Q Noise is very important to traders, whether they understand it or not, because noise makes analysis more difficult and less reliable. It even can make reliable analysis impossible. http://www.miapavia.it/homes/ik2hlb/timef.htm UQ
I can see that I have rebirthed a heated debate. As such I feel I am getting arguments/statements being picked up midstream. Here's what I understand to be "noise," Linear formula 'x' yields results 2.001, 1.989, 2.005, etc. in real world testing. The researcher (or trader) views these variations as "noise." The noise then is the variation of real world results from what the linear model has predicted. The problem that arises is called the Butterfly Effect. The initially small variations quickly begin to magnify as time passes so that the model can only accurately predict into the very near future. The promise of a chaos based model is it could acurately account for these small variations. In an ultimate sense I do not believe "noise" exists. Noise is only the failure of any model to explain a phenomena. It is the degree of error that determines how much "noise" occurs. The real problem is that what seems to be insignificant noise quickly becomes very significant. Note: It is my style to make strong assertions as I have done here, but as I have stated earlier my understanding of this topic is limited. I therefor am open to any corrections in the above terms and/or reasoning.
Hi rlb, Don't worry about making strong assertions. Yours are pretty mild and cogent compared to some stuff that you encounter on ET. In fact you bring some sanity in this world wondering about what is meant by "noise" in the trader's jargon. This term is often used very thoughtlessly. My non-contribution would be to ask: "where do we go from here?" nononsense
Thankyou nononsense. As my studies continue I am sure to have more ideas, but for now I would love to see some of the math. A basic linear function looks like, y = mx + b. What does a non-linear function look like? In Chaos by James Gleick there is a reference to the tendency for gold and silver traders to view the markets as periodic. I am not sure exactly who or what method he is referencing but I know economists looking at a four-year business cycle would have a periodic viewpoint. The math describing this phenomena might be some variation of a sine wave, whereby a simple wave pattern is repeated ad infinitum. How would one produce an aperiodic description mathematically? If anyone is aware of Anders Johansen's work I suspect he is using a nonlinear approach in describing market collapse. I have yet to work through his papers, but a link can be found via the Wall Street Uncut Interviews website.
You'd better or I will be after you You give me the idea for adding some precisions I put in the conclusion of my site (read the last phrase) <IMG SRC=http://www.elitetrader.com/vb/attachment.php?s=&postid=333847>
Posted in the past harrytrader 02-07-03 05:28 PM http://www.elitetrader.com/vb/showthread.php?s=&postid=200167&highlight=non+linear#post200167 About non-linearity, well the term can have different sense depending on the context, for example many people think that non linearity means that a model is just different from a straight line. But in the context of chaos theory, a model that does not give a straight line isn't necessarily non linear. To really understand I need to write that a linear model can be writen x[n+1]=a*x[n]+b where a and b are parameters (not dependant on time whereas x is a variable whose value depends on time n) You will remark the iterative form definition above. For example the interest compounding is linear since S[n+1] = S[n]*(1+r) where r is the interest rate (here b=0) when a > 1 this give not a straight line and there is no limit to S which can tend to infinite ! A non linear model cannot be written as above. the most well known and studied is the logistic function where you "dump" the infinite growth of a*x[n] by a new term (x[n]-1) so that the growth is finite and cannot go higher than Xmax. 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.
FWIW, here are the opinions of a mathematical fool who tried for years to apply advanced signal processing techniques to the markets: it don't work, it can't work, and it will never work. The market is in no way analogous to a physical system, although it exists physically. The key supporting proof is that the market can reverse direction instantaneously, like an angry woman turning on her heel. It can move from one price to another with high order time derivatives (velocity, acceleration, surge, and higher) which would turn to mush any physical object so propelled. It is not random, because all the events are totally deterministic. There are just so many players and events that it looks stochastic. Neither is it chaotic, because it cannot be descibed by the simultaneous nonlinear differential equations of chaos theory. Before I understood this (duh!), I tried to apply tranform theory, Kalman filtering, time sequence statistics, ad nauseam. IMO, at lower time intervals than those in which the secular trend is manifest, the market is manipulated so the pros can take money from the ams. Winning consists of learning how to take a free ride on their coattails. Will Rogers said it best: "If it don't go up, don't buy it!" Now I must go, for the attendants are returning.