Why is it that the largest market fluctuations, by a large majority, mainly happen in September, October and November? What about those three months causes the massive fluctuations? It happened in 1929, 1987 and 2008.
At present, I am not aware of a widely accepted academic research in economics and finance that would provide a definitive explanation for the exact calendar timing of major financial market fluctuations in the United States for the time period following the establishment of the Federal Reserve System in 1913. (Periodic financial crises prior to the establishment of the Fed in 1913 are typically attributed to the crop cycle---please see the link to a NYT article below.)
In part, the absence of a comprehensive explanation may be due to the fact that the episodes of enormous fluctuations such as those that happened in 1929, 1987, and 2008 have been fairly infrequent to enable a rigorous statistical analysis.
In recent years, substantial market fluctuations (but of slightly lesser magnitude) have often fallen on calendar months other than September, October, and November. For example, the magnitude of the volatility of the S&P 500 index's daily returns in March 2009 and August 2011 was similar to that in September 2008. Also, financial market fluctuations accompanying the burst of the "dotcom" bubble in the early 2000s do not seem to follow the September-to-November pattern.
Thus, while there may be little inherent nowadays regarding the months of September, October, and November that literally causes market fluctuations, what may be contributing to the magnitude of fluctuations during these months is the release of company earnings and other performance data at the end of the third quarter (i.e., September), a possible increase in trading activity following the end of the summer vacation period, a change in the phases of the annual political cycle (e.g., Congress returning from the summer break), and a change in the phases of the agricultural production cycle (e.g., fall harvesting and shipping of crops accompanied by corresponding financial flows).
For a brief, "popular press" explanation of the timing of early financial crises in the United States---related to the crop cycle---please see a NYT piece by C. Rampell: "Why Do Financial Crises Happen in the Fall?"
For a hypothesized explanation of the timing of modern financial crises---related to the political cycle---please see an opinion by R. Grossman: "Historically, October is the month for economic crises."