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The thesis examines the predictability of stock index futures in Taiwan. The lead-lag relationships between the stock index and index futures, as well as across futures markets are first investigated. Empirical results confirm previous findings that there is an asymmetric lead-lag relation between cash and futures markets - the feedback from the futures markets into the cash market is much stronger than the reverse. On the other hand, the weak evidence that the spot index leads the futures diminishes as interval enlarges and the leadership becomes a unidirectional relation that only the futures leads the case index. Although short-selling constraint is a reasonable hypothesis to conjecture the leadership relationship between the cash and futures, there is no evidence to support it from Taiwan markets. Secondly, the mechanism of the index futures spread arbitrage is described and spreads between index futures in Taiwan can be constructed so as to result in risky arbitrage. The long-term relationships among index futures are detected by cointegration tests. The prices of related index futures in this study are found to be cointegrated and the spreads derived from the cointegration relationships are mean-reverting. The trading-rule simulations suggest that the average profit from spread arbitrage is statistically significant after transaction costs and the rates of return of spread arbitrage are very attractive. The long memory properties of the spreads derived from the cointegration relationships is further investigated. Both spreads are revealed to be mean-reverting but non-stationary long memory process. Furthermore, there is strong evidence that Spread II is a double long memory process but Spread I lacks the property of long-range dependence in volatility.