sle wrote: Nice example. Technical analysts would think of the other side of the coin: non-martingale markov random processes.
The uncertainty principle http://www.mtnmath.com/whatth/node53.html Uncertainty in quantum mechanics is not connected to the probabilistic nature of the wave function. It is inherent in any wave function including those in classical physics. The inability to assign exact position and momentum to a particle may only mean that there is no such thing. The inability to make those assignments need not be an obstacle to deterministic predictions. For classical waves frequency and location cannot be simultaneously assigned, but those models are completely deterministic. [...] In 1932 the renowned mathematician and physicist von Neumann published a proof that no more complete theory could be consistent with the predictions of quantum mechanics[27][26]. Von Neumann's reputation was so great that the proof stood for thirty years in spite of Bohm's publication in 1952 of a more complete theory that was consistent with quantum mechanics [7]. Bohm thought at the time there were subtle differences in the predictions of the two theories and thus his result did not contradict von Neumann's proof. In 1966 Bell published a paper revealing a problem with von Neumann's proof[5]. The mathematics was fine but the assumptions von Neumann made about the constraints a more complete theory had to meet were not justified. Bell went on to show that quantum mechanics was not a local theory. Bohm's theory was an explicitly nonlocal theory and Bohm's work was an important influence for Bell. This story continues in Section 6.4. Locality and quantum mechanics http://www.mtnmath.com/whatth/node57.html Locality is the denial of action at a distance It requires that all the information useful in predicting what will happen at a given location and time is contained in a sphere of influence. For an event that will occur in one second the sphere has a radius of 300,000 kilometers, the distance light travels in one second6.1. Locality is the most powerful simplifying assumption in physics. Without it any event no matter how distant can influence any other event. Prediction would be impossible without locality or some other powerful restriction on what events can affect other events. Otherwise one would need to know the state of the universe to predict anything. Quantum mechanics is a local theory in configuration space but not in physical space. As mentioned in Section 5.10 Bell refuted von Neumann's proof that no more complete theory could be consistent with quantum mechanics. In proving this Bell was influenced by Bohm's development of a more complete theory that was explicitly nonlocal. This led him to a proof that no local theory with hidden variables could reproduce the statistical predictions of quantum mechanics. Hidden variables were defined by Bell in a general way to include any more complete theory with a mechanism for explaining the conservation laws. He suggested that it should be possible to test some of the nonlocal predictions experimentally[4]. Realistic theories and randomness http://www.mtnmath.com/whatth/node58.html Often Bell's result is presented as showing that quantum mechanics is not a realistic theory rather than showing that it is nonlocal. The focus is on the reference to hidden variables in Bell's proof. Eberhard developed a version of Bell's argument that did not involve hidden variables[13]. In turn some physicists objected to Eberhard's proof because he assumed "contrafactual definiteness". That is he assumed one could argue about all possible outcomes of an experiment including those that did not happen. Arguments like those about hidden variables and contrafactual definiteness are philosophical. They have no clear resolution unlike problems that can be formulated mathematically. Such arguments are rare in the hard sciences. They occur here because of the claim in quantum mechanics that probabilities are fundamental or irreducible. There is no mathematical model for irreducible probabilities. There is not even a mathematically definition of a random number sequence. There are sequences that are recursively random. Loosely speaking this means that no recursive process can do better than chance at guessing the next element in the sequence. The problem with recursively random sequences is that they are more complex than any recursive sequence. If somehow one could generate such a sequence one could use it to solve recursively unsolvable problems. This suggests that a truly random sequence cannot exist. Any sequence that we would consider to be truly random must be recursively random. Otherwise there is some computer program that can guess with some degree of accuracy the elements in the sequence. Yet no recursive random sequence can be truly random. This presents a philosophical problem for the claim that quantum mechanics is truly random. The randomness claimed for quantum mechanics has no foundation in mathematics and it appears to be impossible to construct such a foundation. This does not make it wrong but suggests there are problems in our existing conceptual framework. It also means that physicists when arguing about these issues are debating philosophy with no objective way of deciding the issue.
The term "noise" hasn't been by derivation of time more and more denatured see: "Wavelet decomposition ... and noise " http://www.elitetrader.com/vb/showthread.php?s=&postid=431481#post431481 <IMG SRC=http://www.elitetrader.com/vb/attachment.php?s=&postid=431481>
Same thing for Neural Nets: http://www.elitetrader.com/vb/showthread.php?s=&postid=433050#post433050 ANNs (Neural Net): A Little Knowledge Can Be A Dangerous Thing ANNs: A Little Knowledge Can Be A Dangerous Thing by Dr. Halbert White Introduction When it comes to analytics, neural networks have to be one of the hottest commodities going. As of this writing, they are being used by everyone from MasterCard and American Express to Wal-Mart and KayBee Toys for everything from fraud detection and medical diagnosis to product marketing and stock forecasting. Still, while neural networks are undoubtedly a powerful tool, their use is laden with pitfalls, and as Dr. Halbert White points out, like all statistical techniques, they must be applied with both knowledge and care. White, a professor of economics at University of California, San Diego and a Senior Partner of Bates, White, and Ballentine, a business consulting firm, is one of the worldâs foremost experts on neural networks. He is also a member of the advisory board of Stone Analytics, sponsor of Second Moment, which recently sat down with Dr. White to discuss the current state of the art.
Yeah but what I mean is that to know if something is noise or not is a question of Knowledge and the idiots who think that knowledge comes from Wavelet or Neural Nets and whatever other sophisticated tools are really lacking basic paradigm about scientific approach: tools are like hammers: just tools, knowledge comes from the architect guy or knowledgeable man who has experience of the field. Now without tools and methods this knowledgeable man won't go very far but the contrary is far worst and very widespread due to confusion between technology (tools) and science (knowedge and research paradigm). Walter Shewart, the father of Statistical Process Control, and his spiritual son, Demings, once again, have always insisted upon that: datas don't bring knowledge by themselve. Knowledge means a theory for interpreting datas. The theory can be false and so the usefulness of a scientific approach which then need tools to investigate but tools alone cannot do this work ! Also fashionable so called data mining techniques doesn't substituate to Intelligence and knowledge. Some people who don't know that descriptive statistics is not inferential statistics will fool themselves and make false conclusion and discovery about datas significance.
=== Thought that was you Harrytrader by your question. Answer, no. ===== Bottom picker traders tend to wind up cottonpickers; a non random trading truth.
Q This would be an operational definition of a random procedure. A sample is neither random nor not random. It is the peocedure of selection that we must focus on. The procedure that selected the sample satisfies the prescribed definition of a random procedure, or it does not. A random variable is the product of a random operation. It is presumed that one uses a standard table of random numbers, or generates random numbers under the guidance of a mathematician who knows the prossible fallicies of generation of random numbers. --- Out of The Crisis (page 292), W Edwards Deming UQ