High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable screening are applicable to time dependent data, and even fewer methods are developed which utilize the unique aspects of time series data. This paper introduces several model free screening procedures developed specifically to deal with dependent and/or heavy tailed response and covariate time series. These methods are based on the partial distance correlation, and are developed both for univariate response models, such as nonlinear autoregressive models with exogenous predictors, and multivariate response models such as linear or nonlinear VAR models. Sure screening properties are proved for our procedures, which depend on the moment conditions, and the strength of dependence in the response and covariate processes, amongst other factors. Finite sample performance of these procedures is shown through extensive simulation studies, and we include an application to macroeconomic forecasting.