The long answer is that Daniel's chronology is approximated to the passage of time between the word of Jerusalem's restoration during the Babylonian Exile in the 6th century B.C. (Jeremiah xxx.1, 18) and events in the 2nd Century B.C.
Within this time frame, the events the author describes find perfect correspondence with the suppression of Jewish religion by oppressive Hellenization under Antiochus Epiphanes. At the 69th week an anointed one is cut off/murdered (the high priest Onias III) in 171 B.C. (Josephus, Antiq. Book xii.237), which began the 70th week in Daniel's Chronology. Antiochus made a covenant around 167 B.C. (corresponding with Daniel's middle of the 70th week) with Hellenized Jews (see 1Maccabees i.11-15; Antiq. xii.240), but then betrayed them and ransacked the city (1Maccabees i.29-31; Antiq. xii.248-49), burned and destroyed much of it (1Maccabees i.30, 31; Antiq. xii.252), ended Jewish sacrifice (1Maccabees i.44-45; Antiq. xii.251), and then erected the 'abomination' the book of Daniel speaks of (1Maccabees i.54; Antiq. xii.253).
This matches Daniel's chronology just fine.
Thanks,
Eric