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Chart patterns or Chaos attractors?


Can we analyse the chart patterns as chaotic attractors?

That is a modern explanation of the chart patterns that make sense. I will give a definition of an attractor using the Wikipedia. The problem is that the traders do not understand the science of chaos, and the scientists do not understand the trading. As for me I do not understand them both but I will try my best.
An attractor is a set towards which dynamical evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor.Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
Please read this short article in the Wikipedia


What is important is that "A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamic system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers."
And The Fibonacci numbers are defined using the linear recurrence relation. And they can be helfull in the analysis.


According to my analysis the chart patterns can be analyzed as chaotic attractors.
Fixed points: In a trend environment, Higher highs, or lower lows, does it look familiar


Limit cycle: Oscillating price patterns: In fact all the technical analysis chart patterns are in this category: Triangles, Wedges, Harmonic patterns etc.


Limit tori: Complex patterns. It is arguable if they are a part of the technical analysis.
maybe the Elliott Wave Sequence may be close, but I am not sure.


Strange attractors: are not part of the technical analysis. Of course the Elliott wave theoreticians claim that they can predict a lot but their instruments are not adapted to the this task. Moreover those attractors are not necessary for trading, it is better to use lower order attractors for trading.


What is important that the price in the Forex markets are not in the void. They are in a phase space.
The phase space is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.


For example the daily volatility can be analyzed in practice as a phase space of the price time series for the day. Of course as according to the hypothesis that the distribution is not normal but stable paretian with infinite variance this does not holds true, but is an useful practical approach (in fact we can detect in real time with the peaks of Hurst difference how and when the a powerful shift occurs).


Sensitivity to initial conditions

Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.

In practice a powerful spike even it is corrected will influence the future price action and will set a new set of solutions. If a spike modifies the current phase space (current volatility) it is a signal that the system will be perturbed.

In practice we can analyze the beginning and the end of the market periods.


So we can analyze the price action as chaotic attractors in a particular phase space. What is important to know when a powerful shift in the structure occurs. We cannot know how, when, and why and that cannot be predicted. You can analyze that by your experience or you can use an algorithm (like this which is posted on this blog).


The most common errors that is made by the technicians is when a powerful shift in the structure occurs they try to use a pattern that was in force before.

That is a point when the complex neural net models fail, because they are used for a structure that is not anymore valid and a new structure is about to emerge.

This is just a theory guys and gals. But the calculation of the Hurst exponent showed a clear long term process in the markets. The lyapunov exponents calculations showed that even sometimes the processes are really not dissipative.


  • JohnLast 4586 days ago

    When I think about the chaos attractors I think that chaos attractors can be found in the accumulation of market orders. Those orders act as point attractors for some big market players.

    This is closely related with the group about Oanda market orders information

    The idea is that the attractors are not only in the price itself but also in the market as accumulation of open orders. The idea is that to look only the price is a reductionist approach, the market orders are a part of the price. 

    And to say that the accumulation of market orders acts as a chaotic attroctor for the price fits well, even if it is not scientifically proved, and of course it is not a science, however all the applications of mathematical methods in finance is not science at all (otherwise we would not have crisis of any kind).

    Consider it as a hypothesis not even a tentative theory. 

    When I did some tests with Support Vector Machine model. On one model I applied the price alone, on another I applied the levels of market orders accumulation and how they change. The second level performed much better.

    Unfortunately I did not made any extensive testing because it is too much work to input those levels by hand and to input them into excel spread sheets in order to feed the rapid miner model. And I doubted too much of the relevance of the results.



  • JohnLast 4493 days ago

    As for chart patterns and chaos attractors I updated the following post. It is about 

    Accumulation of orders: accumulation and distribution between market participants and market makers in the Forex market. 

    The hypothesis is a somewhat extension of the principles of the VSA (Volume Spread Analysis) in the modern markets where the big institutional volume is not a king anymore. 

    The smart algorythms are trying to front run the big isntitutional volume, to that extent that it is using super fast algorythms itself to place the orders without revealing the direction (or even is using dark pools).

    So the accumulation of open orders is a case of attraction point for some market participants. With those levels you can even project beforehand the support and resistance zones.

    An extension of those ideas are the shots between the relationship of the market orders accumulation acting as chaos attractors and the market state characterized by the volatility and and fractal dimension.

    This stuff is interesting, because you can see how the market participants are responding to the market  and placing orders at specific spots (not randomly). Especially in EURUSD it is very pronounces with accumulation of orders at the round numbers acting as chaos attractors.