**3. Empirical Results**

### *3.1. Results for Statistical Independence of Index Returns*

The first test is to see whether index returns are statistically independent. Consider the returns to the DSE index. In Table 3, we observe that the total number of runs based on DSEX returns equals 1334, below the lower bound of the 95% confidence interval. We reject the null hypothesis of statistical independence, and the fact that there are fewer runs than expected suggests a positive, serial correlation. For returns on the DSE index, similar sign returns follow each other more than expected, a result that indicates that the markets are slow to adjust to new information.

**Table 3.** Statistical Independence of Index Returns.


For returns on the Dow Jones Industrial Average, the number of runs equals 1727, which is slightly higher than the upper bound of the 95% confidence interval, 1685. This result also rejects statistical independence, instead implying a negative serial correlation of returns. A finding of slight negative serial correlation is in line with earlier studies of U.S. markets. Fama (1965), for instance, finds that 8 of the 30 stocks listed in the Dow had negative serial correlations, but that most of the serial correlations are less than 0.05. French and Roll (1986) repeat Fama's tests for NYSE and AMEX stocks during 1963–1982 period. They report a small but significant negative serial correlation of daily returns. To ge<sup>t</sup> a better idea of the runs distribution for both indexes, Figure 2A,B plots the number of n day runs and the 95% confidence intervals. From Figure 2A, the number of runs observed from −2 to +2 is well below the lower bound of each confidence interval. Conversely, the number of obtained longer runs tend to be higher than expected. In comparison, Figure 2B illustrates the runs distribution for the Dow Jones index. Short runs ( −2 to +2) occur slightly more often than expected, while longer n day runs happen within expected boundaries. These results further confirm our previous findings. For the DSE index, information is more slowly digested in the market, thus yielding positive, serial correlation. On the other hand, for the U.S. index, runs accord nearly as anticipated, with only slightly more short-term runs than one might expect in an efficient market. In the next section, we consider the runs pattern for the individual stocks in both the DSE and DJ indexes and see if similar results are obtained.
