FR H-Volatility - page 15
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I suggest, let's use one little technique that I think will help us understand each other, and most importantly will define the direction of research.
It's a little hard, but I think it will help.
What characteristics of this curve are important for its prediction ?
My version, m.o. variance, etc. i.e. initial and central moments, correlation coefficient. Research by many has already shown that all these characteristics are time dependent, i.e. we are dealing with a random unsteady flow. We should try to reduce this flow to stationary one using various transformations, and then we can use well-known methods of stationary flow research.
The point is that mathematical methods of analysis are rather universal and they do not care what kind of curve it is (flow of quotes or number of bacteria).
I have a request, help me to explain to a dummy whether this curve has efficiency, inefficiency, arbitrability ? How to translate these concepts into the language of mathematics ? How to calculate them?
(only when you answer think of bacteria, and that the curve itself can not kill, it is you wrongly acting to kill yourself).
I agree with you on most things, except for those two phrases highlighted above.
I'm not trying to model a TS (trading system). I'm talking about the curve you see on the screen (quote flow), which is a completely different thing. It's important to correctly predict the "behaviour" of that curve, if we can do it correctly, only then maybe we will get a good TS.
But the second phrase I have to take back to you. There's no getting ahead of yourself there. I apologise, but you have a gap in your knowledge. Stochastic differential equations can be written both in the Ito and Stratonovich form. And there is an unambiguous relationship between these forms. Each has its own advantages and disadvantages. And the Stochastic Stratonovich integrals allow handling them according to the usual rules of mathematical analysis (replacement of variables, integration by parts, etc.), which requires special rules when dealing with ITO. And there are dissertation councils that do not allow to defend dissertations mentioning ITO, require an entry in the form of Stratonovich (IHMO correctly do, we must know our scientists and be proud of them).
Once again I apologize, but I have to recommend you a book. Yarlykov M.S. Connection of two forms of writing of equations of optimum nonlinear filtering for posterior probability distribution. - Izv. Vuzov SSR. Radioelectronics, 1978, vol.21, no.5, pp.33-37.
Special thanks for correctness, I see that someone couldn't stand my abruptness :) However, I still have to keep my opinion that the essence of Startanovitch's integral is hidden from you. That is, you write nearly everything correctly and I agree with you in those points (about connection of two forms; about how Startanovitch integral is intuitively clear and simple (it is somehow trajectory-like, contrary to Ito)). But most importantly: the Stratonovich integral runs ahead - indeed it does. Let me now say a certain thing, and if it is not clear/strict enough for you, I will say it more strictly: Partial sums of Ito's integral take a function value at the left end of the partition interval (which we know); partial sums of Stratonovich's integral take a value in the middle. And since we no longer know this value in the middle of the segment, we get ahead of ourselves. This phrase is extremely meaningless, but perhaps you will remember in what context my words make sense and agree with the original premise: the Stratonovich integral gets ahead.
About dissertation boards, frankly, I will tell you nonsense: today in the world, for better or for worse, Stratonovich integral is mostly unused and has only historical value; there are some computational applications, but I for example have not seen in any article on random processes an integral in the form of Stratonovich. This is partly related to what I said above: in financial mathematics the Stratonovich integral is meaningless.
On the topic of conversation, about Pastukhov's thesis, the Gaussian/Martingian nature of the price process, etc. - Because I have been accused here (not without reason) of being more of a jerk to people than of making the point.
I read Pastukhov's thesis a year ago, if I'm not mistaken (it was posted somewhere on investor.ru forum by the way), and on the whole I got a positive impression. To be more exact, I agree with kniff's opinion that the practical applicability of this method in FOREX is small, but in due time this article was one of many factors which influenced the stock market image in my head.
The fact is that while the Gaussian model of the market (geometric Brownian motion) has a lot of inaccuracies, what Mandelbrot and co. propose seems wrong to me. Yes, it is possible to consider that the price is a fractal databank and even to count the fractal parameters (someone in our department has counted for the RTS Index and obtained that actually not half); it is possible to believe that the Levy process with marginal distributions of the Cauchy type and to onvert many things - but it is important to remember one thing: all these "tweaks" make the model terribly complicated, totally unmanageable by analytical calculations, and often wrong: as Aristotle said, it makes no sense to choose an accuracy of approach greater than the accuracy of the observed phenomenon. In short, all these additions are a woe from the mind, and do not give any meaningful advantages. Yes, there are models of Heston type, local volatility type, fractal type, Levy type - what not. And such models are used in decent banks, they are used. But 1) to understand the difference between them, you need to understand the theory very well and 2) to understand where they are applicable, you need to know the practice. And finally 3) in trading such models will not give an advantage because they are all based on the idea of arbitrage-free market. And this is the key point really: do not expect profit from these models, because they do not allow making such profit.
But to crown it all, in order not to play the role of "ideas killer" here I'll tell you a very simple idea, which I used to push in my article here at mql4.ru, and which becomes more and more important as I gain practical experience as a trader: the standard Gaussian model of geometric random walks is saved from all problems by rethinking only one parameter: time. This idea has already been mentioned here, but it's not a sin to repeat it again: look at the tickframe! And the effects like "heavy tails", like "volatility", and many other things will disappear.
Pastukhov - only one work - is attached. The discussion refers to his work, so it should be here too.
P.S. By the way, Brownian motion is hardly frontal, it's more fractal...
It is possible to have a meaningful conversation without using special terminology, without turning the discussion into shamanism with the invocation of spirits
It is very close to my understanding. Though the special terminology sometimes allows expressing oneself more clearly :) . But it would be interesting to know an opinion of esteemed kniff and kamal on the topic Stochastic Resonance.
I have a request, can you help me to explain to a moron whether this curve has efficiency, ineffectiveness, arbitrability ? How to translate these concepts into the language of mathematics? How to calculate them ?
(only when you answer think of bacteria, and that the curve itself can not kill, it is you wrongly acting to kill yourself).
The curve itself can't kill: but the results of your various actions over the curve (strategies) are a property of the curve, not strategies. Do you agree?
Conclusion of the post: again, a lot of noise, and complete nonsense from a logical point of view.
Moving on.
I have long suspected that price is not a martingale, although it does look like one. which is why Doob Th. or its generalisation does not seem applicable to the flow of quotes to me.
Now, I'm not against "on your fingers" explanations, but I am against speculation around maths that degenerates into complete nonsense when you don't even have a clear understanding of what is S.V. VARIABILITY DISTRIBUTION.., and what there is a DIVISION OF VARIABILITY S.V. - this misunderstanding was telling, you have everything "on your fingers". Please, but then DO NOT refer to Shiryaev, because it simply does not make sense in this case.
The point is clear to me, I have already said - I am a trader. I am only telling you that with such "definitions" references to Shiryaev and others have zero value.
You couldn't even distinguish density from the distribution f-fi recently! :-D
Because if the people who participate here would not be lazy to study the essence of the concepts, which are operated (for example, learn the theory of random processes), then the usefulness of this conversation in 15 pages will be ten times more ))
At least don't put yourself to shame)) Arguing with a person who has a 5.0 grade point average in Mech-mathematics and at the same time is doing financial maths :-D Lol really )))) Sorry about that.
//Sorry, folks, I'm writing all this for your own good - otherwise all this mostly pseudo-scientific research is useless.
P.S. By the way, Brownian motion is hardly frontal, it's fractal rather...
Nature in general has a fractal basis.
One should not expect any profit from these models because they do not allow to make such profit.
Finally, in order not to play the role of "ideas buster" here I have a very simple idea which I put forward even in my article here at mql4.From all misfortunes the standard Gaussian model of geometrical random walks can be saved by rethinking only one parameter: time. This idea has already been mentioned here, but it's not a sin to repeat it again: look at the tickframe! And effects like "heavy tails", like "volatile volatility" will disappear, and many things will disappear.
Can we have a little clarification here? I missed the point... What is worthwhile and what is not worthwhile and what to expect?
In other words, do you believe that creating a profitable trading system is possible in principle (without randomness, fitting, etc. )?
It has been suggested here that we should forget about profitability shown by the current Championship leaders. What do you think of the limits of what is possible?
Special thanks for the correctness, here I see someone has not withstood my bluntness :)
On behalf of someone I express gratitude for return to correctness. Correctness is such a tricky thing, it only makes sense on a reciprocal basis.
I read Pastukhov's thesis a year ago, if I'm not mistaken (it was posted somewhere on investor.ru forum by the way), and on the whole there was a positive impression. To be more exact, I agree with kniff's opinion that the practical applicability of this method in FOREX is small, but in due time this article was one of many factors which influenced the stock market image in my head.
The fact is that while the Gaussian model of the market (geometric Brownian motion) has a lot of inaccuracies, what Mandelbrot and co. propose seems wrong to me. Yes, it is possible to consider that the price is a fractal databank and even to count the fractal parameters (someone in our department has counted for the RTS Index and obtained that actually not half); it is possible to believe that the Levy process with marginal distributions of the Cauchy type and to onvert many things - but it is important to remember one thing: all these "tweaks" make the model terribly complicated, totally unmanageable by analytical calculations, and often wrong: as Aristotle said, it makes no sense to choose an accuracy of approach greater than the accuracy of the observed phenomenon. In short, all these additions are a woe from the mind, and do not give any significant advantages. Yes, there are models like Heston, like local volatility, like fractal, like Levy - just about anything. And such models are used in decent banks, they are used. But 1) to understand the difference between them, you need to understand the theory very well and 2) to understand where they are applicable, you need to know the practice. And finally 3) in trading such models will not give an advantage because they are all based on the idea of arbitrage-free market. And this is the key point in fact: you should not expect profits from these models, as they imply the impossibility of making such prof its.
What I do not understand is why people are so passionate about normal distribution and arbitrage-free market. If only there were some fundamental reasons. But there aren't. And yet...
And Pastukhov's dissertation is a thesis, not a TC. You don't get a PhD for the development of TC. He did what made purely scientific sense - he constructed a value that can act as a measure of arbitrability and proved the correctness and consistency of his construction. Can this result be used in the market ... ? It's a bit too studentishly straightforward. I think that Pastukhov did not state his practically significant ideas in his dissertation. If, of course, he had any. And his work is interesting precisely because it leads to such ideas.
Well and all the rest is, as you have fairly noticed, woe from mind.
I'm not referring to tickframes, of course. Prival has already expressed the same idea in this thread. And even earlier in this forum this topic has been discussed more than once. And in general, those who understand that the market has its time, have already implemented this idea a long time ago.
One should not expect any profit from these models because they do not allow to make such profit.
Finally, in order not to play the role of "ideas buster" here I have a very simple idea which I put forward even in my article here at mql4.From all misfortunes the standard Gaussian model of geometrical random walks can be saved by rethinking only one parameter: time. This idea has already been mentioned here, but it's not a sin to repeat it again: look at the tickframe! And effects like "heavy tails" will disappear, like "volatility", and many things will disappear.
Can we have a bit of clarification here? I missed the point... What is worth and what is not worth and what is to be expected?
In other words, do you believe that creating a profitable trading system is possible in principle (without randomness, fitting, etc. )?
It has been suggested here that we should forget about profitability shown by the current Championship leaders. What do you think of the limits of what is possible?
In general it is worth remembering that the inability to put their quotes extremely badly affects the yield, especially in such an extremely liquid (and therefore efficient in the usual sense of the word) market like forex. Come to us on the RTS, in fact, on USDRUB, say - that's where there is room for the speculator (on the rights of advertising ;))