I am currently running an event study, for which I need to find out if my events are clustered and/or if their frequency is tied to the stock market. Creating a scatter plot of the event dates and the stock market index gives me a rough idea that they are correlated (points on the scatter plot are denser during market upswings, and become less so in downturns), however I do not know how to prove this at a statistically significant level.
During my search I have come across a Seemingly Unrelated Regression, but I am not sure if this is the right tool to use and, if it is, how to use it. I have attached the scatter plot, the x-axis is the date of the event and the y-axis is the S&P 500 index at the time of the event.
If you know how I can quantify this, please let me know, as I would like to use something more solid than "look at the graph".
LE: to get a better idea of how I have my data structured, I have only two variables: date which is the date of the event and sp500 which is the level of the S&P 500 for every date. From these two, I am trying to see whether date is clustered (happen at the same time or closely related to each other) when the sp500 is high, and viceversa.