Chaos - A Nonlinear Approach

Quote from harrytrader:

In that case you will have different behavior:

If a = 0 x will tend towards 0: it is the attraction point

If 1 < a < 3 the attraction point will depend upon a

When a > 3 you will have 2 or more attractions points. this is called bifurcation and give the image of a system be chaotic.
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I follow you until: "If a = 0 x will tend towards 0: it is the attraction point." Would the result of this not be 0, or a flat line determined by 'b'. I have seen the terms attraction point and bifurcation but do not yet understand. How might these play out given an example?

Thankyou,
rlb
 
Just thinking out loud: If the market is indeed fractal, "noise" should occur on all time frames, and at all magnitudes. So any noise filtering would have to work on all time frames and magnitudes.
 
Hi,

As some confusion seems to exist about what is a linear system, here it is (any other stuff is garbage!)

Definition of a linear system:

If
Input1 yields Output1

Input2 yields Output2

then a system is linear if a linear combination of these two inputs yields the same linear combination of the outputs, thus:

(a1 * Input1 + a2 * Input2) yields (a1 * Output1 + a2 * Output2)

One can also say that a linear system admits superposition.

A nonlinear system is a system that does not follow the above definition - it does not allow superposition.

nononsense
 
Price movement is a current reflection of agreed upon price between a buyer and a seller. Macroeconomics 101 states that where a supply and demand line intersect, that will be the market price and quantity of a product. However, there are always people willing to purchase a product at a higher price or sell a product at a lower price, but the market price is what is considered a fair value at that point in time.

I don't understand where one will discard certain data because it falls under the parameter of noise. What appears as noise on a longer time frame may be a very real trend on a smaller time frame. That little "one month" spike on a 30 year chart was probably quite a trend on the daily charts as it was occurring.

I also don't think that any mathematical model is going to describe the market to any real degree of accuracy. You would have to have a model that covers the thoughts and decision making of thousands of traders while also predicting what will happen internally within a company.

If Joe owns a publicly traded diamond company and his little cousin trips over a stone in a deserted desert and they find out she just discovered a vast untapped diamond mine, how is it that any mathematical model would account for what would happen to the price of Joe's stock? Obviously the stock will go up quite a bit -- and it is doing so because the market is now pricing in new information about Joe's company.

However, if you look at the trades, someone started to purchase the stock before everyone else and that is the organization or person who will be making consistent money in the market -- the person who has more information than the market as a whole.

The mathematical models work great for higher signal compression so we can get 250 channels from our cable company. They also work great in for a bunch of other scientific purposes, but I don't think mathematics and the market should be used together -- at least not for prediction some future occurrence based on what the market has already priced into the stock.

Now if you have a fast connection and some inside information that is greater than what the market holds in general at that specific time, then great. Otherwise I don't think chaos theory, signal processing algorithms, quantum theory or any other form of esoteric math or science is going to unlock the market.

Then again, I don't know a damn thing about the market so who am I to give an opinion.
 
Quote from aphexcoil:

Price movement is a current reflection of agreed upon price between a buyer and a seller. ...
Then again, I don't know a damn thing about the market so who am I to give an opinion.
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Nononsense, thankyou once again. I have now atleast a surface understanding of the mathematical implications of linearity. It will be up to me to deepen that understanding.

Aphex, I do not think I want to enter into a lengthy debate about whether there exists a mathematical explanation of the markets. However, you do raise some interesting points and I will address what I can.

Firstly, I think you do have some understanding of the markets and likely more than I so you need not qualify your comments for me.

Secondly, I completely agree with your notion of 'throwing away data,' as I feel this is exactly the problem a chaotic approach is trying to address. Chaos theory attempts to eliminate so called noise by taking it into account, by including it within the predictive process.

Thirdly, I would ask whether you would agree that as a collective entity humans portray certain tendencies? Would you agree that we tend to act irrationally under certain circumstances, e.g. overly-optimistic when times are good and overly pessimistic when times are bad? If so, then I would ask whether you believe that these tendencies can be quantified? This is the issue at hand. And, since the decisions of buying and selling are in fact quantified into the price of a security would one not be capable of deriving useful and quantified formulae from this data? If so, then the only question that remains is how? This is what I would like to tackle.

As you have brought forth there are many variables which come into play, but as a technical analyst one would certainly agree, atleast in part, that price and volume act to summarize these many variables. Whether price and volume can be manipulated for predictive purposes I am not sure, but I am not yet ready to forgo this possibility as I have seen some evidence of this possibility. For an example, listen to the Anders Johansen interview by Dave Allman (Wall Street Uncut Interviews). Anders Johansen is a physicist who has found a mathematical tool for prediciting the breakdown of hyper-growth systems. Hyper-growth is beyond exponential growth and is witnessed in a number of physical systems. Check out the interview for more details.
 
Quote from nononsense:



... what is meant by "noise" in the trader's jargon.

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What is noise, anyway? :confused: :D

It seems a noise (in Casti's terms for chaos and complex system) can be analysed and classified into white noise, brown noise, tan noise, and (even) pink noise.

Are we going to apply all these concepts to trading?

If yes, what are they in trader's jargon?

:confused:
 
Q

William Brock's work has focused on two central questions:

1. Do stock price fluctuations come about as the result of an underlying chaotic rule of behavior?

2. If so, can we make use of this structure in the data to develop successful trading strategies?

...

In an extensive series of statistical experiment on stock price data, Brock and his collaborators have concluded that although stock returns do appear to exhibit chaotic structure, the departure from pure randomness is probably too small tobe usefully employed in any predictive scheme aimed at beating the market.

--- Complexification (by John L Casti)

UQ

It was also mentioned the conclusion may be reversed for other commodities such as FX.

:confused:
 
Quote from rlb21079:

Has anyone attempted to mathematically explain the "noise" surrounding typically linear approaches to trading? I've just begun inquiry into these matters and am thus open to all opinions on this subject.
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There are a lot of people doing a very wide range of exercises that try to further understanding the market and consequently make money from trading in markets. A lot is going on out there.

I believe the most beneficial efforts that anyone can make are best related to making the easiest money first with the lowest risk and then going further along the path by doing more difficult things later.

"Noise" shows up fairly late in the game as a consideration.

It dominates at a certain point and creates so much risk that it is not worthwhile to extract money from the market under "noisy' conditions.

I recognize where that line is drawn in the sand and deal with it accordingly.

It is only a problem for expert traders as it turns out. And noise only shows up, if it does, in trading situations. When longer terms are considered, all of them are out of the realm of noise.

Earlier here, someone pointed out that the market is described by volume and price and these direct variables handle what is going on for traders. Their extensions are, of course, helpful.

If you wish, consider the following. It may very well be possible to consider just the immediate situation and, then, as a consequence always have a plan of action.

If the immediate situation is seriously clouded, it is because there is nothing of value that maybe seen. Approaching the immediate situation is best done directly and expressly as a consequence of only considering a set of data that can tell you something.

I do not run into noise as commonly described here when I pursue the data set of an immediate situation. My quest, at any time, is to be on the "right" side of the market. I deal with the immediate present only to assure that I am on the "right' side of the market.

The reason is, that If I am on the right side of the market, I am making money. I do not connect market noise to this process, except to determine if the market is functioning. If I cannot get a data set, then there is a reason. "Noise" substitutes for my data set and it dominates. When "Noise" is dominating, it demands that I withdraw from the market.

As always, my immediate situation is that either I can obtain a data set or I can't. If I cannot, then "noise" is making the market opaque (seriously clouded).

If I can get a data set, then I execute to be on the right side of the market. Most often my execution is to "continue" as before.

From the thread it is fairly clear that almost no one deals in any way with noise. I have no choice in the approach that I use. If I cannot get a data set, I deem that noise is blocking me. If the market is opaque, so to speak, I must leave.

I use a tree to gather data. This guided collecting goes from gross information to studied focused detail of the situation. Continuing profits are measured at mileposts each time I use the tree. If accumulation declines, then I go on alert. Should accumulation cease I reverse as and when required to continue on the "right" side of the market. Furthermore, I determine if the market is succeeding or failing to run it's course from my position's perspective, especially after a reverse. (This is three levels of data in a given set)

"Noise" can prevent me from declining (analyzing and exiting) the market's condition. I can reach places in my tree where immeasurable situations appear at given moments. This thread chats about mathematics and applications to market data. My view is that the data that is pertinent (say in the approach I use) may not be usable in most mathematical constructs. My data analysis is more go/no go against a standard and/or simply a measure of data presence or absence.

I am oriented to realizing the potential of the money making situation. "Noise" comes into this realization process. "Noise" makes data sets become "opaque".

For me the "right" side of the market disappears occasionally and, therefore, I must leave. All other times I continue to be in the market and I conclude that there is no noise there to impede me.
 
About the role of paradigm one can of course refer to Historian of Science Thomas Kuhn in his major writing "The Structure of Scientific Revolutions" (Chicago University Press 1970).

p. 47
"The pre-paradigm period ... is regularly marked by frequent and deep debates over legitimate methods, problems, and standards of solution, though these serve rather to define schools than produce agreement. ... (p. 48) "Although almost non-existent during periods of normal science, they recur regularly just before and during scientific revolutions, the periods when paradigms are first under attack and then subject to change."

p. 65
"Novelty ordinarily emerges only for the man who, knowing with <font color=red><I>precision</I></font> [italic by Thomas Kuhn] what he should expect, is able to recognize that something has gone wrong. Anomaly appears only against the background provided by the paradigm ... In the normal mode of discovery, even resistence to change has a use ... By ensuring that the paradigm will not be easily surrendered, resistance guarantees that scientists will not be lightly distracted and that the anomalies that lead to paradigm change will penetrate existing knowldege to the core."

p. 89
"Almost always the men who achieve these fundamental inventions of a new paradigm have been either very young or very new to the field whose paradigm they change."


Quote from harrytrader:

Whatever ? yes within a paradigm but not obligatory within ANOTHER PARADIGM. You don't believe it ? Let's take for example the so called Heisenberg Uncertainty Principle that the huge majority of people think that it is a SURE LAW whereas it cannot be as says the physician John Casti (in "Would be worlds" http://www.amazon.com/exec/obidos/s...2286954-1255355 John L. Casti member of the Faculty of the Santa Fe Institute which is one of the most famous center of financial research using chaos theory and artificial intelligence)

"The theorems of Goedel, Turing, and Chaitin are limitations on our ability to know in the world of mathematics. The same limitation applies to statements such as the celebrated Heisenberg Uncertainty Principle in quantum theory, which at first glance appears to refer to an inherent limitation on our ability to measure certain quantities in the physical world. But a more careful examination shows that Heisenberg uncertainty is actually a limitation imposed by certain mathematical formulations of quantum theory, and may or may not be an intrinsic limitation in the structure of the real world itself."

The paradigm used in financial scientific research today is not the good one so scientists can search and search for one million hundred years they will never find the true reality but only its shade since they keep to wear the same sunglasses :) ! It's not a question of being a genious but of being honest (in the sense intellectual integrity not influenced by current overwhelming paradigm - that's why at the time of Einstein's relativity discovery they didn't dare to give Nobel Prize for that but for his brownian motion theory) in front of facts especially those that create financial paradoxes. Efficiency Principle is the counterpart in Finance than Heisenberg Uncertainty Principle in Physics.
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