This was the first episode to be completed, with a shoot running from October to November 2012. David Suchet has suggested on twitter that the episode will have a late 1940s setting (one particular reply mentioned 1946). Hopefully the setting is as late as possible (very late 40s, early 50s), especially if they decide to still make Judith Hastings's daughter. But as of now, the most likely setting is October 1946.
UPDATE NOVEMBER 2013: This episode has been set in October 1949 (see '1949' post for details).
Elephants Can Remember
This episode, featuring Ariadne Oliver, was shot in January and February 2013. It will probably be the first episode of the final series. In chronolgy terms, taking the month of the shoot into account, I assume a January 1938 setting would be the most likely, with November/December 1937 (after Third Girl), December 1938 or January 1939 as possible alternatives.
[UPDATE JUNE 2013: The episode has been set in 1938 (see '1938' post for screencaps and details). I've chosen mid-to-late February, following Murder on the Orient Express.]
The Big Four
This episode was shot in February and March 2013. Hopefully, this will be the third episode of the series, directly preceding Labours of Hercules and following Elephants Can Remember and Dead Man's Folly in chronology terms. Since this is a rather epic case (Christie's story covers an entire year), the adaptation is likely to cover at least a couple of months. Reportedly, the adaptation is said to centre on the looming of war on the horizon. Consequently, I think January/February/March etc 1939 or February/March/April etc 1938 are possible options, the former better than the other in my opinion, though it would be nice to have this episode follow MOTOE (Jan/Feb 1938). Since this reintroduces Miss Lemon, Japp and Hastings for the first time in over ten years (real time) / since Evil Under the Sun / Murder in Mesopotamia in series time, these episodes might have to be moved to fit the chronology (I really hope they don't refer back to these cases too much, as that could jepordize the entire chronology!). For instance, Mesopotamia could easily be moved to January 1937 (Appointment could then be moved to February 1937 or December 1937). Also, if they go for 1938 or 1939, The Clocks would have to be set in May 1938 or May 1939 respectively.
UPDATE OCTOBER 2013: The episode has been set in March/April 1939 (see '1939' post for screencaps and details).
Labours of Hercules
This will reportedly start shooting in mid-April 2013 for approximately one month. Since this is also an epic case (about a year in Christie's collection), the adaptation will probably cover at least a couple of months. I suggest April/May/June etc 1939 or April/May/June etc 1940, though the latter would recquire the introduction of the War in some kind, I should think. See options for the only possible clash, The Clocks, above.
UPDATE NOVEMBER 2013: No particular references, but Countess Rossakoff mentions that it's been twenty years since she and Poirot last met. See '1946' post to see how I've attempted to solve this issue.
Dead Man's Folly
This will reportedly start shooting in mid-May for approximately one month. The story includes Ariadne Oliver and will apparently be filmed at Greenway (Christie's home!). My guess would be that they go for a May/June 1938 setting, possibly making this the final case of the Oliver/Poirot collaboration (unless Elephants is set later). Other options would be May/June 1937 (especially if Whitehaven isn't shown on screen) or July 1937.
UPDATE OCTOBER 2013: No particular references, so I've placed this episode in June 1938 (see '1938' post for screencaps and details).
The above guesses are obviously very tentative and I'll probably be wrong on most of them. But if there's anything I really have expectations for (chronology-wise), then it's a proper reintroduction of Hastings, Japp and Lemon that does not ruin this chronology. In other words, the number of years they've been absent in TV time should hopefully not be referred to too specifically, since the chronology only allows for an absence of about two to three years at the most (the last episode with the three of them and explicit references to a time setting in my chronology is Lord Edgware Dies, which I've set in June/July 1937. That could possibly be changed to fit a 1936 time frame, but that's the absolute earliest). In short, their absence can't have been longer than from 1937 to 1939/40. Also, I really hope they don't mess up with the Judith Hastings appearance. Hopefully she's been changed into a niece or adopted daughter or something along those lines. If she hasn't, then I really hope they've set the episode in the early 50s or something. Episodes with Ariadne Oliver tend not to have too explicit references, so I'm not too scared about those. In any case, we'll just have to wait and see. I'll post the episodes in the chronology as soon as they have been transmitted. Stay tuned.
Oh, and do have a look at my other blog, Investigating Agatha Christie's Poirot, while you're waiting!