ABSTRACT
The random walk hypothesis is a statement about the lack of useful statistical relationships between past and future prices and returns. This chapter discusses the general properties of conditional expectation. One possible reason is the efficiency of the markets that set asset prices, in the sense that those prices reflect all currently available information; hence, past return data does not include any additional useful information about future returns. The martingale model for asset prices has important implications for the properties of the corresponding returns. The random walk hypothesis in finance generally refers to a geometric random walk for asset prices. The Box–Ljung, variance-ratio, and runs tests are useful for detecting association among log-returns from nearby time periods; however, another way in which the random walk hypothesis may fail is if the log-returns are related over a long period of time. The random walk hypothesis is one of the most widely discussed topics in financial statistics.
