Stochastic resonance - page 31

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It's not difficult.
 

This is understandable, Rosh, we know such a function. The problem is to calculate the function, not the covariance of the two data series. Well, to give a sort of array of values for different values of offset "tau", like the FREQUENCY function works. OK, let's think...

P.S. It's about time you showed up here. You've read Peters. Does he say something about stationarity of process?

P.P.S. Yes, I was too hasty with the covariance function: to make the process stationary at least in the broad sense, I'll have to derive a two-dimensional table for all pairs of samples R(ti, tj), i.e. a matrix...

 
If I'm not confused, the processes have a bias, and this very bias changes periodically (one trend changes with another). Therefore, I find it difficult to answer. He cites distribution functions that:
a) have finite MO and infinite variance
b) have infinite OD and infinite variance

And the normal distribution is a special case of a generalised fractal distribution. Here's a definition:
In general case X(t) is considered a stationary process if all its probability characteristics do not depend on time (more precisely, they do not change with any shift of arguments, on which they depend, along the t axis). As a consequence, the mathematical expectation of a random process, its variance and its correlation function do not depend on time.
The definition here is http://www.nntu.sci-nnov.ru/RUS/fakyl/VECH/metod/metod7/vvedenie.htm. Then the returns distribution is not stationary.
 

to Yurixx wrote (a):

"I have an interesting question along the way. Can someone enlighten why such a simple and convenient distribution function with good properties is not used in statistics? And if it is used, why isn't it written about? I've never seen anyone try to approximate an incremental distribution other than the lognormal."

It's most likely a special case of the Rayleigh-Rice distribution. I gave a link to it earlier. Here's the formula. And the figure.

Physically, the Rayleigh-Rice distribution describes a one-dimensional distribution of the envelope of the sum of a deterministic signal and normal noise. Very similar to the problem you are solving. I attach a matcad file with an example. There are detailed comments to the algorithm that allows you to check the analyzed sample for compliance with the theoretical law of distribution, according to the Neyman-Pearson criterion. I hope that something helped.

to Mathemat

I do not know as in Excel, the matcad can calculate the autocorrelation in 2 ways. The file, too, attached with an example. The only remark is that there are two approaches to calculating ACF, each has its own advantages and disadvantages. By the way IHMO very promising, at one time I had to design adaptive tracking filters for the air target. You could try to track the price as well :). The ACF is exactly what determines the coefficients in the equations.

to grasn

Sorry, I got it wrong in a hurry, I should have askedYurixx for a histogram. When I got the images I realized my mistake. I continue to work on the idea of Resonance, based on my definition: "Signal energy moves the market. Noise energy - prevents us from seeing that movement". (Thanks for the tip about IIH or IIH, but about 12 years ago I read lectures on them to cadets and I even remember giving them marks :)).

For all

I've found here on the forum a prototype of FFT_MA and rebuilt it according to the earlier pictures (FFT_MA_mod). The only thing, it overdraws, that makes analysis difficult. If anyone is able to fix this, please help. I am not able to do it. I am also attaching the file with explanations. By the way the law of amplitude distribution at filter output just obey Rayleigh-Rice law - in case of signal presence, if there is only noise, it degenerates into Rayleigh, alpha becomes=0.

If we want to assume we can separate signal and noise in that way then we will have to look for resonance, between which processes we should look for phase coincidence?

If somebody has an idea, then speak out.

And if it's not difficult to suggest what kind of distribution you're talking about. If possible with a simple example. Or at least a link.

Files:
akf.zip  59 kb
 
It's not working :( I can't attach it
Files:
fft_ma_mod.mq4  2 kb
 
Only attaches in edit mode :) Everyone's up in four hours :(
Files:
zr_1.zip  1375 kb
 
Grasn , Sergey, about potential pits I deeply apologize, and confess my own stupidity :) It's true, the level of support and resistance can be compared to a potential barrier, from which the price bounces. But I'm afraid I have to argue about the invention of the phenomenon. Moreover, IMHO it is the only reality on the market, contrary to those fantasies about waves, fibos, pitchforks and alligators. At least, it is the only thing that can be easily explained without involving additional non-obvious postulates. Congratulations on discovering an interesting criterion X ! That's all. Go on reading, I haven't been here for two years and it's been 11 pages since then :)
 
Prival писал (а): Also, if it's not too much trouble, tell me what the distribution you' re talking about is. If possible, with a simple example. Or at least a link.
Returns[i] = Close[i] - Close[i+1], i.e. these are just historical increments of closing prices. If we calculate them on the entire history on a certain TF, load them into Excel and build a frequency histogram (using Excel function WHAT()), we will obtain a curve that somewhat resembles the Gaussian curve, but only externally. In reality, this distribution is not normal - say, because of thick tails and unrealistically high peak at the point near zero.

Underestimation of tails leads the speculator to a strong underestimation of risks: if he thinks the probability of a "four sigma or greater" event is vanishingly small (under the normal hypothesis it is about 0.0063%), then the real market is about 0.7%, i.e. 100 times greater. For larger events the difference is even greater. If I have to, I will post a picture.

Thanks for the archive - I will look at it in the morning. However I will try to do it both in Excel and MQL4.
 
Prival, the Fourier cut-off high-frequency inverse Fourier you write about here is a great idea. Really makes for a perfectly smooth and completely lag-free mouwing. There is only one small drop of tar in this huge barrel of honey. Such an operator is not causal. And the wider your window, the more future samples it depends on. And the narrower the window, the worse the smoothing. Therefore, it will look great on the history, but in reality such an indicator will always redraw near the right border of the screen. Therefore, the high-frequency noise will be highlighted accordingly. It will be marked only on the history. And you will be blind and deaf at the right border of the screen. If that is not what you mean, please excuse me. I haven't finished all the posts yet. I'm only writing on your first two.

P.S. I've read all the posts to the end. Yes, that's the very thing you ducked into in your experience. Alas, no one will be able to help you with redrawing, for this point is fundamental. Such a filtering operator is not causal. In general, my IMHO is that the main contradiction in Forex, as well as in the entire moon world, is a contradiction in the concept of time. In Forex it is manifested in the fact that a good statistical estimation requires a large amount of time. I.e. samples. But while these values are being collected market parameters have time to change. If only somebody would help to solve this contradiction... (das ist little schtick of course :)
 
eugenk:
Prival, the Fourier cut-off high-frequency-inverse Fourier you write about here is a great idea. Indeed you get a completely smooth and completely lag-free mouwing.


According to the topic of the thread, I'm just suggesting how to separate the signal from the noise. The goal is to find resonance, not to build a muwig. For forecasting, and even muwigging, there is a much better mate. All of course IHMO.

As an option, in indicator will be two separate buffers that do not drift, and remember on Close[0]=Open[0], energies of signal and noise.

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