Most scholars today accept the fact that Daniel would have used the system he was best familiar with and that was the Babylonian system of the Tishri based accession year.
Other Jewish writers such as Jeremiah writing from a Judaean national background would favour the Jewish Nisan based regnal, or non-accession system.
In support of this I can quote "The Mysterious Numbers of the Hebrew Kings" by Prof Edwin Thiele. His chapter on "The fundamentals of Hebrew chronology" is particularly informative [Ch 2, pgs 43-60]
This may explain the discrepancy that might appear to exist between the two texts Jer 25:1 and Dan 1:1.
First a brief primer for those on the forum who are unfamiliar with the terms used in chronological research:
Basically there were two systems of counting the reigns of kings as found in the Bible record.
1 The Babylonian system: The Babylonians used a system called the Accession Year System, which basically meant that when a king ascended the throne in mid-year, the rest of that initial year, till the Babylonian "new year" would NOT be his first year, but his accession year. On New Years day, which in was Babylon Tishri 1, he would legally be recognized as starting his reign and from that day what was termed his first year began,
2 The Jewish system simply counted his reign from the time he started his reign. Simple. This was called the "Regnal" year system, or non-accession year system.
Does this make a difference? Yes. Consider it in our modern day context: Suppose Nebuchadnezzar came to the throne on Jan 2, this year. This year period right up till Dec 31,according to the Babylonian system, would not be counted as his first year, simply as his accession year. THEN on Jan 1, next year, he would be counted in Babylon as beginning his first year.
However if you were a Jew, you would already count this year as his first year, and the next year, as his second year. So at times Chronologists, trying to sychronize information found in the Bible, need to take these cultural differences into consideration.
Take Jer 25:1, as an example. There it tells us that in the fourth year of Jehoiachim Nebuchadnezzar came against Judah
But Dan 1:1 describing the same event says: That in the third year of Jehoiachim Nebuchadnezzar came against Judah.
Contradiction? Nope. Simply different ways of saying the same thing.
In this connection, I might just digress a moment and illustrate what I am trying to describe by relating what, in some instances might be an infuriating difference between the American and British/Aust way in counting the floors of a building. I was in the middle of reading a book on the Kennedy assassination, and having grown up on the American system of floor counting as found in books on the subject, I noticed for the first time that this particular author I was reading, stated that the so-called snipers perch was located on the fifth floor of the Dallas Texas School Book Depository. Fifth? I always thought it was the sixth, simply because every book I had read on the subject said "sixth". It was only when I remembered that the author I was reading was British that he had used that system of numbering that was current in British English. Like the pagan Babylonians we are, we don't count the ground floor as the first floor. The next floor above, what to an American would be the second floor, is our first floor. Problem solved.
Probably a poor illustration, however, it may describe the different ways seperate cultures may describe the same thing.
Cheers