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The regression analysis in the chart may be a fine way to trade, but I
don't believe regression lines are chaotic attractors because the bond
market over several weeks or months or years is not a chaotic system. Chaos
theory is the study of how ordered systems change with a fair degree of
consistency into chaotic systems.
Take the example of the lit cigarette. If you put one in an ashtray, it is
true you will not see the same pattern twice. YET, what is remarkably
consistent is that it first traces a thin line upwards, then all of the
sudden turns cloud-like. This point of change to cloudlike pattern will
always be roughly the same given the same wind conditions (and I imagine
brand of cigarette)
Here's another one. Turn on a water faucet a teeny bit till you get a
steady drip. Turn it up a teeny bit more and you'll get a steady drip about
twice the rate. Turn it up a teeny bit more (if you're nimble) to get a
steady drip at four times the rate. But at a point (which will be always
roughly the same for each faucet), the steady drip stops and the drips seem
to randomize. The random pattern will never be the same but the point at
which the dripping changes will always be the same.
How ordered systems change into chaotic systems is fascinating.
HOWEVER, I don't believe markets are ordered systems changing into chaotic
systems. They are in fact chaotic systems changing into ordered systems.
Tick by tick fluctuations may very well function under chaotic conditions
but day-to-day, week-to-week, month-to-month changes are, I believe, due to
order (and of course to occasional random events) but not due to the
characteristics of a chaotic system.
But even if you do not accept my premise, on a practical level chaos theory
can only really tell us where an ordered system such as a market changes
into a chaotic one. As was discussed recently on misc.invest.futures, a
model based on chaos theory (not just mere regression analysis) suffers
from the major change that can happen to a model if the initial parameters
are changed even in the slightest.
Example: Even if you had a super-duper computer that could track every
single molecule of air and water on the planet you still would not be able
to predict the weather very reliably past a few days. Why? If you made a
tiny mistake on the initial settings of one molecule, you could end up with
tornadoes and floods in Kansas instead of bright sunny skies.
Yes, it may be POSSIBLE to apply but it is not very PRACTICAL.
>Hi Bob,
>
>I don't want to take too much time on this but Chaos theory is a little more
>complex than a simple analogy that was presented by the author of the book
>mentioned in your post. There are specific conditions that need to be met
>before a
>system can be determined chaotic. Off the top of my head I don't know them, but
>the book by Devaney on Chaos Theory has some of them. There is also a
>mathematical
>economics text book by Hands (I believe) that also has some accepted conditions
>for chaos.
>
>I think that one is better off sticking to statistics when they use the Raff
>Regression Channel.
>
>Harley
>
>
>BobRABCDEF@xxxxxxx wrote:
>
>> One of the problems with Chaos theory has been in applying it to trading. TA
>> tools already exist in most trading software to apply the theory under
>>another
>> name.
>>
>> Gilbert Raff has a chapter in his book "Trading the Regression Channel". The
>> chapter is titled "The Regression Channel As A Chaotic Attractor". Here are
>> two paragraphs from that chapter:
>>
>> "Let's return to the example of the cigarette. Imagine a cigarette holder
>> standing straight up in a perfectly still room. Theory teaches us there is
>> simply no way to predict the coils and loops the smoke will make as it rises
>> from the cigarette. However, if we were to position a TV camera on the
>> ceiling, and film ten thousand cigarettes in a row, while the smoke would
>> never make the same pattern twice, it would also never travel beyond a thin,
>> conical boundary as it rose in the air. In the new language of Chaos Theory,
>> this reliable boundary enclosing a completely unpredictable pattern is called
>> a Chaotic Attractor."
>>
>> "Regression Channels, with their puzzling property of containing price for
>> years, are like the boundary constraining the smoke. The best theory I can
>> offer for the behavior of price near a Regression Channel Line is that it is
>> tracing out a Chaotic Attractor for the security it is describing."
>>
>> Note that price tends to accelerate towards the "attractors". The attached
>> chart, here and on the next post, show that the attractors based on
>>historical
>> data extend into the future and still maintain an influence on prices.
>>So, if
>> you are looking for an equation to find chaos attractors, look at the formula
>> for regression channel lines.
>>
>> BobR
>>
>> ------------------------------------------------------------------------
>> [Image]
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