In this article, I will try to shine the light on the mathematical aspects of technical trading!
The mathematics behind the harmonic patterns!
What is a dynamical system?
A dynamical system is all about the evolution of something over time. To create a dynamical system we simply need to decide (1) what is the “something” that will evolve over time and (2) what is the rule that specifies how that something evolves with time. In this way, a dynamical system is simply a model describing the temporal evolution of a system.
The state-space
The first step in creating a dynamical system is to pin down what is the special “something” that we want to evolve with time. To do this, we need to come up with a set of variables that give a complete description of the system at any particular time.
By “complete description,” we don't necessarily mean that the variables will completely describe a real-life system we may be trying to model. But, the variables must completely describe the state of the mathematical system. In a dynamical system, if we know the values of these variables at a particular time, we know everything about the state of the system at that time. To model some real-life system, the modeler must clearly make a choice of what variables will form the complete description for the mathematical model.
The variables that completely describe the state of the dynamical system are called the state variables. The set of all the possible values of the state variables is the state space.
The state-space can be discrete, consisting of isolated points, such as if the state variables could only take on integer values. It could be continuous, consisting of a smooth set of points, such as if the state variables could take on any real value. In the case where the state space is continuous and finite-dimensional, it is often called the phase space, and the number of state variables is the dimension of the dynamical system. The state space can also be infinite-dimensional.
Geometry and Fibonacci Numbers
Harmonic trading combines patterns and math into a trading method that is precise and based on the premise that patterns repeat themselves. At the root of the methodology is the primary ratio, or some derivative of it (0.618 or 1.618). Complementing ratios include: 0.382, 0.50, 1.41, 2.0, 2.24, 2.618, 3.14 and 3.618. The primary ratio is found in almost all-natural and environmental structures and events; it is also found in man-made structures. Since the pattern repeats throughout nature and within society, the ratio is also seen in the financial markets, which are affected by the environments and societies in which they trade.
By finding patterns of varying lengths and magnitudes, the trader can then apply Fibonacci ratios to the patterns and try to predict future movements. The trading method is largely attributed to Scott Carney, although others have contributed or found patterns and levels that enhance performance.
The Bat
The bat pattern is similar to Gartley in appearance, but not in measurement.
There is a rise via XA. B retraces 0.382 to 0.5 of XA. BC retraces 0.382 to 0.886 of AB. CD is a 1.618 to 2.618 extension of AB. D is at a 0.886 retracement of XA.
Conclusion:
No matter which approach you use, try to pick the one that works for you!
Reference:
https://mathinsight.org/dynamical_system_idea
https://www.investopedia.com/articles/forex/11/harmonic-patterns-in-the-currency-markets.asp
You can see the most important support(green line) and resistance (red line) levels.
Best,
Moshkelgosha
DISCLAIMER
I’m not a certified financial planner/advisor, a certified financial analyst, an economist, a CPA, an accountant, or a lawyer. I’m not a finance professional through formal education. The contents on this site are for informational purposes only and do not constitute financial, accounting, or legal advice. I can’t promise that the information shared on my posts is appropriate for you or anyone else. By using this site, you agree to hold me harmless from any ramifications, financial or otherwise, that occur to you as a result of acting on information found on this site.
The mathematics behind the harmonic patterns!
What is a dynamical system?
A dynamical system is all about the evolution of something over time. To create a dynamical system we simply need to decide (1) what is the “something” that will evolve over time and (2) what is the rule that specifies how that something evolves with time. In this way, a dynamical system is simply a model describing the temporal evolution of a system.
The state-space
The first step in creating a dynamical system is to pin down what is the special “something” that we want to evolve with time. To do this, we need to come up with a set of variables that give a complete description of the system at any particular time.
By “complete description,” we don't necessarily mean that the variables will completely describe a real-life system we may be trying to model. But, the variables must completely describe the state of the mathematical system. In a dynamical system, if we know the values of these variables at a particular time, we know everything about the state of the system at that time. To model some real-life system, the modeler must clearly make a choice of what variables will form the complete description for the mathematical model.
The variables that completely describe the state of the dynamical system are called the state variables. The set of all the possible values of the state variables is the state space.
The state-space can be discrete, consisting of isolated points, such as if the state variables could only take on integer values. It could be continuous, consisting of a smooth set of points, such as if the state variables could take on any real value. In the case where the state space is continuous and finite-dimensional, it is often called the phase space, and the number of state variables is the dimension of the dynamical system. The state space can also be infinite-dimensional.
Geometry and Fibonacci Numbers
Harmonic trading combines patterns and math into a trading method that is precise and based on the premise that patterns repeat themselves. At the root of the methodology is the primary ratio, or some derivative of it (0.618 or 1.618). Complementing ratios include: 0.382, 0.50, 1.41, 2.0, 2.24, 2.618, 3.14 and 3.618. The primary ratio is found in almost all-natural and environmental structures and events; it is also found in man-made structures. Since the pattern repeats throughout nature and within society, the ratio is also seen in the financial markets, which are affected by the environments and societies in which they trade.
By finding patterns of varying lengths and magnitudes, the trader can then apply Fibonacci ratios to the patterns and try to predict future movements. The trading method is largely attributed to Scott Carney, although others have contributed or found patterns and levels that enhance performance.
The Bat
The bat pattern is similar to Gartley in appearance, but not in measurement.
There is a rise via XA. B retraces 0.382 to 0.5 of XA. BC retraces 0.382 to 0.886 of AB. CD is a 1.618 to 2.618 extension of AB. D is at a 0.886 retracement of XA.
Conclusion:
No matter which approach you use, try to pick the one that works for you!
Reference:
https://mathinsight.org/dynamical_system_idea
https://www.investopedia.com/articles/forex/11/harmonic-patterns-in-the-currency-markets.asp
You can see the most important support(green line) and resistance (red line) levels.
Best,
Moshkelgosha
DISCLAIMER
I’m not a certified financial planner/advisor, a certified financial analyst, an economist, a CPA, an accountant, or a lawyer. I’m not a finance professional through formal education. The contents on this site are for informational purposes only and do not constitute financial, accounting, or legal advice. I can’t promise that the information shared on my posts is appropriate for you or anyone else. By using this site, you agree to hold me harmless from any ramifications, financial or otherwise, that occur to you as a result of acting on information found on this site.
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