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This chapter develops a no-arbitrage, futures equilibrium cost-of-carry model to demonstrate that the existence of cointegration between spot and futures prices in the New York Mercantile Exchange (NYMEX) crude oil market depends crucially on the time-series properties of the underlying model. In marked contrast to previous studies, the futures equilibrium model utilizes information contained in both the quality delivery option and convenience yield as a timing delivery option in the NYMEX contract. Econometric tests of the speculative efficiency hypothesis (also termed the “unbiasedness hypothesis”) are developed and common tests of this hypothesis examined. The empirical results overwhelming support the hypotheses that the NYMEX future price is an unbiased predictor of future spot prices and that no-arbitrage opportunities are available. The results also demonstrate why common tests of the speculative efficiency hypothesis and simple arbitrage models often reject one or both of these hypotheses.