From theory to practice - page 578
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You have to read from Chapter 2 onwards. And the shapes of the distributions are the same as in Forex. And the neural network determines the parameters of these distributions. All in all, it's a good book.
We have finally got to anomalous diffusion. A couple of remarks:
1) That in the beginning of 2-th chapter - flights of Levy - is not suitable for the market, because it is processes with stationary increments. It is better to think of the increments as Gaussian, but not stationary.
2) It seems to me that the "spatial" variables are not only price, but also some kind of market state - there are many different things to think of and it is not very clear what and how to choose.
:)
You shouldn't laugh. Is there any reason to think of the square of the variance as the measure of variance? Why is the variance most often taken as a measure of variance, and the proximity criterion derived from it applied when approximating dependencies? I know of only one reason - a radical simplification of calculations when the measure of variance is taken as the variance of their series, and the task of minimizing it (MNC) is posed. However, the result of the very first characteristic - the mean - already depends on the chosen measure of variance. For a deviation |di|^2 (OLS), the minimum of the sum of the deviations is obtained when the mean is equal to the arithmetic mean. If we take as criterion the sum of deviations in the first degree (sum |di|^1), then the median will be the mean, it is its mathematical property. It's all about the problem. If we're talking about wage levels, we're not going to believe the arithmetic mean, but the median https://clubtk.ru/chto-takoe-mediannaya-zarplata:
"Sometimes the statistics concerning income levels are surprising: where did the information come from with such high figures. When informing the population about changes in wages, they are referring to income, which is actually the arithmetic mean between the maximum and minimum figures.
The criteria in Russia
Median wage - what is it? This kind of income is an artificial figure. It is a figure which characterises the wage of an employee who is in the middle of the payroll. It means that ½ of the employees included in the calculation have salaries higher than the chosen figure and ½ have salaries lower than the chosen figure."
End of quote
Alexander, as far as I understand, is looking for the opposite, not the average, but the furthest values - the outliers. For them it is natural to take the index of degree in the sum |di|^n (analogue of variance) above 2. Another thing is that this may not be possible for Vissim, the scope of which Alexander is limited.
You shouldn't laugh. Is there any reason to think of the square of the variance as the measure of variance? Why is the variance most often taken as a measure of variance, and the proximity criterion derived from it applied when approximating dependencies? I know of only one reason - a radical simplification of calculations when the measure of variance is taken as the variance of their series, and the problem of its minimization (MNC) is set. However, the result of the very first characteristic - the mean - already depends on the chosen measure of variance. For a deviation |di|^2 (OLS), the minimum of the sum of the deviations is obtained when the mean is equal to the arithmetic mean. If we take as criterion the sum of deviations in the first degree (sum |di|^1), then the median will be the mean, it is its mathematical property. It's all about the problem. If we're talking about wage levels, we're not going to believe the arithmetic mean, but the median https://clubtk.ru/chto-takoe-mediannaya-zarplata:
"Sometimes the statistics concerning income levels are surprising: where did the information come from with such high figures. When informing the population about changes in wages, they are referring to income, which is actually the arithmetic mean between the maximum and minimum figures.
The criteria in Russia
Median wage - what is it? This kind of income is an artificial figure. It is a figure which characterises the wage of an employee who is in the middle of the payroll. It means that ½ of the employees included in the calculation have salaries higher than the chosen figure, and ½ have salaries lower than the chosen figure."
End of quote
Alexander, as far as I understand, is not looking for the average, but for the most distant values - outliers. For them it is natural to take the index of degree in the sum |di|^n (analogue of dispersion) higher than 2. Another thing is that this may not be possible for Vissim, the scope of which Alexander is limited.
It seems to me that the question of what to minimise should be decided in terms of statistical decision theory. That is, it should come down to minimising the average error loss. In standard problems of mathematical statistics, this approach naturally often leads to minimisation of the mean square (or modulus) of the deviation. For the problems interesting for us, it may lead to something else.
It seems to me that the question of what to minimise should be decided in terms of statistical decision theory. That is, it should boil down to minimising the average error loss. In standard problems of mathematical statistics this approach naturally often leads to minimisation of the mean square (or modulus) of the deviation. For the problems we are interested in, something else may result.
Our retail forex rates do not obey probability laws at all, which is clearly demonstrated by the figure from Yuri Asaulenko's post https://www.mql5.com/ru/forum/221552/page162#comment_6399653. In particular, the relative frequency does not tend to probability, the laws of large numbers are not followed. In probability theory, the nature of statistical fluctuations of event frequency around its probability is subject to the laws of large numbers. The available statistical inference theory always relies on probability theory, using its postulates.
In particular, the most popular maximum likelihood method requires that data 1) be distributed according to a known probability law and 2) that deviations from that law be distributed normally. Therefore it is not suitable for forex courses.
The theory of statistical deduction does not work, because the theory does not exist for Forex rates. There are rudiments of describing their behaviour with an inclination to the known terminology accepted in the probability theory:
I.I. Gorban THEORY OF HYPERSLUTE EVENTS. Theory and practice. Section 7. System Analysis.
I.I. HURBAN, THE PHENOMENON OF STATISTICAL STABILITY KIEV NAUKOVA DUMKA 2014.
Our retail forex rates do not obey probability laws at all, as the figure from Yuri Asaulenko's post https://www.mql5.com/ru/forum/221552/page162#comment_6399653 clearly demonstrates. In particular, relative frequency does not tend to probability, the laws of large numbers are not followed. In probability theory, the nature of statistical fluctuations of event frequency around its probability is subject to the laws of large numbers. The available statistical inference theory always relies on probability theory, using its postulates.
In particular, the most popular maximum likelihood method requires that data should 1) be distributed according to a known probability law and 2) deviations from that law should be distributed normally. Therefore it is not suitable for forex courses.
The theory of statistical deduction does not work, because the theory does not exist for Forex rates. There is a rudimentary description of their behaviour with an inclination towards the known terminology accepted in the probability theory:
On the one hand, I quite agree with you that the nature of the market is not described by statistical methods. Rather, by game theory methods. But methods for solving game theory problems are often quite statistical - mixed Nash equilibria, for example. You can look at fluctuations around these equilibria.
There is also an econophysics approach. There the market is modeled by potential games that are studied with a large number of players. The ideas of statistical physics are used there.
In general, inapplicability of some models does not mean inapplicability of science as a whole, but only that it is necessary to build other models.
Well, yes - the sum of the increments in the sliding window, if I understand correctly. Nice indicator, but it doesn't do much about trends. But - cool... But not great... I'm confused.
I'm reading a book right now. It's the best I've found in a while. There's a lot in it that we've talked about in this thread + neural networks.
I'm publishing it again.
Thank you!
replied in person
5. On my chart, I have the expectation +- std deviation*quantile.
Well, this is the channel itself, but the role of price? The sum of changes? Or does the channel is based on the price?
Well that's the channel itself, but the role of price? The sum of increments? Or is the channel based on the price?
Well, Warlock recommends working not with the price, but with the sum of the increments (the sum of the increments is the price from some initial coordinate).
He is probably the only person here (is he a person?) whose opinion I trust.
Well that's the channel itself, but the role of price? The amount of increments? Or is the channel built from the price?
work not with price, but with the sum of the increments (the sum of the increments is the price from some initial coordinate).
Well, that's what I'm looking at.