Fibonacci Relationships

Fibonacci ratios are named for the famous 13th-century mathematician
Leonardo Fibonacci of Pisa, the most important mathematician
of the Middle Ages. Fibonacci popularized the current
decimal and Hindu-Arabic numbering systems. He also discovered
(actually rediscoered) the numeric sequence that bears his name,
the Fibonacci sequence which begins with the number 1 and in
which each subsequent number is the sum of the previous two:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. The sequence in
turn gives rise to several unique ratios, including .618, .382 and
1.618 — the Golden Ratio. These ratios exist throughout nature, in
everything from population growth to the physical structure within
the human brain, the DNA helix, many plants and even the cosmos
itself.
Many investors today know that Fibonacci ratios are used
for market forecasting. But few realize that Fibonacci analysis of
the markets was pioneered by R.N. Elliott. The use of Fibonacci
ratios requires a valid Elliott wave interpretation as a starting
point. Unfortunately, many non-Elliott analysts try to find Fibonacci
proportions between market moves that are not related to each
other in any way. This has made the approach appear far less
valuable than it is.
Elliott had two chief insights concerning Fibonacci relationships
within waves. First, corrective waves tend to retrace prior impulse
waves of the same degree in Fibonacci proportion. That’s a common
relationship. Other frequent wave relationships are 50% and 62%.
Second, impulse waves of the same degree within a larger impulse
sequence tend to be related to one another in Fibonacci proportion.