bdixon, thanks for the link. I don't think I understand the math behind the page. in f(x)=a*(1-x)*x, I assume y = f(x) is plotted on the vertical and x is plotted on the horizontal. Is "a" a constant? I guess not. Also, I don't understand how the plots can keep diverging ... this is obviously not a quadratic equation as it appears on first glance. Since this is a chaos math page, I assume "a" must be some kind of chaos variable that I don't understand. I am quite sheepish to admit that I was a math major back in college
You were a math major and don't understand it? Man, what chance does an average joe like me have to understand it? I was just using it because it was a quick representation of what I really was trying to get across...the point about Victor counting and how counting leads to probabilities. Whether Vic is particularly enamored of statistical inference (as you said Bayesian / correlation results) or not the idea of counting things and keeping track of relative frequencies does confer a small informational edge in trading. In order to understand the math behind the bifurcation diagram you might first study the logistic equation. Note how it seems to have an initial very periodic cycle that begins to deviate from strict periodicity after a constant or 'tuning factor' is iteratively increased. I think, think mind you, this is how a bifurcation diagram is developed. It is also similar in nature to the predator/prey relationships studied by biologists. The reason I find it attractive in the context of the market is because of the Bull/Bear relationship exemplified by the Lorenz attractor. First the market is attracted to one locus of the attractor and then shifts to the other locus. Using the Lorenz attractor as a picture of my market view I can then realize that these shifts can have probabilities associated with them. Hence, the use of a bifurcation diagram to spark the IDEA of setting up a probability table to track the conditions surrounding the attraction of the market to each of the locii. Crazy, huh? http://mathworld.wolfram.com/LogisticMap.html
Neural Nets, Fuzzy Systems, and advanced methods of reasoning about markets, I humbly offer: http://sipi.usc.edu/~kosko/ http://bioeng.binghamton.edu/faculty/klir.html I spent a good bit of money on a fuzzy logic system a long time ago after first reading about ANN's and fuzzy logic. The system I use has a neural net to speed processing of data.
bdixon, thanks for the Wolfram link - I GET it now. The formula is recursive. Formulas (2), (3), (4) and (5) provide the key explantions. duh - I should have remembered that chaos stuff always starts with recursion. I guess one of the consequences is that certain small changes in the variable "a" should work its way into the system and cause large and unexpected consequences - the butterfly effect.
... believes in things like an IBM/Yen spread trade. It's certainly testible and plausible (esp once you buy into this interconnected / butterfly effect business). The incredulity that most people would automatically greet such a spread trade is also a good barrier to entry. There are thousands of edges out there in the world, so I can't pretend to know them all Vic's a brilliant guy, so I trust he knows what he is doing.
Thanks, I can understand that. I once plotted out the logistic equation using Excel. My math skills are not very deep. As far as the butterfly effect, yeah. But in DT-waw's posted paper the researchers were recalibrating their neural net and predicting 4 hours ahead. Hopefully, that is a short enough time frame that butterflies could not have much of an effect. LOL.
Someone I respect a lot, Howard Simons, writes for Futures magazine about various kinds of spread trading. I'm not interested in that area especially. But if you are you can get Futures subscriptions just for asking sometimes.
bdixon, if you can point me to the right article, that would be great! I don't do these exotic macro spreads myself either, but it is interesting to learn about them for future reference. I understand butterfly effects on a conceptual level, but am not sure how it could be rigourously implemented on a trading level.
Just subscribe to Futures. Howard writes about spreads a lot. Alternatively, you could do a web search. Looks like he writes for theStreet.com as well: http://find.thestreet.com/cgi-bin/texis/author?au=A0805375 Quoting from John Holland author of Emergence: From Chaos to Order "Chaos theory is often cited as an explanation for the difficulty of predicting weather and other complex phenomena. Roughly, chaos theory shows that small changes in local conditions can cause major changes in global, long-term behavior in a wide range of 'well-behaved' systems, such as weather. In an oft-cited example, the flapping of a butterfly's wings in Argentina can (eventually) cause worldwide changes in the weather. There is a sense in which this is true: if we knew all the values for all relevant variables worldwide, we could predict the weather indefinitely far into the future. With such a model we could determine the long-term weather pattern with and without the butterfly's wings. We could see that the two weather patterns would eventually diverge to a point of no correlation. This explanation ignores important factors in real weather prediction. Because meteorologists do not know the values of all relevant variables, they do not work at a level of detail, or over time spans, in which chaos would be relevant. The predictions work with with large masses of atmosphere over short time spans; so butterflies, or jet airplanes, produce negligible effects. Moreover, rather than trying to develop predictions based on remote intial conditions, as with the butterfly effect, meteorologists start anew each day, using the most recent data. These observations continually bring the state of the model into agreement with what has actually occurred. Under this regime chaos theory has little relevance."