Profit from a random price range - page 5

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usdjpy писал (а):
..................................
For autotrading
Yuri Reshetnikov "MTS and money management techniques"
Is your name not Yury by any chance?
I have had this doubt for a long time ...
 
Mak:

The principle point is that there are random series with and without memory.
A random series with memory has a distribution function of increments of a random variable (e) which depends on the previous values of the series.
It's a bit of an aberration altogether. The nerd's new definition is Mack's definition of a random variable.

In probability theory, a random variable is defined as one that is independent of previous values. One of two things is either dependent or random. There is no third.
 
Mak:
usdjpy wrote (a):
..................................
For autotrading
Yuri Reshetnikov "MTS and money management techniques"
Is your name by any chance Yuri?
I have had that doubt for a long time ...

Well, in general, the aggressiveness and manner of communication reminds me very much.
Though, probably, it is a corporate move. You have to attract people to your resource somehow.
 
You're a nerd yourself...
Do you know the difference between a random variable and a random series?
And don't teach me about probability theory, read what it is first.
 
Mak:
olexij:
Well, about the normal distribution - the quotes as it were, as S.W. wrote and what lies in the palm of his hand, are normally distributed around the moving average, so we're in the clear here.
Correction.
1. The kind of distribution function of the differences in price and the average depends on the variance of that distribution and the value of the average.
2. The distribution function of this difference is asymmetric, so it cannot be Gaussian.
3. Under certain conditions, the distribution of the difference tends to a Gaussian distribution, but never becomes one.

You know Mac, my statement was probably premature, yours by the way is also unsubstantiated unless you show the tests or relevant literature :)
 
As a matter of fact, I looked through Peters and found on page 132 the formula for fractal distribution. So, normal distribution is a special case of fractal distribution. Who is interested, take link above and open this page. That is, if you want to do as suggested, you find the coefficient of fractal distribution experimentally by testing hypotheses. Then you turn it into a normal distribution by spitting out the thick tails and trimming off the tops. Thus you return to the efficient market theory, discarding all the charms of fractal modelling. And here the question arises: why? If you need a normal distribution, then adjust the coefficient according to it! Why do you need it? Well, all your conclusions will then be about an imperfect efficient market theory. My opinion so far: it's a load of rubbish and a waste of time. I will gladly take it back if I have misunderstood something and someone can convince me otherwise...
 
olexij:
Mak:
olexij:
Well, as for the normal distribution - the quotes as it were, as S.W. wrote and what lies in the palm of his hand, are normally distributed around the moving average, so we are in the clear here.
Correction.
1. The kind of distribution function of the differences in price and the mean depends on the variance of that distribution and on the value of the mean.
2. The distribution function of this difference is asymmetric, so it cannot be Gaussian.
3. Under certain conditions, the distribution of the difference tends to a Gaussian distribution, but never becomes one.

You know, Mack, my statement must have been premature, by the way yours is the same unsubstantiated, if you will not show me tests or appropriate literature :)
It's elementary, Watson ... :))
Simple logic, you don't even need mathematics.

1. Price is a strictly positive value (which is probably already obvious).
2. Price can aspire to zero, but cannot reach it (unless you consider the discreteness of money, which can always be circumvented)
3. So the distribution of the difference in price and the moving average will ALWAYS be bounded from below by some value, whereby the value of the difference can tend towards that bound, but can never reach it.
4. The effect of this limit depends on the coefficient of variation, actually the ratio of the RMS to the average. The smaller this value, the smaller the impact of the constraint ...

And besides, we should not forget about "heavy tails".
The price increment distribution function actually consists of a mixture of distribution functions.
It has its own distribution function for different states (one function at the flat, another one at the news).
This, too, leads to non-normality of the FR of the price difference and the average.
 
So what difference does it make whether the distribution function is normal or not?

If this FR is independent of history and has zero expected payoff - you cannot build a profitable system on such a random series (see Oaks).
Otherwise it cannot be stated.
For some FRs it is possible to construct a working system.
 
olexij, you yourself have guessed what I meant about converting fractal to normal. But the conclusion about going back to efficient market theory is, in my opinion, wrong. The normal data that is obtained in this way are synthetic data. They are not directly related to the market.

Well, it would be better to ask S.V. about the details. He started this mess, on many pages he tried to justify the possibility of profitable work on normal, and then he also threw in this idea of transformation without showing its implementation. I respect the opinion of both S.V. I respect S. and Rosh' s opinion, but I strongly doubt that it is possible to build something long-term profitable on normal data. But on a pure fractal distribution with a decent Hearst index (close to 1), I think it is possible, because it is clearly a persistent series. Weeks, for example, have H significantly higher than minutes...

2 Mak:
3. So the distribution of the price difference and the moving average will ALWAYS be bounded from below by some value, and the value of the difference may aspire to this limit, but can never reach it. <br/ translate="no">

Mak, you've bent it the wrong way on something. Price never intersects with the muving?!
 
Mathemat:
.... I respect the opinion of both S.V. and Rosh. and Rosh's opinion, but I strongly doubt that it is possible to build something long-term profitable on normal data. ...
I claim that it is impossible to build something profitable, even momentarily, on an abnormal distribution.
Because the point is not in the form of FR, but in the dependence of FR parameters of time series increments on previous values of this series.
If it is there - there is a probability to build a working system.
If it is not there - it is not.
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