Discussing the article: "An Introduction to the Study of Fractal Market Structures Using Machine Learning"
It's beautiful.
But if we consider attractors (of chaotic processes) in conjunction with fractals, we should take into account that attractors are trajectories in a hidden multidimensional space of attachments, of which we see only a narrow section (projection) as a price series. That is, an attractor is not a temporary point (or a vertical line) on the chart, but a "figure" along a fragment of the price series (for the expected length of the attractor cycle = time delay tau between samples * dimensionality of the embedding space). This multidimensional space is where one would look for fractal similarities.
But for an open (for external influences) market, this approach does not work, because very often (and unpredictably) there is a "push" from which prices jump from one attractor to another.
Probably, it is possible to glue the overnight flat and find relatively constant attractors for such a synthetic series.
It's beautiful.
But if we consider attractors (of chaotic processes) in conjunction with fractals, we should take into account that attractors are trajectories in a hidden multidimensional space of attachments, of which we see only a narrow section (projection) as a price series. That is, an attractor is not a temporary point (or a vertical line) on the chart, but a "figure" along a fragment of the price series (for the expected length of the attractor cycle = time delay tau between samples * dimensionality of the embedding space). It is in this multidimensional space that one would look for fractal similarities.
But for an open (for external influences) market, this approach does not work, because very often (and unpredictably) there is a "push", from which prices jump from one attractor to another.
Probably, it is possible to glue the overnight flat and find relatively constant attractors for such a synthetic series.
There are many options, any thoughts on this are welcome. There were some thoughts to use the Takens transform somehow.
So far I have limited myself to correlation and/or regression.
The second question is whether it is necessary to calculate Lyapunov indices at all and for what purpose? In particular, in order to estimate the chaoticity it seems to be not necessary to use the senior index, and it is quite enough that we determine the saturation region (if any) at the stage of finding the embedding dimension m and the correlation dimension D, and this kind of dependence itself means chaoticity and predictability? Otherwise we would not have m. So far it is only obvious that the full set of non-negative Lyapunov exponents is used to estimate the Kolmogorov entropy, and from it the interval of predictability. Though it is better to recalculate the forecast at the first convenient case without waiting for the expiration of this very interval, and hence Lyapunov exponents and entropy are not needed?
Another question, what values of the small neighbourhood r should be run in the cycle of calculation of the correlation integral? I have not seen any recommendations in any paper.
Finally, I would like to clarify the algorithm for recovering predictions from m-dimensional space to 1-dimensional series. It is not obvious to me in which discrete sample the predicted value falls, given that we formed vectors from samples spaced by τ during the forward transformation. +τ? Then we should use "slightly" outdated data to predict the nearer future from +1 to +(τ-1)?
The consensus of opinion of the forum members (at least then) is negative.
Testing of forecasting in practice through pip trading on EURUSD D1 for several months (according to V.A.Golovko - Neural Network Methods of Processing Chaotic Processes) showed mixed results. Then I did not return to this topic.
I did:
Consensus of opinions of forum members (at least then) - negative.
Testing of forecasting in practice through peiper-trading on EURUSD D1 for several months (according to V.A.Golovko - Neural Network Methods of Processing Chaotic Processes) showed mixed results. Then I did not return to this topic.
Imho, it is a question of multiple experiments and selection of the right features/pattern marking. Maybe you will be lucky, maybe not so lucky.
did it ever seem like Hearst was kind of a no-brainer when it was dynamic?
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Check out the new article: An Introduction to the Study of Fractal Market Structures Using Machine Learning.
Chaos theory describes systems with "sensitive dependence on initial conditions", meaning that a tiny error in initial conditions can lead to drastic long-term changes. This phenomenon is often referred to as the "butterfly effect". Chaotic systems are unpredictable in the long term due to this sensitivity, as well as their aperiodic behavior, fractal dimensions, non-linearity, and strange attractors.
Financial markets are not completely random, but operate within chaotic, non-periodic structures called strange attractors that constrain price behavior to certain ranges.
This limited unpredictability allows for the identification of statistical patterns and support/resistance levels. The concept of chaotic attractors explains why prices exhibit repetitive, but not identical, movements.
The fractal markets hypothesis (FMH), proposed by Edgar Peters, states that market data has a fractal structure that depends on investment horizons. During crises, the structure collapses, which leads to increased volatility and decreased liquidity. Unlike EMH, FMH allows for periods of market inefficiency and predictability, particularly under stressful conditions.
Author: dmitrievsky