Any opinion on this paper :
http://arxiv.org/abs/cond-mat/0602316
"We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion....."
Multi-fractal stuff, Mandelbrot is mostly right
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crowlogic
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- Joined: Thu Jan 01, 2004 12:00 am
Multi-fractal stuff, Mandelbrot is mostly right
[b]lexx[/b] wrote:
[i]Any opinion on this paper :
http://arxiv.org/abs/cond-mat/0602316[/i]
Looks fascinating.. basically shows that any process where h != 0.5 can be rescaled in time so that H becomes 1/2. But also looks like the author is desperately trying to justify the EMH and saying that H != 1/2 is NOT a stand-along sign of non-markovianness... while true I would say that it is completely obvious that the markets are non-markovian so it seems like a waste of time to prove they are not. Agents work on all time frames and they also use past information to make decisions, whether a picosecond ni the past or 10 years so therefore using simple reasoning it is non-markovian. UNLESS you use hidden variables and then say that there are some unobserved hidden variables that all the "past" is mapped into and then these hidden variables are only present instantly in time so you could retain the markov formalism.. but then you have to extend your defintion of state to unobservable things like volatility, etc.
[i]Any opinion on this paper :
http://arxiv.org/abs/cond-mat/0602316[/i]
Looks fascinating.. basically shows that any process where h != 0.5 can be rescaled in time so that H becomes 1/2. But also looks like the author is desperately trying to justify the EMH and saying that H != 1/2 is NOT a stand-along sign of non-markovianness... while true I would say that it is completely obvious that the markets are non-markovian so it seems like a waste of time to prove they are not. Agents work on all time frames and they also use past information to make decisions, whether a picosecond ni the past or 10 years so therefore using simple reasoning it is non-markovian. UNLESS you use hidden variables and then say that there are some unobserved hidden variables that all the "past" is mapped into and then these hidden variables are only present instantly in time so you could retain the markov formalism.. but then you have to extend your defintion of state to unobservable things like volatility, etc.
One should respect public opinion insofar as is necessary to avoid starvation and keep out of prison, but anything that goes beyond this is voluntary submission to an unnecessary tyranny. --Bertrand Russell
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dehaan
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- Joined: Thu Jan 01, 2004 12:00 am
Multi-fractal stuff, Mandelbrot is mostly right
Hi,
sorry to have dug out this old thread.....
"Mandelbrot is mostly right"...can someone explain what does this phrase mean, please, in the context of price evolution modeling?
That one can somehow calibrate the history of the DJ to a deterministic fractal/multifractal model, and that predicitve power of this model would be satisfactory?
Or at least what are his "mild randomness" and "wild randomness"?
Thank you
sorry to have dug out this old thread.....
"Mandelbrot is mostly right"...can someone explain what does this phrase mean, please, in the context of price evolution modeling?
That one can somehow calibrate the history of the DJ to a deterministic fractal/multifractal model, and that predicitve power of this model would be satisfactory?
Or at least what are his "mild randomness" and "wild randomness"?
Thank you
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tristanreid
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- Joined: Thu Jan 01, 2004 12:00 am
Multi-fractal stuff, Mandelbrot is mostly right
I can't answer your question as well as many others here, so I won't even try. I'd recommend "An Engine, Not a Camera", by Donald MacKenzie. There's a chapter that describes Levy distributions in laymen's terms, and gives a brief history on Mandelbrot and finance.
I think the idea of mild vs. wild:
Mild randomness is like the normal distribution. It's random, but given some history you have a pretty good idea of where the data will go. This is 'thin-tails', where large changes are extremely unlikely. In other words given a probability, say 95%, you could put an upper bound on how large a movement will happen.
Wild randomness is when you have fat tails. That means large movements are more likely to happen than with normal distributions, and it means that you can't put an upper bound on the size of a movement in your data.
-t.
I think the idea of mild vs. wild:
Mild randomness is like the normal distribution. It's random, but given some history you have a pretty good idea of where the data will go. This is 'thin-tails', where large changes are extremely unlikely. In other words given a probability, say 95%, you could put an upper bound on how large a movement will happen.
Wild randomness is when you have fat tails. That means large movements are more likely to happen than with normal distributions, and it means that you can't put an upper bound on the size of a movement in your data.
-t.
If you can make computers as smart as humans you will have invented a machine that can sing the words to the Flintstones tune but will forget to pay the phone bill.