Randomness obeys statiscial laws. Randomness is relative. What could be pure randomness in one context can be perfect order in another. For instance, an ant scurrying around on it on may appear to have random movements but when the entire line of ants is viewed the individual fits it perfectly with the ebb and flow.
"Probability (random processes)": NO that's the very point Probability concept (based on the 3 founding Axioms: P(Sample Space)=1 etc. ) is not to be confounded with Randomness concept . As for the dice if it is used for defining operationally a random process by analogy - as would do Shewart - it is supposed to be "fair" implicitly so independancy is then implied.
This is an example where the term random is used more and more fuzzyly so the express need for a definition . It is preferable to use the term "Stochastic processes" than the term "random processes" if one wants to reserve the word random to its original definition. Of course one can use the term "random processes" but it is ANOTHER CONCEPT than the original random concept: it's two different concepts as if one would talk about two different animals like a cat or a dog. The use of Poisson process to modelise jumps - which I have already mentioned myself in another thread - doesn't mean that the process is random in the sense used by Walter Shewart for example. For him the existence of jumps is suspicious of existence of "special causes" which makes the process behave not randomly stricto sensus (by refering to the definition of operational definition like coin flipping) but only behave stochastically. Practical consequences for him is that it is then worth to study such causes and so improve the prediction of the system whereas when the system behave randomly there is no need to make any special study.
harrytrader wrote: Lest anyone be confused, words "stochastic" and "random", as in "stochastic process", "random process", "random variable", etc. are used interchangeably -- there is no difference in mathematics. Check out any standard textbook like: http://www.statslab.cam.ac.uk/~grg/books/prp.html What people do with these words outside of mathematics is no doubt confusing and imprecise.
Once again you can confuse if you want, like you can confuse the term noise, but if some people wants to distinguish between different type of noises some then use the expressions "white noise", "brown noise", etc. ... but usually noise without precising context would mean white noise. Why don't we designate the cat and the dog by the single term animal huh ? Because sometimes one needs to distinguish between categories. The term "random" used in the context of Statistical Process Control (used in Quality enginiering Field) for example is very strict, it is in this sense that I use it, as well as Kolmogorov complexity. That you want to englobe other categories doesn't really matter, we don't talk about the same animal. And if statistical control restrict the sense it is not by puritism it is because it has PHYSICAL SIGNIFICANCE that a process doesn't follow randomness in the strict sense of this definition: it implies the presence of what Shewart called "special causes" (in Stock Market this could be used for example for detecting breakout zones). In real world we are interested by physical phenomenas not by mathematical conventions purely.
There is no question that we know what is random in nature: The decay of particles due to the weak force is the best known random generator in the whole of existence, inside a computer or out. In fact, I believe that it is "proven" that the decay is a truly random event. As far as mathematical randomness, there is no question that defining it is a deep question. Whether that says anything about EMH or other market theories, is well, interesting... nitro
Yes but once again it is only by referring to a PHYSICAL PROCESS (decay of particles, brownian motion or trivially coin flipping - no need to even look for high tech for that ) that one defines RANDOM concept. That's what Shewart is saying: without this reference to TRUE PHYSICAL RANDOM PROCESS it is IMPOSSIBLE to define RANDOM PROCESS not partially - like with the 3 probability axioms - but COMPLETELY because (partial) ORDER COUNTS in PHYSICAL PROCESS that are not "random" and this partial order requires knowledge of the field that are OUT FROM the FIELD of the STATISTICIAN that's why he says the STATISTICIAN CAN'T BE the only JUDGE when the process IS NOT in "CONTROL STATE" (he prefers to use this term which is connected to real operation): he is NOT COMPETENT FOR JUDGING in that case. Today, econometrics is a field invaded mostly by mathematicians and statisticians beginning with econometrist Irving Fisher - who I remind is the author of the "immortal prediction" of permanent plateau before the 1929's crash - and they have become the ultimate judges with so called "Cowles Commission" - created by the same Irving Fisher above - and their "EMH" hypothesis. Under the pretext of Science they betray Science : Science is not about VIRTAL MATHEMATICS it's about REAL PHYSICAL PROCESS and economics belongs to PHYSICAL PROCESSES not to MATHEMATICS WORLD. Looking at financial education, students learn more maths than economics and when they go into real world, most of them should think that real world conform to the maths they learned instead of being critics that what they learn is more due to convieniency of (simplist) mathematical models than with reality. Of course these models are useful but only as reference (a random process is useful as I said above without knowing what it is you cannot deal recognise non-random process) and the problem is that education is more focused on calculation techniques (like the 36000 way of finding an optimum in a non-minear space ) than on epistemology.
Random is a human concept and exists as a concept in direct relationship to man's concept of order. So which comes first, the concept of order, or the concept of a lack of order, i.e. random? Is there actually order/chaos/random/pattern outside of man's concepts or do we simply project our concepts onto the physical world? Can something be random from one point of view, yet orderly from a different point of view? When we see an ant farm we don't see orderly motion, we see random behavior of movement, yet, if that random behavior is planned to be random by the ants, it is then following the order of the plan, and is not random at all. I laugh when I see a list of "random" numbers, a list that was designed to be random by human beings or computer programs. Unless we have an absolute point of view, our conclusions of order and random are realtive.