Outrun - consider it done!

QuoteOriginally posted by: outrunIn our company we apply 'chaos theory' to model and detect stochatic driven deterministic patterns in time series. It's certainly not dead, it's growing up together with datamining in general! There are of course many chaos theory interpretations. I mostly think about the Lyapunov dynamical system interpretation (which isn't very philosophical) : small changes in initial conditions will result on large difference over time, ..and some deterministic systems can show such complicated behavior that the behaviour looks random.Maybe it should not be called 'chaos' but something like 'generalised eigenvalues'. This maths has been around since Hamilton.

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: outrunIn our company we apply 'chaos theory' to model and detect stochatic driven deterministic patterns in time series. It's certainly not dead, it's growing up together with datamining in general! There are of course many chaos theory interpretations. I mostly think about the Lyapunov dynamical system interpretation (which isn't very philosophical) : small changes in initial conditions will result on large difference over time, ..and some deterministic systems can show such complicated behavior that the behaviour looks random.Maybe it should not be called 'chaos' but something like 'generalised eigenvalues'. This maths has been around since Hamilton.Yes, the word 'chaos' comes burdened with negative connotations. The terminology does not matter that much (OK, terminology does matter if one is trying to dig into the literature or explain stuff to non-technical clients.)The key, that outrun mentions, is the distinction between "complicated behavior" and "random behavior" and the dangers of using stochastic models on deterministic systems. Are we back to Paul's magician example?

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: outrunIn our company we apply 'chaos theory' to model and detect stochatic driven deterministic patterns in time series. It's certainly not dead, it's growing up together with datamining in general! There are of course many chaos theory interpretations. I mostly think about the Lyapunov dynamical system interpretation (which isn't very philosophical) : small changes in initial conditions will result on large difference over time, ..and some deterministic systems can show such complicated behavior that the behaviour looks random.Maybe it should not be called 'chaos' but something like 'generalised eigenvalues'. This maths has been around since Hamilton.Yes, the word 'chaos' comes burdened with negative connotations. The terminology does not matter that much (OK, terminology does matter if one is trying to dig into the literature or explain stuff to non-technical clients.)The key, that outrun mentions, is the distinction between "complicated behavior" and "random behavior" and the dangers of using stochastic models on deterministic systems. Are we back to Paul's magician example?Is outrun saying that the random terms in a time series are NOT random or are nor N/A or not present?

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: outrunIn our company we apply 'chaos theory' to model and detect stochatic driven deterministic patterns in time series. It's certainly not dead, it's growing up together with datamining in general! There are of course many chaos theory interpretations. I mostly think about the Lyapunov dynamical system interpretation (which isn't very philosophical) : small changes in initial conditions will result on large difference over time, ..and some deterministic systems can show such complicated behavior that the behaviour looks random.The key, that outrun mentions, is the distinction between "complicated behavior" and "random behavior" and the dangers of using stochastic models on deterministic systems. Are we back to Paul's magician example?Is outrun saying that the random terms in a time series are NOT random or are nor N/A or not present?I suspect he refers to the folowing two possibilities (more so the first, than the second):1. The time series has NO random terms at all even if it appears statistically random. The state at each timepoint might be 100% determined by past values or some error-free algorithmic process. (BTW, a computer pseudo-RNG or a calculation of the digits of pi are excellent examples of a 100% deterministic systems that seem to produce statistically-random outcomes.)2. The time series may have small random terms, but the effects of the Lyapunov propagation of deltas causes significant amplification of the random perturbations. The amplified "random" disturbances may be very dependent on their point of influence in the state space so that a small disturbance sometimes causes qualitative changes in behavior (e.g, regime switching) and sometimes has almost no effect.The issue is whether a system's "unpredictability" can be accurately modeled by one of the usual tractable statistical distributions (or lagged linear combinations thereof). For many real world financial systems (e.g., options and defaults), the excursions or extrema of the system path dominate the outcome. A deterministic chaotic dynamical system may display very different excursions than a GBM stochastic model.

QuoteA well known dynamical system is a population of foxes and rabbits: the foxes eat the rabbits, the rabbit population declines sharply, the fox population declines because of lack of food, rabbits flourish because of lack of foxes etc. etc. For certain reaction speeds and delay reactions between the populations (the time a fox survive without eating) the population cycles will become chaotic. http://www.geocities.com/CapeCanaveral/ ... erra.htmIt almost seems that you are using mathematical biology models to do the same with time series? Anyways, we are talking of ODEs (Volterra/Lotka predator prey) or their discrete analogues. A good analogy is bond yield and price and supply/demand models? QuoteIn extreme parameter sets, the populations dynamics will start to look random, even though the evolution equations are deterministic... ..so some random time timeseries can in fact be deterministic (and predictable), the C++ rand function is one of them, the evolution equation is probably very simpleI think rand() is just a one-step difference scheme, so calling it an evolution equation might be stretching it.

QuoteWhat I was trying to point out was:1) that rand() is deterministic (not stochastic) even though we call is a random number generator.. So the fact that a time series passes test for randomness -or look complicated- doesn't imply that it's not deterministic. (nor the opposite)2) it's highly sensitive -nonlinear- to change in state (seed)3) it is (in principle) possible to reconstruct f() from observation!Actually, it's a pseudo RNG but never mind(). A LCG is of the formX(n+1) = aX(n) + c mod mX(0) is the seed. So, I kind of see. Any better examples?

QuoteOriginally posted by: CuchulainnQuoteWhat I was trying to point out was:1) that rand() is deterministic (not stochastic) even though we call is a random number generator.. So the fact that a time series passes test for randomness -or look complicated- doesn't imply that it's not deterministic. (nor the opposite)2) it's highly sensitive -nonlinear- to change in state (seed)3) it is (in principle) possible to reconstruct f() from observation!Actually, it's a pseudo RNG but never mind(). A LCG is of the formX(n+1) = aX(n) + c mod mX(0) is the seed. So, I kind of see. Any better examples?X(n+1) = c*X(n)*(1-X(n)), 0<c<4 is one of my favorites.

Collector, first, I confess again that this topic might be out-of-my-think-capacity. And serious mistakes are not impossible at all.I know, chaos theory is about the observation that the behaviour of certain mathematical systems are sensitively dependent on the details of their initial conditions (but complexity can be studied as a fundamental independent phenomenon).I touched (computational) universality. In history, it was assumed that the threshold of universality will be high, like with electronic computers. But there are, surprisingly enough, universal systems whose rules are so simple hat they can be described in a sentence? And universal systems can be on top-of or embedded-in universal systems (languages on top of computers are universal). And even embedded systems are not "closed"?Systems based on simple rules can create reapeated patterns (repetition, nesting, localised structures, ..) . (click "watch web .")With a similar set-up you can produce systems which are fully random .Intuitively you would think that certain cellular automata (ca) based on certain rules will be capable of doing certain computations, while other do not seem to ...And yes, the intuition holds that systems with repeated patterns are not universal, but systems with complex random behaviour are (even if their underlying rules are as simple).And yes, universality means, you can emulate any other simple rule on the same set up.But is this the seed for the emergence of order?There are ca that never settle down to a stable state but show behaviours that is in many respects random.At the other hand OUR programs receive operational semantics when running on a computer. You might call this a seed?(But due to the universality of the underlying system, they cannot decide on their own whether they ever halt ... )Abstract nonsense, probably. p.s. question, is a free market derived from simple rules universal or showing repeated patterns. Or if universal, will order emerge inevitably over time?(or is it our programming that creates the patterns )

exneratunrisk , I will answer you in detail I hope in about one year from now (I hope, could take two...), in the book I now are working on. (In your case I will be more than happy to send you a copy free of charge, post me your address in private message if you want, or wait until I announce the publication of it). I am not just another philosopher with twisted words, so yes my book is also a very empirical one. It contains lots and lots and lots of observations to back up my twisted words. It is not mainly about chaos and order, but yes will contain a chapter or two on this as well. But please keep up the discussion on chaos and order...a rather good one I would say ! Yes the definition of chaos and order is also a rather important one.exneratunrisk wrote : "P .s. question, is a free market derived from simple rules universal or showing repeated patterns. Or if universal, will order emerge inevitably over time?(or is it our programming that creates the patterns )"Why are you interested in modeling free markets???? I am only making my money from real markets, not from free markets! 100% free markets is a fantasy assumption in the head of some academics. Well at best free-markets models can be good approximations, but they could also be bad approximations (and I would say more likely bad approximations). To model real markets you should take into account they only partly are free.And even if my view on the reason for not having free markets is very different from yours or Fermions, we both seem to agree on markets are not free:"QuoteOriginally posted by: exneratunriskAnd I am with Fermion, we NEVER had a situation where markets were free (IMO, because we always mix economic with ideological and final social aspects)?"But since I think I have a different view on reason for non-free markets I would think I model it very differently.

Chaos