Abstract: The changeable relationship between future price and the spot price discloses the efficiency of the future market.And it is one problem which the investors concentrate.The authors study the effects of the copper and aluminum future price changes on the copper and aluminum spot price in shanghai future exchange market with ADF，co-integration，ECM and Granger.Furthermore,the changeable relationship is described accurately.Finally,the result demonstrates that the future price and the spot price have a long balanced relationship,the future price and the spot price interact each other,and there is mutural causality between them.

Key words: future price, spot price, co-integration, Granger causality