FILTER RULES AND STOCK-MARKET TRADING 227 typically be interested in whether the de- and Morgenstern [7], and Godfrey, gree of dependence in successive changes Granger, and Morgenstern [6] also lend is sufficient to account for some particu- support to the independence assumption lar property of the distribution of price of the random-walk model changes or whether the dependence is Nevertheless, it is difficult to deter- sufficient to invalidate the results pro- mine whether these results indicate that duced by statistical tools applied to the the random-walk model is adequate for data. For example, price changes may be the investor. For example, there is ne one variable in a regression analysis and obvious relationship between the mag- the statistician will want to determine nitude of a serial correlation coefficient hether dependence in the series might and the expected profits of a mechanical produce serial dependence in the resid trading rule. Moreover, the market pro- als. If the amount of dependence is low, fessional would probably object that he will probably conclude that it will not common statistical tools cannot measure seriously damage his results. From the the types of dependence that he sees in it of however, the de- the data. For pendence may make the expected profits relationships that underlie the serial cor from some mechanical trading rule relation model are much too unsophist greater than those of a simple buy-and- cated to identify the complicated"pat hold policy. terns that the chartist"sees in stock 6b It is important to note, however, that prices. Similarly, runs tests are too rigid dependence"is always specific to the case and downward movements in prices. A at hand, the ultimate criterion is always run is considered terminated wheneve practical. In an encounter with a more there is a change in sign in the sequence complicated alternative, the theory of of successive price changes, regardless of random walks is overthrown only if the the magnitude of the price change that alternative leads to a better action than causes the reversal in sign. The market the random-walk theory would have sug- professional would require a more sophis gested ticated method to identify movements Previously the independence assump- a method that does not always predict tion of the random-walk model has been the termination of the movement simply tested primarily with standard statistical because the price level has temporarily tools, and in most cases the results have changed direction tended to uphold the model. This is true, Not all the published empirical tests of of Cootner [3], Fama [4], Kendall [8], and statistical models, however: Most no Moore [11]. In these studies the sample table, for example, is the work of Sidney serial correlation coefficients computed S. Alexander [1, 2]. Professor Alexander's for successive daily, weekly, and monthly filter technique is a mechanical tradin price changes were extremely close to rule which attempts to apply more so zero-evidence against"important" de- phisticated criteria to identify move- pendence in price changes. Similarly, ments in stock prices. An a per cent filter Fama's [4] analysis of runs of successive is defined as follows: If the daily closing price changes of the same sign and the price of a particular security moves up at spectral analysis techniques of Granger. least a per cent, buy and- hold the securi