From the excellent Hussman Funds weekly Market Comment:
While a two-month period with an average historical return of zero is interesting, what is more interesting is the variation in those returns. Investors rarely operate in a vacuum, so a given piece of data really matters only in the context of other pieces. As investors, we are very much interested in conditional return, which requires that we base our analysis on a wider context than a single indicator.
With regard to September-October performance, Jim Stack of Investech points out that if you restrict the set of Sep-Oct periods to only those that followed the end of a bear market, the returns for the S&P 500 during that subset have been positive by a couple of percent, on average. The difficulty, from my perspective, is that the close of a bear market isn't an observable variable, except with the benefit of hindsight. Better to use conditioning variables that can be measured directly.
For example, at any point in time, we can observe directly where the S&P 500 Index is in relation to its 6-month moving average. Using this variable to measure the recency of a market weakness or strength, we find that Jim is still right, but he's right in an interesting way. Specifically, if you look at the set of periods where, at the end of August, the S&P 500 was more than 10% below its 6-month average, it turns out that the S&P 500 has indeed advanced by an average of about +2.5% during the subsequent September-October period.
On the other hand, if you look at the set of periods where the S&P 500 was more than 10% above its 6-month average (as it was at the end of August this year), we find that the September-October returns have been clearly negative, averaging a -5.6% decline for the S&P 500.