Cross-sectional and time-series tests of return predictability : what is the difference?

We compare the performance of time-series (TS) and cross-sectional (CS) strategies based on past returns. While CS strategies are zero-net investment long/short strategies, TS strategies take on a time-varying net-long investment in risky assets. For individual stocks, the difference between the performances of TS and CS strategies is largely due to this time-varying net-long investment. With multiple international asset classes with heterogeneous return distributions, scaled CS strategies significantly outperform similarly scaled TS strategies