My new chaos findings implemented in forex trading

[Paul&Paul]

You have seen evidence in my pioneer work that multipliers like 3.5699 and 4.669 are present in financial markets. F=4.669... is the Feigenbaum's value.
Considering that the classical logistic map x(n+1)=rx(n)[1-x(n)] becomes z(n+1) = z(exp2) + c through a linear transformation, we also see evidence the Mandelbrot set is there too. We know it how it looks like in theory, yet in reality we can only see some fragments. The history of the markets is too short to see more.
The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal. Correspondence between the Mandelbrot set and the logistic map looks amazing and beautiful in itself.
http://en.wikipedia.org/wiki/File:Verhu ... cation.jpg

[Paul&Paul]

The idea of chaos control is not a theoretical or philosophical issue at all. You may refer to OGY concept which outlines a method for stabilizing an unstable periodic orbit (UPO). The main idea consisted in waiting for a natural passage of the chaotic orbit close to the desired periodic behavior, and then applying small judiciously chosen perturbation, in order to stabilize such periodic dynamics. By constructing appropriate goal dynamics, compatible with the chaotic attractor, an operator may apply small perturbations to produce any kind of desired dynamics, even not periodic, with practical application in the coding process of signals.
A small perturbation can give rise to a very large response in the course of time. It is also true that a judicious choice of such a perturbation can direct the trajectory (of prices) to wherever one wants in the attractor, and to produce a series of desired dynamical states. This is exactly the idea of targeting.
I want to stress that for a non-chaotic dynamics the perturbations to be done for a desired behavior must be of the same order of magnitude as the un-perturbed evolution of the dynamical variables. For a non-chaotic dynamics
central banks intervention must be of the same order of magnitude as the
current interbank volume over a given stretch of time.
As a consequence, it is evident that stability of the system can be ensured easily only if the system is chaotic (with a hidden order inside).
From now on you may consider verbal interventions and expressions of worries with a pinch a salt. Nothing looks the same now. Read the above over and over again. It needs to be properly digested and it will take some time before you realize that there is a price to pay for the comfort of stability whatever it means to different market participants. There is a strong conviction that small players pay an unduly unproportionately big price. Does the situation not resemble tax laws and the problem of wealth distribution? Pareto principle may be referred to.

[Nikitafx]

I am sorry but this is all so Greek to me. God forbid if this is the maths I need to know in order to make some profits trading. Its way out of my league. I find statistics confusing most of the time.

Yet what I cannot understand is if there is such clarity to all this as you advocate, then why seek donations from us mathematical peasants who trade hourly candles?... Why not throw in a few lots yourself?

Just wondering.

[Paul&Paul]

Please refer to my GBPJPY post from February 1. Trigger C marked there (28 pips)
yielded 134.23 on February 10 which is exactly 14.208 times 28. Why? Because GBPJPY is a system. Not any system but a chaotic system which exhibits very special properties and sets borders to chaos. The road to 134.23 was not a straight road. GBPJPY moved higher and retreated, moved higher and retreated. It touched 134.23 and retreated. We cannot always predict that the market will make 14.208 instead of mere 4.669. Still, when it moves away from a low due to the energy of the trigger, it does not go anywhere but it goes to a next predetermined orbit. There is a hidden order of changes and hidden borders of chaos.

One should endeavour to study what happened on the previous visit above 134.00. That was September 20 of 2010. What a war! We can see how fierce was the fight and how heavy was the selling above the big figure 134.00. 14.208 of the trigger down from that date was set at 126.86. Though no names we know who was shorting GBPJPY, today it is evident that it matters to somebody to defend those levels and some other players want to break them all the way to 135.00.

[Paul&Paul]

The recent update of GBPJPY shows trigger B and its targets beyond some stops from September 20. We should remember however that there is no straight road to any target. But there is the opportunity to get it and forces behind the curtain won't stop.
There are three UPOs at 133.16, 133.22 and 133.31.
UPO@133.16 is identical with 4.669 of the trigger down.

[Paul&Paul]

Gold stabilizes near 1254.05, the well known target 14.208.

[Paul&Paul]

From this chart below we see pressure downwards.
0.9952 is waiting to be visited some time, possibly pretty soon. This is concluded from the decisive penetration of 3.5699.
1.0083 acts as a repeller now. There needs to form a new trigger up to get there in the near future, from a fresh low, why not.

[Paul&Paul]

For a reason I would like to present some longer term picture of EURUSD based on an M216 chart.
Roughly speaking, stability means that in phase space the trajectories group into bundles without any significant spread as time passes, or with an at most linearly growing spread as time passes.
During instability the trajectories seperate in an explosive fashion. A locally exponential magnification with time of the distance between initially close space trajectories is the hallmark of deterministic chaos.
In terms of the market, stability can be seen during consolidation, instability during a trend. A strong trend means also the market is very unstable in one direction and it may require some perturbations applied in order to stabilize it near certain orbits.
In layman's words, when the market breaks a certain price level with no counter-reaction, it is evident that it cannot stabilize there. Hence such a price level is not going to be remembered. But when the market breaks a certain price level and generates some zigzag in the neighbourhood, it is evident that such a perturbation stabilizes the market and this orbit is going to be important in the future behavior of the system.
EURUSD was tested on M216 chart for stability vs. instability conditions.
In other words, the aim of the study was to discover when a local uptrend began and possibly when a local downtrend began. To this end an attractor was reconstructed to find possible clusters/bundles and the spots from where
trajectories started to seperate in an explosive way. There is no exaggeration in the term 'explosive' given the fast growing distance from a bundle of trajectories to a new region in the phase space of the attractor. One can easily establish where the market left the border of the bundle.
Both places are marked in blue. The closes of the marked candles show the beginning of instability, the beginning of a trend. It is interesting to note that after the signal candle one could easily doubt the trend due to a few chaotic movements up and down. However, the attractor gave ways a firmer picture than the candle work.

[Paul&Paul]

EURUSD slid from 1.3737 being the 4.669 and 3.5699 of two triggers up.
The low level 1.3509 is important but more shocking is a huge 99-pip trigger down. It is so huge that a small rally to 1.3615 suffices not to change the pressure.

[Paul&Paul]

A stochastic process is the counterpart of to a deterministic process and is also the counterpart to a chaotic process. Instead of dealing with only one possible reality of the process might evolve under time, in a stochastic process there is some indeterminacy in its future evolution described by probability distributions. Some paths may be more probable and others less so.
In a study of a chaotic system the moment we use words like probable/more probable/less probable, we refer to a stochastic process, not a chaotic process. If reason and intuition are applied where chaotic behavior prevails we are doomed, because chaos is counter-intuitive as a rule.
Chaos does not deal with probabilities but with certainties. And those determinants come from fractal geometry, the most natural geometry of all. It is possible to study the evolution of a rainforest by studying a single tree how it grows over time. It is possible to study the evolution of the market by studying single trajectories. The behavior of a small part reflects the behavior of the whole. We conclude from relatively short time scales, and go into longer time scales. This is targeting with the known multipliers like F=4.669...
Scaling is important, more important than time itself. Time seems to be stretched and shrunk, sometimes reversed. Changes are never evenly distributed on the time axis.
When you see how targeting works, it looks simple. It only looks simple. In fact, there are many more mysterious things in it.
GBPUSD looks messy as compared with GBPJPY. The trigger down is really big (74pips).