Was the "abomination of desolation" Caligula's proposed statue in the Temple? In Mark 13:14 (and similarly in Matthew 24:15) Jesus is reported as saying: 

"When you see ‘the abomination that causes desolation’ standing where it does not belong—let the reader understand—then let those who are in Judea flee to the mountains"

A leading theory is that this refers to the Roman standards being placed in the ruins of the Temple after Titus destroys Jerusalem in 70 AD.

But there is evidence that Caligula wanted to place a statue of himself in the Temple thirty years earlier. He sent Petronius to Syria to lead an army into Judea to force the Jews to accept this statue. The Jews were getting ready to resist this imposition. Luckily Caligula died in 41 AD before this order was carried out.

Perhaps this is evidence that the gospels of Mark and Matthew were written at some time during the period between Caligula's edict in 39 AD and his death in 41 AD? By contrast Luke's description of these events in Luke 21:20-24, which was probably composed using Mark's gospel, seems to clearly indicate Jerusalem's fall so that puts the composition of Luke-Acts later than 70 AD. 

The web page  http://virtualreligion.net/iho/pilate.html gives the following three passages (but seems to use 43 AD instead of the standard 41 AD for the date of Caligula's death):

Edict to Erect Imperial Statue in Temple [39 AD]

Now Gaius (Caligula) bore a grudge for being ignored only by the Jews in this respect [i.e., honoring him as divine]. So he sent his legate, Petronius, to Syria to take the rule over from Vitellius and ordered him to lead a large force into Judea. If they received him willingly, he was to place a statue of (Caligula) in the temple of God. But if they treated him with arrogance, he still was to do this after mastering them in battle ---  Josephus, Antiquities 18.261

Jews Prepare to Fight Caligula

Under Tiberius there was quiet. Then at the command of Gaius Caesar to place a statue of him in the temple, (the Jews) took up arms instead. But Caesar's death put an end to the commotion.
    --- Tacitus, Histories 5.9

Caligula's Death Averts War [41 AD]

Indeed, the Jews had given the appearance of rising up in revolt; (but) after the news of (Caligula's) murder there was no need for compliance (with his order). (Yet) fear remained that some emperor would command the same thing.
    --- Tacitus, Annals 12.343

P.S. In 2 Thessalonians 2 Paul seems to imply that, after a rebellion, the "man of lawlessness" will have himself worshiped as a god in the Temple. Caligula and his proposed statue in the 40s AD seems to fit this description better than Titus' standards in 70 AD. Also Paul goes on to mention that someone is holding this event back. This could well be Petronius whom sources say was delaying putting up Caligula's statue in the Temple as he knew what trouble it would cause.
On page 81 of http://ellisskolfield.com/pdf/2012-T.O.pdf Ellis Skolfield argues that the building of the Dome of the Rock on the Jewish Temple mount following Khalifa Omar's conquest of Jerusalem is the abomination of desolation. The original source is Bishop Sophronius, who was the bishop of Jerusalem at the time and made the connection to Daniel's prophecy (Daniel 11:31), as well as Jesus' words in Matthew.

It is likely that Daniel's earlier prophecy refers to Antiochus IV Epiphanes' slaughter of a pig on the altar in Jerusalem. Comparing Daniel's prophecy and its supposed fulfillment with Matthew's prophesy may be helpful.