FR H-Volatility - page 8
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This is where it gets interesting, Yurixx. It seems to me that with our level of access to the market we are simply doomed at most to a phenomenological description. Roughly speaking, classical thermodynamics, not statistical thermodynamics. Doesn't the classical one work well? Even if within it we don't understand very well what entropy or temperature is, it still works, and very well at that.
Classical works well. But before it worked, and before it was born, the three-headed dragon Charles-Boyle-Mariotte worked in the sweat and the laws which he derived phenomenologically turned out to be special cases of the Mendeleev-Clapeyron equation. That is, from phenomenology he managed to rise to reveal the real laws. And if this were not the case, what would classical thermodynamics be all about?
And we are doomed to the phenomenological description only insofar as we have a purely utilitarian goal - to create TS and make money. But if someone with a lucid mind abstracts from mercantile interests and dedicates his time to a deep market study, he will have everything necessary for interesting discoveries - tools, data, etc.. Necessary but not sufficient ... :-)
Of top, but don't know where to write. If I am not mistaken the Guinness Book of Records has a record of 1200% p.a. Larry Williams http://web-investor.academ.org/index.php?action=articles&id=71
In the Stochastic Resonance thread, when I posted my work, I asked a question about the FR in question. There was no answer to it. And there were only three attempts. And it turns out it is a particular case of a well-known and researched function called Gamma distribution. I stumbled across it by chance, while reading a book on Bayesian statistics.
I don't consider myself a statistician, but here are the p.v. plots of these distributions. And most likely your distribution is a Rayleigh-Rice distribution, but not a gamma distribution, if I understand the formula correctly.
Sqrt(x^2+y^2) is the Rayleigh distribution, very often used in radar, it is the distribution of noise amplitude in Fourier series decomposition (x is real component, y is imaginary component). The square of this quantity is the lognormal distribution - closely related to the signal energy. The Rayleigh distribution, is a special case of the Rayleigh-Rice distribution, which does have a thick tail.
P.S. If necessary I can try to scan necessary pages and send them to you, but I can do it next week. Try to contact me or leave coordinates, I will try to help. All these distributions are well described in Levine B.R. Theoretical foundations of statistical radio engineering. - Moscow: Radio and Communications, 1989.
I am mostly on Skype -> privalov-sv
I attach matcad file, where they are all constructed and there are their characteristics + how to model it
Hi colleagues.
I don't abandon my attempts to qualitatively model the tick history of currency series using nth-order AR models. Let me remind you that the first difference series X[i]=Y[i]-Y[i-1] of the original AR is directly modelled: , where a[i] is the autoregressive coefficients, sigma is somehow a distributed random variable.
How do you think we can relate the FA of the first difference of the currency series and the FA of the first difference of the model series, via the FR of a random variable (sigma) in the AR model?
The problem has a solution. You can hand-pick the "right" sigma distribution law, but it's a painful procedure! Yurixx, it seems that the problem in this formulation is of some interest to you. In case of a positive outcome we would have in our hands an algorithm for constructing a BP identical to the generating one in the sense of volatility and preserving relations between ticks (bars on different TFs), which, as Mathemat pointed out , is necessary for representative testing of a TS.
FA abbreviation ? decipher it please. Is it a function of autoregression X[i] ?
FA abbreviation ? decipher it please. Is it a function of autoregression X[i] ?
Oh! I'm sorry. Throughout, it should read FR instead of FA.
How do you think the FR of the first difference of the currency series and the FR of the first difference of the model series can be related, via the FR of a random variable (sigma) in the AR model?
The problem has a solution. Manually we can find the "right" sigma distribution law, but it is a painful procedure!
Well, if one assumes that sigma is supposed to lead the FR of the model series to the FR of the currency series, then the FR of sigma should be constructed as the FR of the difference of the two SVs: model X and real Y. However, since sigma is involved in the formation of X and the entire random nature of X is determined by sigma, it is difficult to say so immediately.
Maybe try the opposite. How to build X distribution if Xi+1=Xi + sigma, and FR sigma is known ? If you solve this problem, then you can solve the one you set.
It is not yet clear how this can be implemented.
My question, colleagues, is off-topic. You probably now show a certain interest in possible application of neural networks (NS) in TS. Answer me, do I understand correctly that the use of NS is justified by a sufficiently large number of input parameters, when the use of a usual search for TS optimization (even with the use of genetic algorithm) is unjustified for technical reasons? We can also emphasize the ability of NS to self-learning in the process, but this task is not difficult to solve using the procedure of automatic optimization of the usual logical construction.
I think that's right, but I also think that's not all there is to it.
I don't know what is "automatic optimisation of ordinary logical design", but in NS I am attracted just by the ability to implement very complex decision-making logics. Even with a not very large number of parameters, the phase space of the system turns out to be too multidimensional for human perception. If the approach is correct and the chosen estimates enable clustering of the phase space, then the location and shape of the clusters can have a very complex topology. We either need to visualise it somehow to describe the decision logic, or blindly introduce classes and membership criteria. NS handles this as well as probabilistic evaluations (as we can see) much better.
In the Stochastic Resonance thread, when I posted my work, I asked a question about the FR in question. There was no answer to it. And there were only three attempts. And it turns out it is a special case of a well-known and researched function called Gamma distribution. I came across it by chance, reading a book on Bayesian statistics.
I don't consider myself a statistician, but here are the p.v. plots of these distributions. And most likely your distribution is a Rayleigh-Rice distribution, but in no way a gamma distribution, if I understand the formula correctly.
The gamma distribution has one parameter. Depending on its value, it can have different shapes, including those similar to the Rayleigh distribution. However, its statistical characteristics and behaviour at large x will be different.
I don't know which distribution I "need". It's just a question that came up at the time and I only found the answer to it some time later. What to do with FR - that's the question. Only when it will be solved the next question will be about the form of distribution function. Then we can go back to this whole gentlemen's kit.