Market phenomena - page 29
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I tried to use (18) from [url=https://www.mql5.com/ru/articles/250]-"Universal regression model for market price prediction"[/url] as a base function. It satisfactorily describes dependencies constructed artificially from various functions in all possible combinations, including sums, products, logarithms, power, exponential, etc.
I am familiar with formula (18). I think you overlook that I am not interested in a priori knowledge about basis functions. I don't care if the basis function is so powerful and universal that it can describe any process in the world. I would like to find an algorithm for automatic determination of basis functions from the time series itself. Note that these are not universal basis functions, but the functions specific to the given time series. Consider the analogy with speech. It also can be described by various universal basis functions, including (18). But all this would lead to inaccurate speech decoding. Using phonemes of English to decode Chinese speech would also lead to poor results. For each process, there must be different "phonemes".
There is a universal pill - genetic algorithms. At the very least, if nothing (or almost nothing) is known about the process, and one still needs to investigate and get a result, then GA is the first place to try.
This is likely to work.
I am familiar with formula (18). I think you miss the point that I am not interested in a priori knowledge about basis functions. I don't care if the basis function is so powerful and universal that it can describe any process in the world. I would like to find an algorithm for automatic determination of basis functions from the time series itself. Note that these are not universal basis functions, but the functions specific to the given time series. Consider the analogy with speech. It also can be described by various universal basis functions, including (18). But all this would lead to inaccurate speech decoding. Using English phonemes to decode Chinese speech would also lead to poor results. For each process, there must be a different "phoneme".
My interest in these structures is due to their more practical application than predicting market prices. I am now more interested in the development of rapid speech recognition systems. ... Price prediction comes down to predicting future phonemes (structures). But I am not interested in this. I am interested in recognizing past and present phonemes (structures). To achieve it one should have a dictionary of these phonemes and correlate the speech with these known phonemes (simplified of course)...
Vladimir, IMHO, this task is unfeasible at this stage. Continuing the beautiful parallel with speech recognition, take note that every tool on the market is its own language, and different dialects get mixed in depending on time of day, season, news, etc. Imagine that you have a set of phonemes for English, need to recognize the babble of drunken Irish longshoreman (or not Irish, not to offend the Irish ;-) ). Speech recognition technology is not yet developed to that extent. And the market is no easier.
In a simplified form the vocabulary of market phonemes can only be obtained from market participants - and those will be the figures, fibo levels, etc., about which it is written in many books. No one can know a clearer description, especially with specifying the type of basis functions.
I am familiar with formula (18). I think you overlook that I am not interested in a priori knowledge about basis functions. I don't care if the basis function is so powerful and universal that it can describe any process in the world. I would like to find an algorithm for automatic determination of basis functions from the time series itself. Note that these are not universal basis functions, but the functions specific to the given time series. Consider the analogy with speech. It also can be described by various universal basis functions, including (18). But all this would lead to inaccurate speech decoding. Using English phonemes to decode Chinese speech would also lead to poor results. For each process, there must be different "phonemes".
google "atomic decomposition by basis pursuit" ?
I agree. There are many different terms: phonemes, structures, patterns, wavelets, basis functions. I like the term basis functions better. I am interested in the following question: how can one automatically determine the basis functions when knowing a time series? Of course, one can visually examine this series and find triangles, flags and other nice-looking shapes. But no one has yet proved that these patterns are statistically important and not just a product of the imagination. Remember as in the anecdote:
The psychiatrist shows different pictures to the patient asking "What do you see in them?" And the patient answers "A man and a woman having sex." "You're some kind of lecher," says the doctor. And the patient says: "Well, you showed me those lewd pictures yourself."
Automatically identifying statistically important basis functions is a complicated process and I don't think anyone has figured out how to do it properly, even with neural networks. Of course, we can simplify the task and assume in advance that the time series is divided into Haar wavelets, or trigonometric functions as in Fourier series, or other basis functions that are often used in regression. And all these basis functions will successfully reproduce our series, whether it is a price series or a speech series. But imagine if we decompose speech into Haar wavelets - they have nothing to do with phonemes. It would be just as meaningless to decompose a price series into Haar wavelets or trigonometric functions. It is appropriate to mention compressive sensing, the essence of which is to describe the signal with the smallest set of basis functions. Although there are many algorithms of this method, they all assume that we know basis functions. If you have any ideas about the algorithm for finding basis functions from the price series, please share them.
google "atomic decomposition by basis pursuit" ?
Thanks. I searched - this method belongs to compressed sensing. It assumes that the basis functions are known. My task is not only to find the most relaxed representation of the signal as a linear combination of basis functions, but also the basis functions themselves specific to this signal.
Vladimir, IMHO, this is an impossible task at this stage. Continuing the beautiful parallel with speech recognition, note that every tool on the market is its own language, and there are different dialects mixed in depending on time of day, season, news, etc. Imagine that you have a set of phonemes for English, need to recognize the babble of drunken Irish longshoreman (or not Irish, not to offend the Irish ;-) ). Speech recognition technology is not yet developed to that extent. And the market is no easier.
Your reasoning is all very correct. Indeed, the market speaks different dialects, at different speeds, with different volumes, with different distortions, etc. depending on the time. So it seems to me that phonemes can only be found by non-linear transformations of speech. So is finding patterns in market prices. So far I don't think so far. At first I am interested in a question: taking a signal which is known in advance to consist of a linear combination of a finite number of unknown basis functions, is it possible to find these basis functions and coefficients of this linear decomposition?
This line of thinking is close to me (I mean, analogies with speech). And a lot has already been done in this direction, you can read articles to find inspiration. It is necessary to quantize a time series into a limited number of states, which are points in compact regions of space. And then, by analogy with speech recognition tasks (training neural networks for statistically stable sequences of phonemes and their combinations), we study recurrent sequences of states. For the first part of the problem a self-organising network is suitable, for the second - a multilayer network. I have done an example of it in this thread: https://forum.mql4.com/ru/40561/page5.
Thank you. I will think about SOM at my leisure.
I like it already... Sergei, what are the main principles of physics behind radio (telegraph, etc.)?
The question stumped me!)
Not the content, but the fact of its appearance.
All the basic principles can easily be taken from the web (some even from school curricula).
It's a little more complicated than that.
In the application to the market many things can be used, because the quotes are very similar to the signal.
Therefore, you can try to apply processing methods known to radio engineering, audio engineering, etc. to them.
Details - rather not for this thread. For reference:
http://nice.artip.ru/?id=doc&a=doc68