Phần I11 và IV sẽ xem xét bằng chứng về hình dạng của sự phân bố của thay đổi giá cả. Mục I11 sẽ được quan tâm với công cụ phổ biến thống kê như phân bố tần số và đồ thị xác suất bình thường, trong khi mục IV sẽ phát triển thêm các xét nghiệm trực tiếp của giả thuyết Mandelbrot rằng số mũ đặc trưng cho các | 72 THE JOURNAL OF BUSINESS Again all the sample serial correlation coefficients are quite small. In general the absolute size of the coefficients seems to increase with the differencing interval. This does not mean however that price changes over longer differencing intervals show more dependence since we know that the variability of r is inversely related to the sample size. In fact the average size of the coefficients relative to sample for the four-day changes is only one-fourth as large as the sample for the daily changes. Similarly the samples for the nine- and sixteen-day changes are only one-ninth and one-sixteenth as large as the corresponding samples for the daily changes. their standard errors decreases with the differencing interval. This is demonstrated by the fact that for four- nine- and sixteen-day differencing intervals there are respectively five two and one coefficients greater than twice their standard errors in Table 11. An interesting feature of Tables 10 and 11 is the pattern shown by the signs of the serial correlation coefficients for lag T 1. In Table 10 twenty-three out of thirty of the first-order coefficients for the daily differences are positive while twenty-one and twenty-four of the coefficients for the four- and nine-day differences are negative in Table 11. For TABLE 10 Daily Serial Correlation Coefficients for Lag T 1 2 . 10 Lag Stock 1 2 3 4 5 6 7 8 9 10 Allied Chemical. .017 .007 .027 .004 Alcoa .118 .038 .022 .009 .017 .007 American Can .034 .015 .025 AT T .000 .026 .005 .002 .027 .007 American Tobacco. .111 .060 .007 .011 .046 .039 .041 Anaconda .067 .000 .009 .016 Bethlemen Steel. .013 .009 . 021 .004 Chrysler .012 .009 .037 .056 .021 Du Pont .013 .033 .060 .027 .020 .011
