Abstract: Based on the five-minute high-frequency data in CSI 300 Chinese index futures and index markets from April 16,2010 to March 31,2014,Geweke-Porter-Hudak(GPH) and Local-Whittle semi-parametric methods were first adopted to estimate the long memory parameters on the market micro-structure indexes,i.e. liquidity,volatility and trading activity,and then frequency domain least squares method was empirically used to analyze the fractional co-integration relations among the above indexes. The results reveal that all variables are long memory,and the liquidity and volatility of two markets share the same fractional order at the 5% significance level,while the fractional order of open interest and two markets' trade volume are equal. In addition,the results of fractional co-integration test show that the liquidity and volatility between futures and spot markets are fractionally integrated,and the volatility of two markets are also fractionally integrated. However,there doesn't exist any fractional co-integration relation among trade volume and open interest of two markets.