According to Juan Baixeras at the next link: "The idea of applying years to
days can be traced back to Jewish rabbis in the first century CE. In the ninth
century more rabbis applied it to Daniel’s prophecy in connection with the time
periods of 1,290, 1335, and 2300 days in reference to when the Messiah would ap-
pear. Among Christians it first appears in the twelfth century by a Roman Cath-
olic abbot named Joachim of Floris. As time passed, an incredible amount of
dates were arrived at by different interpreters. Dates were regularly changed
as one date after another passed without the predicted event taking place."
http://www.geocities.com/athens/olympus/5257/1914.htm
1823 "In the early 1800’s a man named John Aquila Brown published an explanation of
the 2,300 days of Daniel in chapter 12, showing these as ending in 1844. This
view was also adopted by William Miller, the pioneer of the Second Advent move-
ment."
(Miller predicted the 2nd coming would happen in March 21, 1843 to March 21,
1844.)
"John A. Brown also developed another explanation that is intimately related
to the year 1914 as that date figures in the teachings of JWs. Brown was the
real interpreter of the 'seven times' of Daniel chapter four, the interpretation
that produces the 2,520 years by means of the day-year formula. Brown first
published this interpretation in 1823 and his method converted the 'seven times'
into 2,520 years in exactly the same way found today in Watch Tower publica-
tions. This was twenty-nine years before Charles Russell was born, more than
half a century before the book 'The Three Worlds' (co-authored by Russell, which
is where most JW think that this teaching originated) appeared.
"Brown however used 604 B.C.E as his starting point and so arrived at 1917.
After the failure of the expectations of 1844, a split of various Second Advent
groups resulted. One of these groups centered around a man called N.H. Barbour.
Barbour studied Brown’s work and adopted much of his interpretation, but changed
his starting point to 606 BCE and arrived at the year 1914. Actually this is a
miscalculation since that would be only 2,519 years. This would have the end
date at 1915."
You might click around at the web site at the link above to see another way
possible for a believer to play with some of the same numbers and come to other
conclusions. I don't recommend playing prophet about it, though.