a trading strategy based on Elliott Wave Theory - page 288
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Here's a picture from another section of the price, but also containing 1024 counts.
I cut out the central part. As you can see from the picture, I had to indent by 200 counts on the left and almost 300 counts on the right. Nevertheless, the edge effects are clearly visible on the top half.
Of course, the effect of these effects is different for different wavelets. And the smaller the scale, the smaller this effect is also reduced. Nevertheless, it is sad.
........
The structure of this picture is generally speaking quite different from, for example, the picture in Andre69's post on 28.06.07 20:43 on page 141. 141. I would like to understand why.
On the other hand it has too regular structure. Why?
This analysis was performed for a series of 1024 samples.
Scale settings: Min=1, Step=1, Max=512. DMeyer's wavelet
......
Yuri, respected Neutron quite rightly pointed out the boundary conditions. But there are several other factors that affect the look of the CWT picture.
1. Which wavelet we took. Each of these gives slightly different results. Personally, I don't like the Meyer wavelet very much, as it is not very much localized in the time domain, while in the frequency domain, on the contrary, it is too good.
2. The boundary conditions can be handled differently, i.e. the original BP can be continued in both directions in different ways. The best result, in my opinion, gives a constant continuation (but not by zero!). Here at least we do not introduce any artifacts into the result, although there is still no way to get rid of distortion at the edges. Symmetric continuation (with or without saving the first derivative) also works fine.
And it is very important! It is highly desirable to remove the constant component of BP before transformation. We do not need it anyway and it affects the result badly.
3. The CWT matrix of coefficients can be displayed as a picture in a variety of ways - just scaled coefficients, their absolute value, square, etc. The appearance of the picture will change very significantly.
I use CWT coefficients logarithm for visualisation. But actually, it's a matter of taste.
Here is a picture to provide a basis for comparison.
Andrei, thanks for the clarification.
1. I already understood that different wavelets lead to different results. However, it was clear even before practical operations. Much more complicated, but also much more interesting, is the question of how to select the optimal wavelet. For pictures I used Meyer'a only because pictures with it (and some others) are more or less understandable to me. As for bad temporal localization, that's still a dark forest for me.
2. I've already read about the boundary effects. I don't like any of the suggested ways of fighting them. Whichever way you look at it, it's still arbitrary. And I lack knowledge of MatLaba to try some of my own ideas.
The permanent component has not removed, but now I'll try.
3. It's understandable. I wasn't talking about the view, I was talking about the structure. Perhaps I have expressed it wrongly.
Special thanks for the pictures. If there were also ordinate axis scales on them, you could learn a lot more from them.
One belongs to the EURUSD series, the other is a Wiener process, i.e. it is obtained by integrating random increments whose distribution is close to the distribution of the EURUSD series increments:
I am interested in your opinion, colleagues, about the potential of the method to identify hidden patterns and relationships in the BPs under study. When comparing these two pictures, somehow one cannot tell at once that "arbitrage transactions are possible in this process, while in that one the case of an efficient (martingale) market is realized...".
I'm interested in your opinion, colleagues, about the potential of the method to identify hidden patterns and relationships in the BPs under study. When comparing these two pictures, somehow one cannot tell at once that "arbitrage transactions are possible in this process and in that one the case of an efficient (martingale) market is implemented...".
That's what I'm saying!!! The only (as I see it) way to use wavelet transform is to calculate the dynamic characteristics of the system using skeletons and further forecasting using them (already described briefly). And you can't say anything from these muzzles, except that it's quite beautiful.
PS: and as I have already sadly noticed, it will take several years and a whole specialised research institute with "tadpoles" to bring the previously described model to mind.
Removed the constant component and got a much more meaningful result:
It would seem that the wavelet transform does not impose a condition to oscillate near zero on the signal. However, I scratched my head and realized that it is a manifestation of the same edge effects. I have to assume when calculating the expansion coefficients in MatLabe, the signal to the right and left is augmented with zeros. If it has a value, for example, 1.2245 on the edge, it is significant compared to 0. If we subtract the series average of 1.2240, the remaining 0.0005 is quite another matter!
This reduces the significance of the edge effects problem to a certain extent. However !
If we want to extrapolate a signal, we will knowingly distort the future extrapolation by supplementing it with anything on the right side in order to smooth out the marginal effect. I wonder what specialists will say about it ? :-)
2 Neutron
From my very humble point of view, the surface of coefficient values for EUR is significantly smoother, especially on larger scales than for EP. Which means that the real market, compared to the EP, has a certain inertia (or memory).
I am interested in your opinion, colleagues, about the potential of the method to identify hidden patterns and relationships in the studied BPs. When comparing these two pictures, somehow one cannot tell at once that "here it is possible to conduct arbitrage transactions on this process, and on that one the case of efficient (martingale) market is realized...".
Just two pictures are not enough to draw any conclusions. I haven't used wavelets in practice so far, so I won't speculate about their possibilities. At least one advantage has been demonstrated here: when used skillfully, it's a very good way of presenting information. For example in the first series of pictures I saw the ghost of adiabatic window (i.e. the range between noise and external limiting factors, where the situation can be determined by the market's own laws - i.e. the laws of "crowd"). Is it a ghost or a reality? IMHO, if the question is interesting, you should still try to find some more economical methods to investigate it, otherwise you will really need a research institute, and more than one.
Andrew, thanks for the clarification.
1. I have already understood that different wavelets lead to different results. However, it was clear even before practical operations. Much more complicated, but also much more interesting, is the question of how to select the optimal wavelet. For pictures I used Meyer'a only because pictures with it (and some others) are more or less understandable to me. As for bad temporal localization, that's still a dark forest for me.
2. I've already read about the boundary effects. I don't like any of the suggested ways of fighting them. Whichever way you look at it, it's still arbitrary. And I lack the knowledge of MatLaba to try some of my own ideas.
The permanent component has not removed, but now I'll try.
3. It's understandable. I wasn't talking about the view, I was talking about the structure. Perhaps I have expressed it wrongly.
Special thanks for the pictures. If there were also ordinate scales on them, you would learn much more.
1. Temporal localization is a very simple thing. The wider the wavelet function is, the harder it is to pinpoint its exact position on the time axis. Correspondingly - the same reasoning in the frequency domain. When we do a CWT, we sort of try on a wavelet function at different scales to the original BP. The wider it is, the fuzzier it is, the worse (less accurately) we can associate the max/min on the CWT matrix with the features of the original BP. In general, roughly speaking, localization in the time domain determines the resolution of the CWT image on the time axis (X), and localization in the frequency domain on the scale axis (Y).
With the optimal wavelet, it is still unclear. It depends on what features of the price series we want to catch. Most wavelets are non-symmetric. Can this help us? Don't know yet. I purposely cited a picture from db4. It is an asymmetric wavelet with fractal structure. So what?
2. Edge effects are unfortunately a fundamental thing. You can call it an edge effect or a phase delay - there is no getting away from it to the end anyway. The situation can only be improved a little by choosing the right way to continue the curve before the WT. It seems to me that the constant continuation (continue BP with the value of its last term) in this sense is the best choice - there is the least amount of arbitrariness.
3. I apologize for the lack of scales. It was done very quickly. On axis X - time - 2048 counts. Y-axis - scale - 1...1024.
PS. Finally I made a movie of CWT matrix images. For one currency pair for about a year (~ 1.5 min of video). It turned out funny. Now I am having fun watching this video. I can see for myself that there are structures that are stable for a long time.
There are no negatives in science, and as a result of a huge number of experiments I have come to the following conclusions (however, I wrote about this in my newsletters a year and a half ago).
1. At present there are no methods of constructing mechanical trading systems, i.e. those described by strict rules, which have an acceptable efficiency over a more or less long period of time, and it is impossible to develop them until a method of time travel is invented. Personally, I am not going back to it, nor am I searching for the Grail.
2. any more or less reasonably constructed tactic for any given period of time (for any given market character) shows high efficiency, and all tactics are approximately equally effective. That is, each market behavior needs its own tool, and the task comes down to determining - which is the period and which tool is most suitable now. On the other hand, there is a limit, it's about 80 - 120 points per month, and there is no tactic, which would allow to work with the higher efficiency at an acceptable level of risks. (You can, of course, open with the whole deposit and, if you are lucky, get into a move and pick 400 - 500 pips. That's super profitable. But the next use of such parameters will destroy everything that was obtained earlier.) On average, any tactic or a combination of tactics allows making 100 to 400 points of profit. So you should give up your dreams of making a million during the year from 10K.
3. Complicating almost any simple tactics, the use of sophisticated mathematical methods, does not lead to significant improvement. And often - on the contrary - worsens the efficiency. Why this happens - I do not understand, it is a mystery to me as a scientist. It's a mystery so far. The most unpleasant thing is that we often fall under hypnosis of complex terms and methods, our faith in science is very strong, and we start to unreasonably trust various "neural networks using multivariate analysis and wavelet transform with preliminary filtering based on the genetic algorithm". All this is bullshit, pardon the expression, and a show to lure more money from gullible traders.
Each new experiment frustrated me - no, you know, methods against Kostya Saprykin! But I had to work out all the versions, which I had faithfully "killed" for a year. Are you upset now? Well, don't be. After all, if you think about it more carefully, you realise that it is fine. The wonderful thing is that there is still space for creativity, for intuition, for inspiration and, finally, for luck. Otherwise we would all have been successfully replaced by machines and successfully traded. And the more powerful the piece of metal, the more successful it would be. Who do you think would have a more powerful computer, you or the City Bank? But everyone is on an equal footing, only your qualities and skills determine the results, regardless of your financial situation, where you live or any other conditions. And the fact that financial groups are hiring crowds of analysts and using supercomputers to build neural networks, does not give them any distinct advantage over you, even if you live in Shithole and have a 10th grade education. (True, they do have a significant advantage - they have access to information, which we do not. But this is a reality that cannot be changed, so let's not even talk about it). And you are quite capable of showing efficiency at any level, remember, Morpheus in The Matrix said - there is no speed limit, it (the limit) is in your brain.
A quote from "Forex for Beginners, Part 3" http://www.finlist.ru/beginner/beginner3.php