ELLIOTT WAVE CONSULTANCY

Institution of Capital Market and Business Cycle Studies

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FIBONACCI STUDIES

Statue of Leonardo Fibonacci, Pisa, Italy.
The inscription reads, "A. Leonardo Fibonacci, Insigne
Matematico Piisano del Secolo XII."

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• In Liber Abacci, a problem is posed that gives rise to the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on to infinity, known today as the Fibonacci sequence. The problem is this:
   

• How many pairs of rabbits placed in an enclosed area can be produced in a single year from one pair of rabbits if each pair gives birth to a new pair each month starting with the second month?
   

• In arriving at the solution, we find that each pair, including the first pair, needs a month's time to mature, but once in production, begets a new pair each month. The number of pairs is the same at the beginning of each of the first two months, so the sequence is 1, 1. This first pair finally doubles its number during the second month, so that there are two pairs at the beginning of the third month. Of these, the older pair begets a third pair the following month so that at the beginning of the fourth month, the sequence expands 1, 1, 2, 3. Of these three, the two older pairs reproduce, but not the youngest pair, so the number of rabbit pairs expands to five. The next month, three pairs reproduce so the sequence expands to 1, 1, 2, 3, 5, 8 and so forth. Figure 3-1 shows the Rabbit Family Tree with the family growing with logarithmic acceleration. Continue the sequence for a few years and the numbers become astronomical. In 100 months, for instance, we would have to contend with 354,224,848,179,261,915,075 pairs of rabbits. The Fibonacci sequence resulting from the rabbit problem has many interesting properties and reflects an almost constant relationship among its components.

    
Fibonacci Arcs:-

      The calculation and interpretation of Fibonacci Arcs is similar to that of Fibonacci Fan Lines. First, a trend line is drawn between two extreme points. It draws three arcs, centered on the second extreme point, that intersect the trend line drawn between the two extreme points at the Fibonacci levels of 38.2%, 50.0%, and 61.8%.

The interpretation of Fibonacci Arcs involves looking for, or anticipating, support and resistance as prices approach the arcs. A common technique is to display both Fibonacci Arcs and Fibonacci Fan Lines and to anticipate support/resistance at the points where the Fibonacci studies cross.

     The points where the Arcs cross the price data will vary depending on the scaling, because the Arcs are drawn so they always appear circular relative to the computer screen.

Fibonacci Fans:-

     Fibonacci Fan Lines are displayed by first drawing a trend line between two extreme points. It draws an invisible vertical line through the second extreme point. This vertical line is then divided at the Fibonacci levels of 38.2%, 50.0%, and 61.8%. Finally, three trend lines are drawn from the first extreme point so they pass through the invisible vertical line at the above three levels. (This technique is similar to the method used to calculate Speed Resistance Lines

Fibonacci Retracement:-

    Fibonacci Retracements are displayed by first drawing a trend line between two extreme points (i.e., a significant trough and peak). After selecting Fibonacci Retracement from the Insert menu, a series of up to nine horizontal lines will be drawn at the Fibonacci levels of 0.0%, 23.6%, 38.2%, 50.0%, 61.8%, 100%, 161.8%, 261.8%, and 423.6%.

     After a significant move (either up or down), prices will often rebound and retrace a significant portion (if not all) of the original move. As the price retraces, support and resistance levels will often occur at or near the Fibonacci Retracement levels.

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FIBONACCI  IS ONE  PART OF ELLIOTT WAVE