[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 387

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Candid: And also think why Hurst guessed to normalize by RMS, but did not guess to calculate the degree by the ray from the origin. He did, by regression. He was a fool, is that how you see it?

He didn't have Mt4 and MQL...And the forum.

;)

 
Candid:

...


Let me interject a little with your permission. The calculation of the Hurst index is well described by Shiryaev and from an artistic point of view, he was not dealing with "Nile" as such, but with tributaries of Nile (increments, i.e. what forms the process called - Nile). Where was I going with this? Ah! Never mind - this is a lyrical digression in general.

To calculate Hearst's exponent by the spread method is pointless, it's very crude and the estimate comes out with a very big bias (about 20-30% error - just easy). There are two good methods:

  • Wittle's method (based on regression models, works ironclad if the model matches reality)
  • Wavelet-based (the most accurate method, works well "locally")
 
Farnsworth:

Let me interject a little, with your permission. The calculation of the Hurst index is well described by Shiryaev and from an artistic point of view, he did not deal with the "Nile" as such, but with tributaries of the Nile (increments, i.e. what forms the process called - Nile). Where was I going with this? Ah! Never mind - this is a lyrical digression in general.

To calculate Hearst's exponent by the spread method is pointless, it's very crude and the estimate comes out with a very big bias (about 20-30% error - just easy). There are two good methods:

  • Wittle's method (based on regression models, works ironclad if the model matches reality)
  • Wavelet-based (the most accurate method, works well "locally")
Have you tried these methods yourself, do they work? Of course, the one that works locally is particularly interesting.
 
Candid:
Have you tried these methods yourself, do they give you anything? Especially interesting, of course, is what works locally.

I've been doing fractal analysis for quite a long time and have tried many things. Unfortunately, a virus ruined most of the material, but I've stopped getting upset. Someday I'll get myself together - and repeat the most valuable achievements :o) Wittle's method I've even converted to MathCAD, and wavelet-based method is implemented in MathLab, where I've studied it.

Only, why do you need this indicator? It has a very vague predictive property (). That is, even the calculated exact value of 0.8 (even with the confidence interval) will not tell you anything about the "trendiness" that will last and how many counts this condition will stay the same, and will not answer the main question - where the trend will move. Moreover, this indicator calculated using historical series demonstrates only "the propensity" and even a process with trendiness can really show a different behavior than expected (it will just happen) and, what is the most disappointing, "can't be falsified".

For a meaningful estimation the probability is needed, and it means that we should consider the quote as a multifractal and build a "singularity spectrum".

And an entirely unpleasant characteristic is the, literally, "catastrophic" dependence on sample length.

 
Bloody hell, this Hurst crawls up the forum regularly. Maybe someone can explain to me what predictive value it has?
 
Mathemat:
Heck, it's Hurst that crawls out on the forum on a regular basis. Maybe someone can explain to me what predictive value it has?

in fact - none. Did you get it? :о) But it is useful in modelling processes.

ADDENDUM: the only practical value that's hard to automate is analysing the shape of the graph in log-log coordinates. You can clearly tell which part of the series corresponds to a power law, and you can "formally" enter a "memory length" value. And this is valuable. Otherwise they start counting regressions, and often in places where it does not make sense(sometimes, well, the behavior of increments does not correspond to the power law, such as forex).

 

Farnsworth:

And an entirely unpleasant characteristic is the, literally, "catastrophic" dependence on sample length.

Yes, the definition of sample length seems to be the key point in the vast majority of approaches.

Multifractals - hmmm. perhaps, there seems to be an indication that this concept is more adequate, and so does the authority of Mandelbrot.

 
Candid:

Yes, the definition of sample length seems to be the key point in the vast majority of approaches.

Multifractals - hmmm. maybe, there seems to be an indication that this concept is more adequate, and so is the authority of Mandelbrot.

To be honest - I don't understand what you are doing and what is the point of it all?
 
Mathemat:
Bloody hell, this Hurst crawls out on the forum on a regular basis. Maybe someone can explain to me what predictive value it has?

=0.5 random wandering in noise.

<0.5 is even worse - noise randomly wanders :)

>0.5 there's hope about memory...

>0.79 is naturally natural

 
Farnsworth:
To be honest - I don't understand what you're doing and what's the point of it all?
Um... do you mean that in a broad sense or a narrow one? :)
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