This article combined both cross-sectional and time-series longitudinal analysis to identify that factor anomalies are driven by either over-reaction or under-reaction. The basic principle is, first, use a factor to form 10 portfolios in the t quarter, then observe the average prices and returns of the 10 portfolios for the previous four quarters and for the following four quarters as well. Samples in this study contain all stocks listed in the US from 1990 to 2010. The empirical evidence shows that the reason for the abnormal returns of value (book-to-price ratios, earnings-to-price ratios, sales-to-price ratios), scale and liquidity factors is over-reaction. Meanwhile, the reason for the abnormal returns of growth factors (return on equity, return on assets and revenue growth rate) is under-reaction. The results provide significant policy implications. The anomaly returns of the value, scale and liquidity factors last longer and are more appropriate to be employed for long-run investment while the growth factors are better suited for short-run investment. Furthermore, a more profitable stock-selection strategy can be formed by simultaneously considering the above two types of factors to capture both of these two sources of anomaly returns.