Daily Speculations

Spurious Serial Correlation often enters into calculations of momentum. The first such was discovered by working where Kendall used the average of monthly prices and found that series based on averages showed positive serial correlation. But of course if the close today is higher than close one month ago, the average is likely to be higher than last month's average and the close is likely to be higher than the current average. Thus, if no change in the current month from close to close, the average will still be higher. Similar defects with using high and lows to compute averages. Also similar with respect to using the levels of an index rather than the future since the Fisher effect of untraded stocks adds to the spurious correlation.

The Wiz and I discovered an interesting one in a recent study of durations. Given that you're up at close from 4 days ago, i.e., Friday's close is above Monday's close, what is average number of days until today's close goes below the close four days ago close? I.e., until next Tuesday's close below last Wednesday's close or next Monday's close below last Tuesday's close, etc. Answer is 4 days. But given that today's close is above the close 4 days ago, for four consecutive days, the average number of days until the next close is below the close 4 days ago is 8 days. It's not a anomaly but merely a statistical property of random numbers. --Vic (10/7/3)