Fibonacci sequence


In mathematics, the Fibonacci sequence (sometimes wrongly called the Fibonacci series) is the infinite sequence of natural numbers.


The sequence begins with the numbers 0 and 1, and from these, each element is the sum of the previous two. The elements of this sequence are called Fibonacci numbers. This sequence was described in Europe by Leonardo de Pisa, a 13th century Italian mathematician also known as Fibonacci.

It has numerous applications in computer science, mathematics, and game theory. It also appears in biological configurations, such as in the branches of trees, in the arrangement of the leaves on the stem, in the flora of the artichoke and in the arrangement of a cone.

The fundamental concept of the Fibonacci sequence is that each element is the sum of the previous two. In this sense, the sequence can be expanded to the set of integers such that the sum of any two consecutive numbers is the immediately following.

Applications of the Fibonacci sequence

Fibonacci sequences have their application in the stock market study, they are considered a very important indicator to see the magnitude of the retracements in the Stock Market:

Upon confirmation of a decline in the price, we will seek to calculate the probable magnitude of the movement. To achieve this, certain percentages obtained from the Fibonacci sequence are applied to the total magnitude of the previous trend.

The percentages used are the following:

  • 61.8%: Also known as the golden ratio, or golden number, it is the limit of the quotient obtained from the division of one element of the Fibonacci sequence by the next, as the series tends to infinity.
  • 50.0%: It is the most commonly accepted retracement, equivalent to half the advance of the main trend.
  • 38.2%: It is obtained by subtracting 61.8% from the unit (1.000 - 0.618 = 0.382).
  • 100%: Equivalent to the total magnitude of the main trend.

Considerations to take into account of the Fibonacci sequence

The percentages of retracement in the stock market analysis should be calculated only after the end of a trend has been confirmed, never while the trend continues.

Taking into account that trends are always part of a longer-term trend and in turn are made up of shorter-term trends, the question is: On which of these trends should I calculate the setbacks? It may not have a simple answer. In general terms, we must calculate the setbacks on that trend that has given clear signs of termination.

It is considered that a weak trend may have a 31.8% retracement, while a very strong trend may have a 61.8% retracement, before returning to its original direction.

Some books mention a critical zone of 33 to 38.2%, and 61.8 to 67%, instead of the specific levels.

The most important criticisms against Fibonacci retracements are based on random walk theory, arguing that there is no justification for assuming that price action has any reason to respect predetermined retracement levels.

Fibonacci retracements form an important part of the Elliott Wave Theory.

Graphic example

Below we can see a graphic example of the Fibonacci zones:

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