The Fibonacci series are a mathematical sequence in which any number is the sum of the two preceding numbers. The sequence goes as follows: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. The properties of this sequence appear throughout nature and also in the arts and sciences. Most notably the ratio of 1.618, the "Golden Mean", is very common, a relationship already discovered in ancient times. This number can be approached by dividing a Fibonacci number by its preceding number as the sequence extends into infinity. Besides, ratios of .618, which is the inverse of 1.618 are very prominent when analysing Fibonacci relationships.
Elliott didn’t discover the Fibonacci relationships himself, but this was brought to Elliotts attention by Charles Collins.
The wave counts of the impulsive and corrective patterns (5 + 3 = 8 total) are Fibonacci numbers, and breaking down wave patterns into their respective sub waves produces Fibonacci numbers indefinitely.
Analysing Fibonacci relationships between price movements is very important for several reasons.
First you can control your wave analysis. The better the Fibonacci ratios of your wave count, the more accurate your count is, because in some way or the other, all waves are related to each other. Secondly you can project realistic targets once you have defined the wave count correctly or you have distinguished different scenarios, which point in the same direction.
Since Fibonacci ratios manifest themselves in the proportions of one wave to another, waves are often related to each other by the ratios of 2.618, 1.618, 1, 0.618, 0.382 and 0.236. This fact can help you in estimating price targets for expected waves.
If, for example a wave 1 or A of any degree (or time frame) has been completed, you can project retracements of 0.382, 0.50 and 0.618 for wave 2 or B, which will give you your targets. Most of the time the third wave is the strongest, so often you will find that wave 3 is approximately 1.618 times wave 1. Wave 4 normally shows a retracement, which is less than wave 2, like 0.236 or 0.382. If wave three is the longest wave, the relationship between wave 5 and three often is 0.618. Also wave 5 equals wave 1 most of the time.
The same relations can be found between A and C waves. Normally C equals A or is 1.618 times the length of A.
You could even combine waves to find support and resistance zones. For example the net price movement of wave 1 and 3 times 0.618 creates another interesting target for wave 5.
It is worthwhile to experiment a lot with your wave count, Fibonacci will help you to solve the rhythm of the markets.
Targets for wave 1
The first wave, a new impulsive price movement, tends to stop at the base of the previous correction, which normally is the B wave. This often coincides with a 38.2% or a 61.8% retracement of the previous correction.
Targets for wave 2
Wave 2 retraces at least 38.2% but mostly 61.8% or more of wave 1. It often stops at sub wave 4 and more often at sub wave 2 of previous wave 1. A retracement of more than 76% is highly suspicious, although it doesn�t break any rules yet.
Targets for wave 3
Wave 3 is at least equal to wave 1, except for a Triangle. If wave 3 is the longest wave it will tend to be 161% of wave 1 or even 261%.
Targets for wave 4
Wave 4 retraces at least 23% of wave 3 but more often reaches a 38.2% retracement. It normally reaches the territory of sub wave 4 of the previous 3rd wave.
In very strong markets wave 4 should only retrace 14% of wave 3.
Targets for wave 5
Wave 5 normally is equal to wave 1, or travels a distance of 61.8% of the length of wave 1. It could also have the same relationships to wave 3 or it could travel 61.8% of the net length of wave 1 and 3 together. If wave 5 is the extended wave it mostly will be 161.8% of wave 3 or 161.8% of the net length of wave 1 and 3 together.
Targets for wave A
After a Triangle in a fifth wave, wave A retraces to wave 2 of the Triangle of previous wave 5. When wave A is part of a Triangle, B or 4 it often retraces 38.2% of the complete previous 5 wave (so not only the fifth of the fifth) into the territory of the previous 4th wave. In a Zigzag it often retraces 61.8% of the fifth wave.
Targets for wave B
In a Zigzag, wave B mostly retraces 38.2% or 61.8% of wave A. In a Flat, it is approximately equal to wave A. In an Expanded Flat, it usually will travel a distance of 138.2% of wave A.
Targets for wave C
Wave C has a length of at least 61.8% of wave A. It could be shorter in which case it normally is a failure, which foretells an acceleration in the opposite direction.
Generally wave C is equal to wave A or travels a distance of 161.8% of wave A.
Wave C often reaches 161.8% of the length of wave A in an Expanded Flat.
In a contracting Triangle wave C often is 61.8% of wave A.
Targets for wave D
In a contracting Triangle wave D often travels 61.8% of wave B.
Targets for wave E
In a contracting Triangle wave E often travels 61.8% of wave C. It cannot be longer than wave C!
Targets for wave X
Wave X minimally retraces 38.2% of the previous A-B-C correction; a retracement of 61.8% is also common.
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