This paper is the first study to systematically discuss the predictive power of crosssectional asset pricing anomalies on aggregate market excess return time series in the Chinese A-share market. The paper summarizes the anomalies and uses linear methods with different shrinkage techniques to extract predictive information from highdimensional long-short anomaly portfolio returns datasets. We find that long-short anomaly portfolio returns show highly significant out-of-sample predictive power of aggregate market excess returns, both statistically and economically. Unlike similar studies on U.S. stocks, the predictive power stems from stronger limits of arbitrage in the short-leg when using bid-ask spread as a proxy but from stronger limits of arbitrage in the long-leg when idiosyncratic volatility or market capitalization is used as proxies.