According to Production Weekly, Mockingjay will start filming September 16th in Atlanta. In addition to this, Acting-Auditions posted a casting call for Mockingjay specifying the end filming date to be May 20th:
Color Force/C4 Productions in association with Larger Than Life Productions are in pre-production on the feature film "The Hunger Games: Mockingjay - Part 1". This is the first half of the third installment in the blockbuster hit The Hunger Games trilogy, and will be filmed back-to-back with "The Hunger Games: Mockingjay - Part 2". Shooting will run from September 16, 2013 through May 20, 2014 and will take place in Atlanta, GA and Boston, MA. Principal actor casting for the main roles will take place in Los Angeles with additional actor casting in Atlanta and Boston. Extras will be cast throughout the entire production in both cities.
Though this might seem pretty legitimate, keep in mind nothing is official unless Lionsgate confirms it.
Source: Production Weekly and Alan Baltes twitter