Eficient Capital Markets nored. Such a system is called a y% filter. It is obviously a"one security and ash"trading rule, so that the results it produces are relevant for the sub martingale expected return model of (6) After extensive tests using daily data on price indices from 1897 to 1959 and filters from one to fifty per cent, and after correcting some incorrect presumptions in the initial results of [1](see fn. 25), in his final paper on the subject, Alexander concludes: In fact, at this point I should advise any reader who is interested only in practical results, and who is not a floor trader and so must pay commissions, to turn to other sources on how to beat buy and hold. The rest of this article is devoted principally to a theoretical consideration of whether the observed results are consistent with a random walk hypothesis [8],p. 351) Later in the paper Alexander concludes that there is some evidence in his results against the independence assumption of the random walk model. But market efficiency does not require a random walk, and from the viewpoint of the submartingale model of (6), the conclusion that the filters cannot beat buy- and-hold is support for the efficient markets hypothesis. Further support is provided by Fama and Blume [13] who compare the profitability of various filters to buy-and-hold for the individual stocks of the Dow-Jones Industrial Average. (The data are those underlying Table 1.) But again, looking hard one can find evidence in the filter tests of both lexander and Fama-Blume that is inconsistent with the submartingale ef ficient markets model, if that model is interpreted in a strict sense. In partic- ular, the results for very small filters (1 per cent in Alexanders tests and5 1.0, and 1.5 per cent in the tests of Fama-Blume)indicate that it is possible to devise trading schemes based on very short-term(preferably intra-day but at most daily)price swings that will on average outperform buy-and-hold The average profits on individual transactions from such schemes are minis- cule, but they generate transactions so frequently that over longer periods and ignoring commissions they outperform buy-and-hold by a substantial margin. These results are evidence of persistence or positive dependence in very short-term price movements. And, interestingly, this is consistent with the evidence for slight positive linear dependence in successive daily price Ions 15. Though strictly speaking, such tests of pure independence are not directly relevant for els, it is interestin persist slightly longer than would be expected under the martingale hypothesis is also supported by the results of non-parametric runs tests applied to the daily data of Table 1.(See [101,Tables .2-15. For the daily price changes, the actual number of runs of price changes of the same sign is less than the expected number for 26 out of 30 stocks. Moreover, of the eight stocks for which the expected number, five of the ame stocks have positive daily first order serial correlations in Table 1 that are more than standard errors. But in both the statistical "significance"of the results is largely Just as the serial correlations are small in absolute terms (the average is ,026), the differences between the expected and actual number of runs on average are only three per cent of the total expected number On the other hand, it is also interesting that the runs tests do not support the suggestion of slight negative dependence in four and nine day changes that appeared in the serial correlations In the runs tests such negative dependence would appear as a tendency for the actual number of runs to exceed the expected number. In fact, for the four and nine day price changes, for 17 and