Statistical arbitrage refers to a suite of quantitative investment strategies employed chiefly by hedge funds and proprietary trading firms. The arbitrageur can draw on a number of different approaches to identify and exploit an arbitrage opportunity, though the literature is broadly segmented by the canonical distance, cointegration and time series perspectives. Since the initial academic investigation of statistical arbitrage, its profitability has continued to diminish thanks largely to the increasing proportion of non-convergent opportunities. This paper surveys the existing literature, with particular emphasis given to evidence of statistical arbitrage failure, before unifying the distance, cointegration and time series perspectives under a single explicit model. The failure of statistical arbitrage opportunities is shown to be the direct consequence of implicit model assumptions that are inconsistent with the empirical literature. An alternative model is proposed, and evidence of its relative performance discussed.