Use of the Fibonacci sequence on stock markets
Since decades, the Fibonacci sequence is used to try to predict the movements of the stock market. A bullish or bearish trend is never linear. When the trend is rising, downward phases are called "correction" and when it is going down, upward phases are called "rebound" Fibonacci retracements are commonly used tools to try to predict those corrections and rebounds. They are automatically taken into account in the algorithms and are offered as basic tools for traders.
How the retracements are produced? Let's recall the sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 The retracements are the ratios between two Fibonacci numbers. Two consecutive numbers in the sequence tend to the golden ratio, for example 55/89 = 0.618. Other ratios are obtained by the ratio between a number of the suite and another, not consecutive. For example 34/89 = 0.382, 0.236 13/55 = 1/2 = 0.5 and 1/1 = 1. Translated into percentages Fibonacci retracements are: 23.6%, 38.2%, 50.0%, 61.8%, 100%. When it exceeds 100%, it is called Fibonacci extensions (1000, 1382, 1618 ...). We could also mention the Fibonacci projections: 61.80%, 100.00%, 138.20%, 161.80%, 271.80%. 
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Elliot is doing waves
Born in the late 19th century, Ralph Nelson Elliott, spent many years analyzing stock market waves to find a prediction model. He stated that markets follow a repetitive series of five waves in the direction of the upward or downward trend, and three corrective waves in the opposite direction (movement "53").
Elliot is doing waves
Born in the late 19th century, Ralph Nelson Elliott, spent many years analyzing stock market waves to find a prediction model. He stated that markets follow a repetitive series of five waves in the direction of the upward or downward trend, and three corrective waves in the opposite direction (movement "53").
The trend waves are denoted 12345 and the correction waves a, b and c.
From his observations, and without being able to suspect it, the economist introduced an economic dimension to the relationship between beauty and numbers. When he was told that the numbers in his schemes were all "Fibonaccis", he replied that he had never heard of it. On the other hand, he preceded with his discovery 60 years, Mandelbrot fractals, pillar of the mathematical beauty.
The question of whether Elliot's model is reliable or not continues to make waves, but thanks to him also Fibonacci does it in the world of finance.
A little word on economy
As regards to financial markets for a long time we know that market psychology is critical to anticipate price dynamics. Therefore finance distinction is made between fundamental analysis (GDP, unemployment benefit of businesses, interest rates, etc.) and technical analysis (Fibonacci, moving averages, MACD, etc.)
Group psychology
Technical analysis, to simplify greatly, study herd behavior of investors, it is group psychology applied to finance. In technical analysis, the "chartists" have invented a number of technical indicators. Basically there are two types of indicators: momentum (measured "belief", the strength of the market moving in this direction) and directional (in which direction the market will evolve, increase drop, etc.)
Some of these indicators have been used since the 17th or 18th centuries).
The Fibonacci sequence is part of the technical indicators, it serves to indicate the levels to which the price will reach. These levels are called "resistance" (in a bullish phase) or "support" (in a downturn). The same level may be a resistance or a medium according to the dynamic price.
Why does it works?
In finance, we do not really know why the Fibonacci sequence work, it is simply based on market psychology. The following article demonstrates a link between the golden ratio and psychology and mentions both ratios 0.618 and 0.382 (golden ratio) in how people stigmatize other. https://thepsychologist.bps.org.uk/volume22/edition3/strikinggoldensectionstigmaresearch
The relationship between fractals, Fibonacci and society are studied by the socionomics institute. See the following video, go to 14'10" for the ratio and social psychology.
From his observations, and without being able to suspect it, the economist introduced an economic dimension to the relationship between beauty and numbers. When he was told that the numbers in his schemes were all "Fibonaccis", he replied that he had never heard of it. On the other hand, he preceded with his discovery 60 years, Mandelbrot fractals, pillar of the mathematical beauty.
The question of whether Elliot's model is reliable or not continues to make waves, but thanks to him also Fibonacci does it in the world of finance.
A little word on economy
As regards to financial markets for a long time we know that market psychology is critical to anticipate price dynamics. Therefore finance distinction is made between fundamental analysis (GDP, unemployment benefit of businesses, interest rates, etc.) and technical analysis (Fibonacci, moving averages, MACD, etc.)
Group psychology
Technical analysis, to simplify greatly, study herd behavior of investors, it is group psychology applied to finance. In technical analysis, the "chartists" have invented a number of technical indicators. Basically there are two types of indicators: momentum (measured "belief", the strength of the market moving in this direction) and directional (in which direction the market will evolve, increase drop, etc.)
Some of these indicators have been used since the 17th or 18th centuries).
The Fibonacci sequence is part of the technical indicators, it serves to indicate the levels to which the price will reach. These levels are called "resistance" (in a bullish phase) or "support" (in a downturn). The same level may be a resistance or a medium according to the dynamic price.
Why does it works?
In finance, we do not really know why the Fibonacci sequence work, it is simply based on market psychology. The following article demonstrates a link between the golden ratio and psychology and mentions both ratios 0.618 and 0.382 (golden ratio) in how people stigmatize other. https://thepsychologist.bps.org.uk/volume22/edition3/strikinggoldensectionstigmaresearch
The relationship between fractals, Fibonacci and society are studied by the socionomics institute. See the following video, go to 14'10" for the ratio and social psychology.
Fibonacci sequence and the golden ratio, Phi
The Fibonacci sequence is directly related to the golden ratio. Although no ratio can rule on the golden ratio, which is the irrational among the irrationals numbers, the ratio of two successive Fibonacci numbers draw always closer to the golden ratio as it grows.
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