his note shows how random walks and technical analysis of futures prices T can coexist and, as a corollary, illustrates the difficulty of determining whether or not a particular, finite price series is a random walk. The abstract definition of a random walk is well known, but the implications of the random walk model for technical analysis of futures prices are difficult to appreciate. Thus, after reviewing the model and its implications, moving average techniques are applied to hypothetical data generated by random walk processes. These simulations demonstrate that a price series generated by a random walk process can have "systematic components" over a finite period and that technical analyses applied to such observations can be profitable for specific time periods.
RANDOM WALK MODEL
In perfect markets, logical reasons exist for believing that daily, if not intraday, prices are random walks or, more generally, martingales (Samuelson, 1965;Working, 1958). The empirical evidence using actual prices is mixed (Kamara, 1982), but serial correlations in futures prices are typically small (e.g., Brinegar, 1970). Nonetheless, technical analysts believe that profitable trading rules can be derived from historical data. This is not as surprising as it may first seem, and indeed Working pointed out in 1934 that a random series can appear to move systematically.
There is a tendency, however, to believe-incorrectly-that random walks cannot have runs or that after a run (say, a series of price increases) the probability of a further run has somehow changed (for background and discussion on this topic see, e.g., Feller, 1957, pp. 135f). Considering just the direction of change rather than the magnitude of change, the binomial and negative binomial distributions can be used to provide insights into the probabilities associated with a given number of successes (say, price increases) and the waiting time for these successes. For exam-