LETTERS TO S&C
I have some doubts about the procedures explained in one of Arthur Merrill's recent columns, "Testing
Indicators" (STOCKS & COMMODITIES, May).
Mr. Merrill outlines a method of assessing the significance of an indicator by reviewing the performance
of the DJIA in the weeks and months after the indicator turns positive. He prepares a "batting average" of
the number of times the DJIA showed gains versus the number of times the DJIA showed losses, and he
also tests the significance of the indicator with a chi square formula.
I think the upward bias of the overall market distorts these tests. To illustrate: I've attached a similar score
prepared by assessing all of the monthly S&P 500 closes from 1947 to mid-1991. No indicator was
tested— or you could think of these figures as testing an indicator that has always been positive since
January 1947. The batting average and chi square test showed that this non-indicator was followed by
gains more often than chance would explain, with 0.999 confidence would explain, with 0.999
confidence throughout. My data is in Figure 1.
You would expect a batting average around 0.5 and a confidence below 0.9 for a truly random
distribution. A correction for bias needs to be incorporated. Would simply taking the natural logarithm of
each period's close be effective?