This article surveys the evolution of stock market trading over a 60-year period. It begins before 1960, when there was no database widely available to conduct a statistical analysis of stock price movements. This changed in the 1960s with the introduction of the Center for Research in Security Prices database. A major finding was the heavy-tailed nature of stock returns. The 1960s also brought major theoretical developments, including the martingale theory of stock price processes and the efficient market hypothesis. This hypothesis prevailed until the 1990s, when the discovery of market anomalies led to statistical arbitrage strategies. We describe the use of modern machine learning methods, such as AdaBoost and random forests, which can combine some of these strategies into an improved trading strategy. The twenty-first century was marked by the rapid evolution of electronic markets and the rise of computer-driven high-frequency trading based on computing technology, low latency access, and limit order book modeling.


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