sources of advice on how to beat the buy-and-hold benchmark. Alexander (1964) also tests other mechanical trading rules, such as Dow-type formulas and old technical trading rules called formula Dazhi, formula Dafilt and finally the also nowadays popular moving averages. These techniques provided much better profits than the filter techniques. The results led Alexander (1964) still to conclude that the independence assumption of the random walk had been overturned.
Theil and Leenders (1965) investigate the dependence of the proportion of securities that advance, decline or remain unchanged between successive days for approximately 450 stocks traded at the Amsterdam Stock Exchange in the period November 1959 through October 1963. They find that there is considerable positive dependence in successive values of securities advancing, declining and remaining unchanged at the Amsterdam Stock Exchange. It is concluded that if stocks in general advanced yesterday, they will probably also advance today. Fama (1965b) replicates the Theil and Leenders test for the NYSE. In contrast to the results of Theil and Leenders (1965), Fama (1965b) finds that the proportions of securities advancing and declining today on the NYSE do not provide much help in predicting the proportions advancing and declining tomorrow. Fama (1965b) concludes that this contradiction in results could be caused by economic factors that are unique to the Amsterdam Exchange.
Fama (1965a) tries to show with various tests that price changes are independent and that therefore the past history of stock prices cannot be used to make meaningful predictions concerning its future behavior. Moreover, if it is found that there is some dependence, then Fama argues that this dependence is too small to be profitably exploited because of transaction costs. Fama (1965a) applies serial correlation tests, runs tests and Alexander's filter technique to daily data of 30 individual stocks quoted in the DJIA in the period January 1956 through September 1962. A runs test counts the number of sequences and reversals in a returns series. Two consecutive returns of the same sign are counted as a sequence, if they are of opposite sign they are counted as a reversal. The serial correlation tests show that the dependence in successive price changes is either extremely small or non-existent. Also the runs tests do not show a large degree of dependence. Profits of the filter techniques are calculated by trading blocks of 100 shares and are corrected for dividends and transaction costs. The results show no profitability. Hence Fama (1965a) concludes that the largest profits under the filter technique would seem to be those of the broker.
The paper of Fama and Blume (1966) studies Alexander's filters applied to the same data set as in Fama (1965a). A set of filters is applied to each of the 30 stocks quoted in the DJIA with and without correction for dividends and transaction costs. The data