In this study, cross-sectional and time series longitudinal analysis were combined to identify that factor anomalies are driven by either over-reaction or under-reaction. The basic principle is, first, use a factor to form ten portfolios in the t quarter, then observe the average prices and returns of the ten portfolios for the previous four quarters and for the following four quarters as well. Finally, we are able to discover the reasons for abnormal returns according to characteristics of the changing processes of average stock prices and returns of the ten portfolios. The samples in this study contain all listed stocks on the US stock market from the fourth quarter of 1990 to the fourth quarter of 2010. The results show that (1) the reason for the abnormal returns of scale, value (book-to-price ratios, earnings-to-price ratios, sales-to-price ratios), and liquidity factors is over-reaction, and (2) the reason for the abnormal returns of growth factors (return on equity, return on assets, and revenue growth rate) is under-reaction.