echnical trading systems are mechanical methods of determining price direction T based on past prices. Most of these trading systems have parameters (e.g., the number of days to use in a moving average of prices) which must be specified by the user of the system. One widely used method to select parameters is to test various parameter sets of a technical trading system across past data and pick the parameter that generated the most profit. This is called optimizing over past data. In a survey of public futures fund advisory groups Brorsen and Irwin (1987) found that fifteen of nineteen advisory groups selected parameters by optimizing over historical data. But, Brorsen and Irwin found little agreement about how frequently to change parameters or how much data to use to select the parameters. This paper evaluates a variety of methods of selecting parameters to determine if any are significantly better than others.
The underlying premise of optimization is that if some parameter set worked well in the past, it should work well in the future. Pardo argues that, "As a consequence of rnarket drift, we believe it is necessary to periodically check system values and reoptimize them as market conditions demand" (Commodity Traders Consumer Report, (1986), p. 3). Similarly, Bookstaber (p. 260) argues that, "arriving at the correct parameter values is really of more importance than the selection of the system itself." Schwager, however, has repeatedly argued that optimization is of little value in forecasting which parameters will be most profitable (Schwager, (1984a(Schwager, ( ), (1984b), (1984~);), (1984~); Commodity Traders Consumer Report, (1986)). The only limited statistical evidence on this issue was presented by Schwager (1984b).
Simulated trading results also provide a test of market efficiency, as defined by Fama (1970) andSamuelson (1965). Past studies have used technical analysis to test market efficiency of specific markets, such as grains (Houthakker, (1961); Smidt, (1965);Stevenson and Bear, (1970)), livestock (Leuthold, (1972); Peterson and Leuthold, (1982)), and financials (Dale and Workman, (1981); Taylor, (1985b)). Taylor (1985a) argued that, because of lack of knowledge about the appropriate method to select the pa-
The authors would like to thank Scott Irwin and Jim Binkley for helpful comments.