When Does the TV Show "Arrow" Season Two (2013) Take Place?
"Arrow" season two is a superhero crime television show showran by Greg Berlanti with Marc Guggenheim and Andrew Kreisberg [adapting "Green Arrow: The Wonder Year" #1-#4 (1992-1993) by Mike Grell] that premiered October 9th, 2013. So when is "Arrow" season 2 set?
It takes place on an alternate timeline of the fictional DC Films Universe in the years:
We know this because in season two episode nine "Three Ghosts", a fairly recently completed psychological evaluation file is visible for a random Starling City resident and next to the preprinted words "Date of Birth:" there is a handwritten "June 6, 1976" and next to the preprinted "Age:" there is a handwritten "37". So it must be after June of 2013 AD and before June of 2014 AD.

2013 AD - 2014 AD
We know this because in season two episode nine "Three Ghosts", a fairly recently completed psychological evaluation file is visible for a random Starling City resident and next to the preprinted words "Date of Birth:" there is a handwritten "June 6, 1976" and next to the preprinted "Age:" there is a handwritten "37". So it must be after June of 2013 AD and before June of 2014 AD.
6.1,976 + 37 = 6.2,013.
Also, in the season premiere, season two episode one "City of Heroes" Oliver Queen says, "I spent the past year trying to avenge my father." and though his father, Robert Queen, has been dead since 2007 AD presumably he's referring to the time since he first returned home to Starling City. (This seems likely as in a flashback to before 2012 AD during season five episode one "Legacy" [2016] when someone asks what he's waiting for to begin attacking the people who "failed this city!" he answers, "To be ready." meaning he has not yet started ..."trying to avenge..." his father.) That happened in season one episode one "Pilot" (2012), the main action of which takes place in 2012 AD.
2,012 + 1 = 2,013.
More specifically, in season two episode eight "The Scientist", Roy Harper says, "Hey, this blood drive was a week ago." while holding a pamphlet that reads, "Glades Relief Blood Drive November 22nd" on the front. So it is definitely late November of 2013 AD at this time.
Later, in season two episode nine "Three Ghosts", Oliver is surprised to see a Christmas tree in the Queen family mansion and says, "It's Christmas..." and, in a later scene, he says, ..."he robbed the Applied Sciences Division of Queen Consolidated last week", referring to a crime that occurred at the beginning of the previous episode, "The Scientist", that takes place in late November of 2013 AD. So it is certainly December of 2013 AD at this time and the season continues into a second calendar year, early 2014 AD.
Additionally, the season is full of flashbacks and the first is labeled "5 Years Ago". So it's most likely 2008 AD during the flashbacks.
2,013 - 5 = 2,008.
More specifically, in the first flashback Shado says, "It's been 5 months since we stopped Fyers." and audiences saw that as part of season one's flashbacks of Oliver's time on the island of Lian Yu which take place in 2007 AD. So it must be early 2008 AD.
2007 + 5 months = ?.2008.
It is an early chronological TV series in the DC Films multiverse timeline (the first chronological show to feature Oliver Queen/Green Arrow) and can be watched at its timeline point.

