Apr

10

DJIA daily returns (1929-present) were partitioned into non-overlapping 50 day periods. For each period, counted number of days with return greater than 0 (up days). For the recent 50D period ended Friday, there were 33 up-days (66%), which is in the highest 3.6% count of 50D>0 for the series.

The attached chart shows 50D>0 counts for the entire period, and the stem-leaf below covers the tree aspect:

To clarify the stem-leaf, the rows tally (using the "ones" digits) the number of each 50D up-count. The second column of each row is the "tens", the first column is count for that row and all those larger, and each number to the right of tens row represents an individual count.

eg, for the bottom row: 5 3 44455

3 is the tens, and 4445 are ones. Thus there are five observations in this row: 34, 34, 34, 35, 35 (and they are the top 5 observations in the sample).

The row above the bottom counts: 10 X 32's, and 9 X 33's. "24" before this row says there are 19 in this row + 5 larger (in the next row).

Perhaps the ranking is clearer in the following histogram for the same data, with a marker ("o") above the current "33" count.

 

   

But wait…there's more!

The probability chart below incorporates a Kolmogorov-Smirnov test of normality for "count of up days within 50D periods". The P-value is N.S., and as shown in the graph, the [statistically non-significant] deviation from normality is due to "heavy tails" (too many high and low counts).


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