Market prices are often modelled as a random walk, meaning that each price movement is independent of the last (ie the price movement is driven by white noise) - this doesn't mean we know its probability distribution and it certainly wont be uniform, it is probably closer to gaussian.
There are some economists, for example Burton Malkiel who wrote A Random Walk Down Wall Street, who hold that share price movements are indistinguishable from completely random movements
Which is why they are no good at trading...
What is a random movement?? Can anybody prove that such a thing exists??
Every man and his dog can quickly and easily see that a stock say BHP has moved up from ~$36 to $41 over the last 2 weeks. Consciously or subconsciously this will affect what many participants in the market do with this stock tomorrow. For an event to be compared with 'random' there can be no memory from prior events, clearly in this case memory comes into it.
brty
he generated graphs of a hypothetical share where the next move was completely random
I seriously doubt the graph was completely random, because it was produced by a computer that had been given instructions.
brty
Lol - yep, One certainly gets the feeling that the games have been made intentionally "interesting" - It may not be random - although you can force it to be random, see d) below - but I don't believe it's rigged, for the following reasons :-I tried the jellyfish backgammon for an hour and then promptly removed the program. Strangely the computer 'often' drew more doubles, drew the exact numbers it needed and the last straw was when I finally drew double sixes, jellyfish followed with two double sixes in a row.
And it doubles up all the time which was annoying.
even randomness has to be defined m8 - like .. chosen from pink noise vs white noise etcsome pseudo-random numbers are pretty bloody good, and besides he may have used other sources of randomness - like atmospheric noise
bellenuit,
I am not having a go at you at all, I apologise if it came across that way.
brty
To be fair to Burton Malkiel, I actually misstated what he wrote by that statement and Schnootle corrected me.
I'm really digging into my memory, but he generated graphs of a hypothetical share where the next move was completely random in the sense that it could be up or down (maybe sideways too), but only by 1 unit from where it currently is. The next move after that would be randomly up or down (or sideways) one unit from the new point. So this has the memory of prior events that you mentioned as each move can only be 1 unit away at most from where the previous move ended.
He then showed those graphs to stock chartists who look for the typical patterns that chartists look for (head and shoulder patterns etc.) and mixed then in with some charts of actual stocks. Apparently the chartists could not tell which were the hypothetical stocks and which were the real.
I am not trying to defend his arguments and can't in any case as I remember so little from the book. But it is a fairly well respected work in the industry, so I wouldn't dismiss him offhand.
he may have used other sources of randomness - like atmospheric noise
even randomness has to be defined m8 - like .. chosen from pink noise vs white noise etc
A discrete-time martingale is a discrete-time stochastic process (i.e., a sequence of random variables) X1, X2, X3, ... that satisfies for all n
\mathbf{E} ( \vert X_n \vert )< \infty
\mathbf{E} (X_{n+1}\mid X_1,\ldots,X_n)=X_n,
i.e., the conditional expected value of the next observation, given all the past observations, is equal to the last observation.
Somewhat more generally, a sequence Y1, Y2, Y3 ... is said to be a martingale with respect to another sequence X1, X2, X3 ... if for all n
\mathbf{E} ( \vert Y_n \vert )< \infty
\mathbf{E} (Y_{n+1}\mid X_1,\ldots,X_n)=Y_n. The sequence Xi is sometimes known as the filtration.
Similarly, a continuous-time martingale with respect to the stochastic process Xt is a stochastic process Yt such that for all t
\mathbf{E} ( \vert Y_t \vert )<\infty
\mathbf{E} ( Y_{t} \mid \{ X_{\tau}, \tau \leq s \} ) = Y_s, \ \forall\ s \leq t.
schnootle,
How is atmospheric noise random?
brty
The concept of random is something that exists in the minds of mathematicians, not in the real universe, yet the concept has permeated all types of thinking in the modern world.
My observation of the universe has evidence that everything is in order. Organics are observed to reproduce with the same species and choose their food for example. Whereas non-organics are harder to define but since they are required for organics to exist, then the order is there too.Quantum mechanics as a theory as been incredibly successful, so it is entirely possible that randomness is intrinsic to the universe - not just a mathematical concept.
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.
everything at the quantum level is inherently unpredictable
...is only because we have not worked out how to do it, does not mean it is random.
brty
The solution is
ignore the first number.
if the second number is larger than the first, choose it, else
if the third number is larger than the first, choose it, else
if the fourth number is larger than the first, choose it, else
-
follow the pattern
-
if the second last number is larger than the first, choose it, else
if the last number is larger than the first, choose it, else
choose the last number even though you know it is not the highest.
Using this strategy I determined that the probability of picking the highest number is slightly larger than 0.25. More preciously 0.25*(999)/(998).
What thread was that? I thought I might have posted it on ASF before, but the only puzzle thread I could find was this one and it wasn't here.
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