To make a Cantor set, you start with the interval of numbers from zero to one, represented by a line segment. Then you remoce the middle third. That leaves two segments, and you remove the middle third of each (...). That leaves four segments, and you remove the middle third of each - and so on to infinity. What remains? A strange "dust" of points, arranged in clusters, infinitely many yet infinitely sparse. Mandelbrot was thinking of transmission errors as a Cantor set arranged in time. This highly abstract description had practical weight for scientists trying to decide between different strategies of controlling error. The Nile suffers unusually great variatiion, flooding heavily in some years and subsiding in others. Mandelbrot classified the variation in terms of two kinds of effects, common in economics as well, which he called the Noah and Joseph Effects. The Noah Effect means discontinuity: when a quantity changes, it can change almost arbitrarily fast. Economists traditionally imagined that prices change smoothly - rapidly or slowly, as the case may be, but smoothly in the sense that they pass through all the intervening levels on their was from one point to another. ... But it was wrong. Prices can change in instantaneous jumps, as swiftly as a piece of news can flash across a teletype wire and a thousand brokers can change their minds. A stock market strategy was doomed to fail, Mandlebrot argued, if it assumed a stock would have to sell for $50 at some point on its way down from $60 to $10. The Joseph Effect means persistence. "There came seven years of great plenty throughout the land of Egypt. And there shall arise after them seven years of famine." If the Biblical legend meant to imply periodicity, it was oversimplified, of course. But floods and droughts do persist. Despite an underlying randomness, the longer a place as suffered drought, the likelier it is to suffer more. Furthermore, mathematical analysis of the Nile's height showed that persistence applied over centuries as well as decades. The Noah and Joseph Effects push in different direction, but they add up to this: trends in nature are real, but they can vanish as quickly as they come. -an excerpt from Chaos by James Gleick
Having worked on this stuff for several years (and currently) here is my opinion. Some types of nonlinear techniques may help with discerning some useful patterns and helping with developing trading strategies for a particular market but they do not remove the requirement for experienced trader oversight. Yes its true that some groups with large capital built semi-automated systems that were/are profitable. For the average trader trading smaller accounts the techiques used by these groups will not help much. The best introductory texts that I know of are those by devaney, Gulick, and the classic reference by Guckenhiemer annd Holmes. A good study of the details of the logistic equation in Gulick - or you can go the reference literature for papers by York who at the time I studied this was at the University of Maryland College Park- is probably the best way to approach the subject.
RLB is losing it trying to find the missing pieces. I don't have any answers. You have seen this already, right? http://perso.wanadoo.fr/l.d.v.dujardin/ct/eng_index.html
Thought: Some modelling techniques would be mainly suitable for long term projections which is hard to derive useful strategies for precision trading (,particularly by general traders). This requires a very very fat account to back up, otherwise would face hugh risk/uncertainty when confidence is tested by encountering false signals, i.e. noise. I think the markets would have no obligations to humbly follow whatever projections by any Long-term models. Statistically (based on my previous reading), sometimes not even ever close!!!
i don't accept that statement. a signal is something interpreted from the market, it is not the market itself, you cannot look at a broken signal and say the market is "noisy", all you can say is...the signal is broken. before you can even define what noise in the marketplace is, you have to define what non-noise in the marketplace is. and how can there be noise in the market when the market is always right?
I would have no problems to accept that a noise is a broken or failed signal! Since the market is always right, noise basically would be the only thing to make us wrong, supposing we're always on the same side as the market goes. I would guess, it's due to practically no one would want to change side immediately after a potential signal/noise emerges!
Hi, We could go on endlessly like this. I suppose that if you talk about "signals and noise" you want to do this in the context of what is meant by these in system science. Damir is correct in this. Simply tell us what your "market"signal is, what your "observation"signal is and I 'll tell you what the "noise" is. I don't want to sound too negative, but there is really no point in pretending to manipulate supposedly rigorously defined concepts and not really knowing what we are talking about. nononsense