From theory to practice - page 665
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I'm telling you again - asymmetry and kurtosis of the distribution have a direct bearing on the "memory" of the process. Especially the kurtosis.
Nonsense and ignorance.
And neither process will have anything to do with reality.
and no process will have anything to do with reality.
And how can this be identified? Alexander, you are an expert in distributions, and you demand that any proposals be justified physically and mathematically. How can either traditional or non-parametric statistics of the DISTRIBUTION of a random variable be related to "memory"? After all, no property of a random variable's distribution changes if you rearrange the order in which its values appear as you wish.
For example, in this way which is universal for the rate increments: we order all the available increments in the sample by their values from the lower to the upper ones. The corresponding rate will first decrease, then increase. Irrespective of the multimodality of the distribution. What will happen to the "memory" in this case - complete chaos, it will disappear, if there was one. Although neither asymmetry, kurtosis, mean nor variance will change at all.
It remains to rely on some property that is not in the distribution. For example, time - and then one can try to think about the growth of entropy, although in case of currency interventions it will obviously decrease. It is not enough to analyse only distributions, you need a link to the LETTERS. You think asymmetry and kurtosis are related, tell me on what basis?
So that your decisions can be justified physically and mathematically.
You use the name "diffusion coefficient", but it did not arise by chance - processes of diffusion, heat conduction and filtration are described by the same equations of parabolic type and in absence of perturbations the transfer potentials in them dissipate in space as time goes by. At the same time, entropy increases. By the way, the square root law also works, remember the similarity of thermal nonstationary processes by Fourier criterion at/x^2. Tossing a coin can also be described by the heat conduction equation. And what is the basis of your reliance on kurtosis and asymmetry?
Sleep?
No, of course not. How can you sleep...?
All energies are thrown into the search for excesses and asymmetries.
The excesses and asymmetries found are applied to the sore spot. Then the process of finding excesses and asymmetries is repeated.
;)))And how can this be identified? Alexander, you are an expert in distributions, and you demand that any suggestions be justified physically and mathematically. How can both traditional and non-parametric statistics of the DISTRIBUTION of a random variable be related to "memory"? After all, no property of a random variable's distribution changes if you rearrange the order in which its values appear as you wish.
For example, in this way which is universal for the rate increments: we order all the available increments in the sample by their values from the lower to the upper ones. The corresponding rate will first decrease, then increase. Irrespective of the multimodality of the distribution. What will happen to the "memory" in this case - complete chaos, it will disappear, if there was one. Although neither asymmetry, nor kurtosis, mean nor variance will change at all.
It remains to rely on some property that does not exist in the distribution. For example, time - and then one can try to think about the growth of entropy, although in case of currency interventions it will obviously decrease. It is not enough to analyse only distributions, you need a link to the LETTERS. You think asymmetry and kurtosis are related, so tell me on what basis?
So that your decisions can be justified physically and mathematically.
You use the name "diffusion coefficient", but it did not arise by chance - processes of diffusion, heat conduction and filtration are described by the same equations of parabolic type and in absence of perturbations the transfer potentials in them dissipate in space as time goes by. At the same time, entropy increases. By the way, the square root law also works, remember the similarity of thermal nonstationary processes by Fourier criterion at/x^2. Tossing a coin can also be described by the heat conduction equation. And your reliance on kurtosis and asymmetry is based on what?
This is probably the first time I will refuse to answer you, Vladimir. Because, as I see, you have not read a word of Shelepin's works about non-entropy of the system.
And what is non-entropy? It is "memory". This is a measure of system organization, structurization, formally described by the difference of its probability distribution from the normal one, as having the maximum entropy.
Indirectly, I emphasize - indirectly, it is measured by nonparametric coefficients of asymmetry and kurtosis.
I see no further point in engaging in these bizarre discussions where "consequence" and "memory" are confused. Sorry.
:))))) Go to school, kid. All your questions will be answered there.
:))))) Go to school, child. All your questions will be answered there.