Using Zacks Earning Surprises for the S&P500, I’ve binned the standard deviation of EPS predictions by month and got their average. You can see that the final month of each quarter gets the highest degree of consensus:
In the final month of the quarter you also get the least number of predictions:
Do number of predictions affect concensus? The clustering for the end-of-quarter predictions implies that concensus goes up (lower std. dev.) for those times, but is fairly flat otherwise: