAR(1) models: (i) the number of measurement occasions per person, (ii) the number of persons, (iii) the number of variables, (iv) the collinearity between the variables, and (v) the distributional shape of the individual differences in the VAR(1) parameters (i.e., normal versus multimodal distributions). Simulation results show that pooling information across individuals, and using multilevel techniques prevent overfitting. Also, we show that when variables are expected to show strong contemporaneous correlations, performing multilevel VAR(1) in a reduced variable space can be useful. Furthermore, results reveal that multilevel VAR(1) models with random effects have a better predictive performance than person-specific VAR(1) models when the sample includes groups of individuals that share similar dynamics. Here we also present: The R code necessary to reproduce the three simulation studies. The complete simulation results for each study. Supplementary tables.