Statistics with overlapping periods I've been having a lot of discussions about finance recently in which people will point to some results using overlapping time periods and claim a high degree of statistical significance.  For example, they might say only one 20 year period since 1900 (1900-1920, 1901-1921, etc) has experienced X.  They will say they have 91 data points.  I say they have about 5.5 independent data points and that using overlapping periods overstates the statistical significance of the results.
1) Am I missing something?
2) Is there any respected source I can point to on the subject, such as a widely used textbook?
 A: Let me preface this answer by saying that I'm quite familiar with common risk management practices in finance, although my profession is not statistics per se.
The problem inherent in the statistical analysis of historical financial data is that often your historical data set is quite limited (see "subprime lending"...).  Obviously a lot of the products and markets we are researching haven't even been around that long.  But we must endeavor to try to make the best estimates that we can - a lot of money is at stake, and "no opinion" doesn't help.
The reason they use these "rolling periods" is because if you just pull out the 5 independent data points, as you suggest, your results may heavily depend on exactly where you put your 20-year cut-offs.  Using rolling periods helps eliminate that source of extra variation.
Nevertheless, you are quite correct that these are not independent data points.  Obviously they have a lot of serial correlation.  Also, naively taking the standard deviation of these data points will not be correct.  For an estimate of standard deviation, I'd just calculate the standard deviation based on the 5 points, and then repeat the process rolling forward a year each time, and then perhaps averaging those results together.
Better yet would be to abandon the whole rolling window approach, which I'm not a fan of, and use one year periods and average normally, without any overlapping windows.
Sorry there is not math in this answer!
EDIT:  (added later)
Also, I should emphasize that while rolling windows are useful, they are not typically used by practitioners to make statistical claims (like standard deviation).  Rather, they are used for simple historical scenario analysis, e.g. to answer questions like "What's the worst 10-year period for such-and-such a market" in the last 100 years?  Such questions are useful as a starting point for getting a handle on such things as required capital levels.
