NOTE about the dating:
Sometimes, it is indicated that the "desolation" occurred in 167 B.C.E. Let's consider this date (and 168 B.C.E.) according to the data available. If this has little interest for you, click on SKIP

About the Seleucid years:
In Josephus' Ant., XII, VII, 6:
"This desolation happened in the temple in the hundred forty and fifth year, ..."
Here, the reference year, as for the whole Seleucid era, is the start of the reign of Seleucus I. Unfortunately, there are two starts for the Seleucid calendar:
a) The Seleucid Macedonian Calendar (SMC) starts in October 7th, 312 B.C.E.
b) The Seleucid Babylonian Calendar (SBC) starts in April 3rd, 311 B.C.E.
However, the Macedonian calendar had been adopted by the Seleucid kings after they moved West (with Antioch as their main city) and became the main calendar in the eastern Mediterranean area up to Roman times.

It is widely acknowledged that Josephus drew many of his data from '1Maccabees', one of the O.T. Apocryphal books. Let's examine the dating in it, which Josephus adopted.
a) 1Macc.1:10 "From them came forth a sinful root, Antiochus Epiphanes, son of Antiochus the king; he had been a hostage in Rome. He began to reign in the one hundred and thirty-seventh year of the kingdom of the Greeks."
SMC: October 176 to October 175
SBC: April, 175 to April 174
Antiochus IV Epiphanes took power in 175 B.C.E. according to most.
b) 1Macc.1:20 "After subduing Egypt, Antiochus returned in the one hundred and forty-third year. He went up against Israel and came to Jerusalem with a strong force."
SMC: October 170 to October 169
SBC: April 169 to April 168
Antiochus IV went to Jerusalem in 169 B.C.E. (according to some) or 170 B.C.E. (according to a majority). For the later date (170), the 1Maccabees author could not have followed the Seleucid Babylonian Calendar (SBC).
c) 1Macc.1:29 "Two years later the king sent to the cities of Judah a chief collector of tribute, and he came to Jerusalem with a large force."
d) 1Macc.1:54 "Now on the fifteenth day of Chislev, in the one hundred and forty-fifth year, they erected a desolating sacrilege upon the altar of burnt offering."
1Macc.1:59 "And on the twenty-fifth day of the month they offered sacrifice on the altar which was upon the altar of burnt offering."
SMC: October 168 to October 167
SBC: April 167 to April 166
These two events happened (within 10 days) towards the end (November/December) of 168 B.C.E. (according to some) or 167 B.C.E. (according to others).
e) 1Macc.4:52-53 "Early in the morning on the twenty-fifth day of the ninth month, which is the month of Chislev, in the one hundred and forty-eighth year, they rose and offered sacrifice, as the law directs, on the new altar of burnt offering which they had built."
SMC: October 165 to October 164
SBC: April 164 to April 163
This event happened towards the end (November/December) of 165 B.C.E. (according to some) or 164 B.C.E. (according to others).
f) 1Macc.6:16 "Thus Antiochus the king died there in the one hundred and forty-ninth year."
SMC: October 164 to October 163
SBC: April 163 to April 162
This event happened in late 164 B.C.E. (according to most historians, the NIV Study Bible and the Encyclopaedia Britannica) or 163 B.C.E. (according to few others). Then with 164 B.C.E., the "one hundred and forty-fifth year" (the year of the desecration) would fall from Oct. 7th, 168 to Oct. 6th, 167 and therefore dating the "desolation" in (November/December) of 168 B.C.E.
Conclusion:
According to the available data, the dating of 170 B.C.E. (Antiochus' 1st visit), then "two years later" 168 B.C.E. (desecration) and then after three years 165 B.C.E. (reconsecration) is a lot more plausible (and accepted) than the sequence of 170 (or 169), 167 & 164 B.C.E.

Recapitulation:

Here is the distribution of the different parts of Daniel Part 2 for each of the four kings, as discussed before:
A) The dream/vision of Daniel (7:1-14):
a) Belshazzar: 7:4
b) Cyrus: 7:5
c) Alexander: 7:6
d) Antiochus IV: 7:8,11-12 (7:7 is about Antiochus' Seleucid predecessors)
B) The explanation of the dream/vision (7:15-28)
- Antiochus IV: 7:21-22,24b-26 (7:19-20,,223-24a is about Antiochus' Seleucid predecessors)
C) Daniel's second vision (8:1-14):
a) Cyrus: 8:3-4
b) Alexander: 8:5-8
c) Antiochus IV: 8:9-12
D) First explanation by Gabriel of the (second) vision (8:15-27):
a) Cyrus: 8:20
b) Alexander: 8:21 (8:22 is about the four Hellenist kingdoms)
c) Antiochus IV: 8:23-25
E) Second explanation by Gabriel on the (second) vision: the seventy 'sevens' (9:24-27):
- Antiochus IV: 9:25,26b-27
F) The third vision and final explanation by the demigod (10:1-11:45):
a) The Persian kings: 11:2
b) Alexander: 11:3 (11:4 is about the four Hellenist kingdoms)
c) The Ptolemies and Seleucids up to Antiochus IV's rule: 11:5-20
d) Antiochus IV: 11:21-36

Note: 11:2-20 is a very accurate & historically corroborated sequence of events from the third year (10:1) of the Persian era up to the predecessor of Antiochus IV (Hellenist era): some three hundred and sixty six years! Only the names and dates are missing. Most of the details are about the conflicts between the kings of the South (the Ptolemies of Egypt) and the kings of the North (the Seleucids of Mesopotamia/Syria). These later ones are shown to become stronger and stronger (despite some setbacks) all the way to (and including) Antiochus IV (11:21-31), described as the most powerful (and diabolic) of them all. Of course, Jerusalem was in the middle and changed hand (197, from Egypt to Syria). These alleged prophecies are unique in the O.T. relative to their accuracy and details!

List of the main players of 11:5-20 and corresponding verses:

11:5 Ptolemy I Soter (323-285), "king of the South" (kS) and Seleucus I Nicator (311-280), the first Seleucid king
"Also the king of the South shall become strong, as well as one of his princes; and he shall gain power over him and have dominion. His dominion shall be a great dominion [the Seleucid kingdom]."

11:6 Ptolemy II Philadelphus (285-246) (kS), his daughter Berenice, her new husband Antiochus II Theos (261-246) "king of the North" (kN)
"And at the end of some years they shall join forces, for the daughter of the king of the South shall go to the king of the North to make an agreement [marriage in 252]; but she shall not retain the power of her authority, and neither he nor his authority shall stand [Berenice, Antiochus and entourage got murdered]; but she shall be given up, with those who brought her, and with him who begot her [Ptolemy died at about the same time], and with him who strengthened her in those times."

11:7-9 Berenice's brother Ptolemy III Euergetes (246-221) (kS) and Seleucus II Callinicus (246-226) (kN)
"But from a branch of her roots one shall arise in his place, who shall come with an army, enter the fortress [Antioch] of the king of the North, and deal with them and prevail. And he shall also carry their gods captive to Egypt, with their princes and their precious articles of silver and gold; and he shall continue more years than the king of the North. Also the king of the North shall come to the kingdom of the king of the South, but shall return to his own land [because Antiochus Hierax was trying to claim the throne of his brother Seleucus]."

11:10 Seleucus III Ceraumus (226-223) and Antiochus III the Great (223-187)
"However his sons shall stir up strife, and assemble a multitude of great forces; and one shall certainly come and overwhelm and pass through; then he shall return to his fortress [Raphia] and stir up strife."

11:11-13 Ptolemy IV Philopator (221-203) (kS) and Antiochus the Great (kN)
"And the king of the South shall be moved with rage, and go out and fight with him, with the king of the North, who shall muster a great multitude; but the multitude shall be given into the hand of his enemy [at the battle of Raphia, 217. Antiochus' army suffered huge losses in the defeat]. When he has taken away the multitude, his heart will be lifted up; and he will cast down tens of thousands, but he will not prevail. For the king of the North will return and muster a multitude greater than the former, and shall certainly come at the end of some years with a great army and much equipment."

11:14-16 Ptolemy V Epiphanes (203-181) (kS), Jews who joined the Seleucid's side and Antiochus the Great (kN)
"Now in those times many shall rise up against the king of the South. Also, violent men of your people shall exalt themselves in fulfillment of the vision, but they shall fall [Ptolemaic general Scopas crushed the Jewish rebellion]. So the king of the North shall come and build a siege mound, and take a fortified city [Sidon]; and the forces of the South shall not withstand him [Ptolemy's army lost the battle of Panion]. Even his choice troops shall have no strength to resist. But he who comes against him shall do according to his own will, and no one shall stand against him. He shall stand in the Glorious Land with destruction in his power [Judea changing hand in 198/197]."

11:17 Ptolemy V and Antiochus' daughter Cleopatra I
"He shall also set his face to enter with the strength of his whole kingdom, and upright ones with him; thus shall he do. And he shall give him the daughter of women [got married to Antiochus in 193] to destroy it; but she shall not stand with him, or be for him."

11:18-19 The Romans and Antiochus the Great (his end)
"After this he shall turn his face to the coastlands [around the Aegean sea], and shall take many. But a ruler shall bring the reproach against them to an end [battles of Thermopylae (191) in Greece and Magnesia (190) in Asia Minor]; and with the reproach removed, he shall turn back on him. Then he shall turn his face toward the fortress of his own land [Elymais]; but he shall stumble and fall, and not be found."

11:20 Heliodorus, the usurper of Seleucus IV Philopator (187-175)
"There shall arise in his place one who imposes taxes on the glorious kingdom; but within a few days he shall be destroyed, but not in anger or in battle."

Daniel Part 2, the failed predictions:

Here starts the predictions on what Antiochus IV was going to do, after Daniel Part 2 had been written and read. I repeat the next verse (already quoted) for clarity:

11:36 "Then the king
[NOT any Antichrist but king Antiochus IV, victorious and totally in control. It is the same king as the one in 11:31-32, whose army took care of the opposition (11:32b-35). There is nothing in 11:33-35 to indicate there was a change]
` shall do according to his own will: he shall exalt
[2Macc.5:17 "Antiochus was elated in spirit", after looting the temple]
` and magnify himself above every god, shall speak blasphemies against the God of gods,
[there are many mentions of the existence of other gods, with God seemingly isolated from any mortals]
` and shall prosper till the wrath has been accomplished; for what has been determined shall be done.

11:37 He shall regard neither the gods of his fathers nor the desire of women [Tammuz, another god (Eze 8:14)], nor regard any god; for he shall exalt himself above them all.

11:38 But in their place he shall honor a god of fortresses ; and a god which his fathers did not know he shall honor with gold and silver,
[pillaged from the temple and its treasury:
Josephus' Ant., XII, V, 4 "a great deal of gold ... and many ornaments ... golden candlesticks ... golden altar ... the veils, which were made of fine linen and scarlet."
The author probably suggested that the loot from the temple was used as offering to this "god of fortresses"]
` with precious stones and pleasant things."

11:39 "Thus he shall act against the strongest fortresses with a foreign god,
[the same god as mentioned in the previous verse. This god is foreign because Antiochus' forefathers did not know him. The god, "bribed" by the offering from the treasures of the looted temple, would help Antiochus to take the fortresses in his future campaigns]
` which he shall acknowledge, and advance its glory; and he shall cause them to rule over many, and divide the land for gain."
[it is in this verse that Antiochus IV would fulfill (except for the South) the prophecies of 7:23 "And shall devour the whole earth, trample it and break it in pieces". Since the whole earth, as a Jew of Jerusalem would know it in these days, did not go beyond the Black Sea, the desert of central Asia and the Indus river, Antiochus needed only to conquer little more than Macedonia & Greece from the Romans and western & northern today's Turkey. And of course the Romans hardly existed for Daniel-2.
Let's also say that "the whole earth" in 2:39 means the largest extent of the Persian empire (the third kingdom), which, with the exceptions of Egypt, Asia Minor & Galatia/Cappadocia and the territories east in central Asia (Bactria), was not much bigger that the Seleucid kingdom of Antiochus IV. And in 1Macc.1:3, written later than 'Daniel', we are told that Alexander the Great "advanced to the ends of the earth", even if he never set foot west of Greece.
And for the South, I'll come to that later]

[The following events (Antiochus' return to Egypt), as wrongly predicted in 11:40-45, were supposed to happen before Antiochus' death. It was to be the signal for the arrival of the kingdom possessed by the saints (righteous Jews) (7:18) and brought about by Michael "the great prince"]

11:40 [the demigod is saying to Daniel:] "At the time of the end the king of the South
[the author was thinking that Egypt, a weak military power, would take advantage of Antiochus' army departure. Ptolemy VI had been looking to reclaim Palestine]
` shall attack him; and the king of the North
[Antiochus IV

Note: the expression "king of the South/North" is also used many times in the "historical" section 11:2-36 (immediately preceding this one), to mean king of Egypt/Syria: why would it mean anything different here?]

` shall come against him like a whirlwind, with chariots, horsemen,
[and not tanks and fighter planes!]
` and with many ships;
[this time, Antiochus IV would be well prepared to fight off the nasty Romans, allies of Ptolemy VI! And the ships would be useless inland at Armageddon (Megiddo) but very useful at Alexandria!]
` and he shall enter the countries, overwhelm them, and pass through.
[as he did before!]

11:41 He shall also enter the Glorious Land [Judea], and many countries shall be overthrown; but these shall escape from his hand: Edom, Moab, and the prominent people of Ammon.
[places of refuge (for the remaining faithful Jews) are indicated: Moab is conveniently located at less than a day walk from Jerusalem! Historically, this area, beyond the Jordan river and the Dead Sea, east of Jerusalem (today's the kingdom of Jordan), was spared from invasion: a safe bet]

11:42 He shall stretch out his hand against the countries, and the land of Egypt shall not escape.
[that would have been the third invasion of Egypt by Antiochus: a routine operation!]

11:43 He shall have power over the treasures of gold and silver, and over all the precious things of Egypt;
[which Antiochus did already (except for Alexandria). The Romans were not expected to interfere this time because of Antiochus' stronger army and "many ships"]
` also the Libyans and Ethiopians shall follow at his heels.
[Libya and Ethiopia were considered at the end of the world for the Jews in these days. Beyond (and west of) Libya lays (western) North Africa, (today's Tunisia, Algeria and Morocco), at the time prosperous and civilized. No mention! Evidently, for our author, the world did not go very far westward]

11:44 But news from the east and the north shall trouble him;
[the Armenians were claiming independence and the Parthians encroached on Seleucid territory. On this matter, our author "guessed" right: "in the hundred and forty-seventh year, he [Antiochus IV with his army] passed over Euphrates, and went to the superior provinces." (Josephus' Ant., XII, VII, 2b). There, he defeated the king of Armenia, Artaxias, and the Parthians]
` therefore he shall go out with great fury to destroy and annihilate many.
[that would complete the predicted conquest of the whole known world as postulated in 7:23]

11:45 And he shall plant the tents of his palace between the seas and the glorious holy mountain;
[most likely refer to Jerusalem. A very vague location: between the seas and Jerusalem could be almost anywhere!]
` yet he shall come to his end, and no one will help him.
[Antiochus' death is also mentioned in 8:25b "Yet he will be destroyed, but not by human power". Antiochus died at war, at Tabae in Persia, from illness or accident, in 164/163 B.C.E.]

12:1 At that time
[Antiochus' death, as stated in the previous verse, as also in 7:11b,8:25b,9:27,11:27b & 11:36b]
` Michael shall stand up, The great prince who stands watch over the sons of your people;
[note: "your people", this demigod does not consider the Jews as his. Now, Michael is protecting the Jews, since Antiochus is said to have turned back from his gods (11:37), including the one friendly to the Jews & Daniel. But where is the God of the Jews? Michael seems to be in charge! And it is Michael, as an all-powerful deity, and not a Messiah (or Jesus), bringing about deliverance and the "end of time", with the resurrections & the eternal kingdom]
` And there shall be a time of trouble, Such as never was since there was a nation, Even to that time. And at that time your people shall be delivered, [the start of the "end of time"]. Every one who is found written in the book [as in 7:9-10 quoted earlier].

12:2 And many of those who sleep in the dust of the earth shall awake, Some to everlasting life, Some to shame and everlasting contempt.
[contrary to what is claimed by some Christian scholars or preachers, resurrections and eternal life thereafter are not a Christian concept (on resurrections see also: Isa26:19, Eze37:1-10, Job19:25-26)]

12:3 Those who are wise
[allusion to the ones who died earlier: 11:35 "And some of those of understanding shall fall, to refine them, purify them, and make them white, until the time of the end; because it is still for the appointed time"]
` shall shine like the brightness of the firmament, And those who turn many to righteousness like the stars forever and ever."
[needless to say the events of the last three verses did not happen, when they were supposed to, at the death of Antiochus IV]

Later updating in Daniel Part 2:

The following "updating" was meant to have the fictional prophet Daniel (or rather his friendly demigod!) predict any event affecting the temple as long as Antiochus IV was alive (and still able to fulfill the prophecies of 11:40-45). Antiochus' death happened in 164. Since the desecration of the temple is described as an "abomination and desolation" of ultimate importance, any reconsecration and further disturbance could not have gone "unpredicted". And of course this demigod had been so accurate in his prophecies from the third year of Cyrus all the way to 167 that he could not have "missed" events beyond that!

DANIEL PART 3:

8:13-14,26. Written in very late 165 or early 164 (after the reconsecration of the sanctuary in the temple). The most likely author is Daniel-2 but could be another one: Daniel-3.

8:14 "And He [the demigod] said to me, "It will take 2,300 evenings and mornings;
[1150 days. Notice the great accuracy of this alleged prediction and the next ones]
` then the sanctuary will be reconsecrated."" [quote from the NIV]

Notes:
a) Josephus wrote that three Jewish years (1,080 days) went by between the desecration (start of pagan sacrifices) and reconsecration. Consequently, it seems that the ending of Jewish offering occurred seventy days prior to desecration. In Josephus' Ant., XII, V, 4, the building of a citadel "with high walls and towers" in Jerusalem, next to the temple, took place between "he forbade them to offer those daily sacrifices which they used to offer to God, according to the law." and "when the king had built an idol altar upon God's altar, he slew swine upon it".
A significant time (between the ending of sacrifices and desecration) is confirmed by Josephus' Wars, Preface, 7:
"... Antiochus, who was named Epiphanes, took Jerusalem by force, and held it three years and three months [about 1170 days], and was then ejected ..."
b) According to Daniel Part2 9:27: "... In the middle of the 'seven', he will put an end to sacrifice and offering . And on the wing of the temple, he will set up [Nov/Dec 168] an abomination that causes desolation [Greek altar and swine sacrifices], until the end that is decreed is poured out on him [Antiochus' end]"
there is no mention of the reconsecration of the temple between "the abomination" and Antiochus' death, a sure indication that Daniel Part 3 is an addition.

DANIEL PART 4:

12:11. Written in 164 in early spring (after the Ex-Jews and the Syrian/Macedonian soldiers from the garrison in the citadel managed to defile the temple and interrupt the Jewish animal sacrifice).

This kind of events are alluded to in Josephus' Ant., XII, IX, 3a. "At that time [163 B.C.E.] it was that the garrison in the citadel of Jerusalem, with the Jewish runagates, did a great deal of harm to the Jews: for the soldiers that were in that garrison rushed out upon the sudden, and destroyed such as were going to the temple in order to offer their sacrifices, for this citadel adjoined to and overlooked the temple. When these misfortunes had often happened to them, ..."
and 1Maccabees: 1:33-36 "Then they built up the City of David with a high, massive wall and strong towers, and it became their citadel. There they installed a sinful race, perverse men, who fortified themselves inside it, storing up weapons and provisions, and depositing there the plunder they had collected from Jerusalem. And they became a great threat. The citadel became an ambush against the sanctuary, and a wicked adversary to Israel at all times."

Same author as the one of Part 3.

12:11 "And from the time that the daily sacrifice is taken away, and the abomination of desolation is set up, there shall be one thousand two hundred and ninety days."
According to the 1290 days indication, this event happened around April, a very appropriate time in order to disturb the Passover Jewish sacrifices.

DANIEL PART 5:

12:12. Written later in the spring. The same ex-Jews & soldiers were chased back one and a half month later (likely in early June of 164). Same author as the one of Part 3.

12:12 "Blessed is he who waits, and comes to the one thousand three hundred and thirty-five days."

CONCLUSION:

The death of Antiochus IV occurred in 164 B.C.E. The circumstances of his death were not as predicted in 7:11. However, centuries later, that did not prevent Josephus to declare "this king [Antiochus IV] died on account of his sacrilegious plundering of the temple of Jerusalem." (Ant., XII, IX, 1).
In Ant., X, XI, 7, Josephus gave his own interpretation of Daniel's visions:
"He said that the ram signified the kingdoms of the Medes and Persians, and the horns
[Da8:3b "... was a ram which had two horns, and the two horns were high; but one was higher [the one of the Persians] than the other, and the higher one came up last [early on, the Medes were prominent]."]
those kings that were to reign in them; and that the last horn signified the last king, and that he should exceed all the kings in riches and glory: that the he-goat signified that one should come and reign from the Greeks [Alexander the Great], who should twice fight with the Persian [Darius III], and overcome him in battle, and should receive his entire dominion: that by the great horn which sprang out of the forehead of the he-goat was meant the first king [Alexander the Great]; and that the springing up of four horns [the Hellenist kingdoms] upon its falling off, and the conversion of every one of them to the four quarters of the earth, signified the successors [the Hellenist kings] that should arise after the death of the first king [Alexander the Great], and the partition of the kingdom among them, and that they should be neither his children, nor of his kindred, that should reign over the habitable earth for many years; and that from among them [the Hellenist kings] there should arise a certain king that should overcome our nation and their laws, and should take away their political government, and should spoil the temple, and forbid the sacrifices to be offered for three years' time. And indeed it so came to pass, that our nation suffered these things under Antiochus [IV] Epiphanes"
Most likely (and according to the Encyclopaedia Britannica: "at the end of 164"), Antiochus IV's death happened in the fall, close enough to justify (in some ancient copies only) "a year, two years and a half year" (from the time of the "desolation"), replacing (and "interpreting") "time, times and a half time" (7:25, 12:7). The copyist(s) who did the change probably wanted to be more accurate (with hindsight!) about the time of death of Antiochus IV, especially when, as we saw, some times were given in days! Another interpolation made in those days is 7:12 (& 2:44), a confusing digression about the three ex-kings/beasts outliving the fourth one, out of context in the narration and never explained or repeated. See more explanation here

From 70 C.E., the book of Daniel was mentioned in order to suggest that:
a) The two devastations of Jerusalem were prophesied and consequently part of some God's plan, even proving God's existence. (Josephus' Ant., X, XI, 7b)
b) The destruction of the holy city (in 70 C.E.) was the signal for the "end" to come soon (Mark's gospel (13:1-2,14-27,30), Revelation of John, The Jewish Original Version).