Predicting the future with Fourier transforms - page 13
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Eh... I have my doubts... about the higher harmonics.
Fourier decomposition is only possible for periodic functions.
That means if we take a sample of minutes in a week, decompose it into a Fourier series and then add up the harmonics, the resulting function will be periodic.
In other words, our graph is simply duplicated along the time axis into the future (and into the past). No prediction can be made from it.
Here is an illustration
"A function expressed by a Fourier series is a periodic function, and hence a series made for a function given on the interval [-π, π] converges outside this interval to a periodic continuation of this function (Fig. 2)."
Class references
Fourier series
https://ru.wikipedia.org/wiki/%D0%A0%D1%8F%D0%B4_%D0%A4%D1%83%D1%80%D1%8C%D0%B5
Java applets for Fourier and digital filter demos
http://www.falstad.com/fourier/
http://www.falstad.com/dfilter/
Fourier series expansion is only possible for periodic functions.
Not quite the right conclusions. Any function with a limited spectrum can be decomposed into Fourier series. The essence of the prediction is not to simply do the series expansion, then sum it all up and go back. There are a lot of Walsh decompositions, Wavelet, etc. You need to teach the program to choose those components of the spectrum that determine the motion (the so-called useful component) all the rest is noise, remove (filter it out), then you may get something.
Well, tell me, where did people get the idea that price would move on one of the harmonics?
Is there a theory that proves such a movement? There is no such theory.
Perhaps practical experience proves such a movement ? There is no such empirical evidence ?
People get carried away with the means and forget the goal.
And how much energy and time is spent !
For example, the franc was attacking the level 1.1800 for several days. Tonight the level was broken through to 1.1835.
Let them make a prediction about the franc's further movement.
On the basis of the V.T.E. empirical theory I can assert that the franc will go above 1.1835. And what about the Fourier prediction lovers?
Well, tell me, where did people get the idea that price would move on one of the harmonics?
Is there a theory that proves such a movement? There is no such theory.
Perhaps practical experience proves such a movement ? There is no such empirical evidence ?
People get carried away with the means and forget the goal.
And how much energy and time is spent !
Who knows ? Hypotheses are taken out of thin air depending on the level of imagination, but then they are tested, there would be data - the topic would be exhausted.
Well, tell me, where did people get the idea that price would move on one of the harmonics?
Is there a theory that proves such a movement? There is no such theory.
Perhaps practical experience proves such a movement ? There is no such empirical evidence ?
People get carried away with the means and forget the goal.
And how much energy and time is spent !
1. These are the right questions. You may decompose any movement into several components, not just one.
2. Just the theory, if you would penetrate deeply into it, says, that any function with a limited spectrum (whether it is movement of currency, satellite, sound etc.) can be presented as a Fourier series, and there is a strict mathematical proof.
3. Practical experience says "you just have to know how to cook" and not to kick Fourier, it has absolutely nothing to do with it.
2. Just theory, if you were to penetrate deeply into it, says that any function with a finite spectrum (be it the movement of currency, satellite, sound, etc.) can be represented as a Fourier series, and there is a rigorous mathematical proof of this.
Well, there is the same proof for sigmoid series. Except that this same proof has no effect on the consistency of the extrapolation results with the real data.
Well, tell me, where did people get the idea that price would move on one of the harmonics?
Is there a theory that proves such a movement? There is no such theory.
Perhaps practical experience proves such a movement ? There is no such empirical evidence ?
Do you have a degree in engineering or the humanities, may I ask?
Well, there is the same proof for the sigmoid series. Except that this very proof has no effect on the consistency of the extrapolation results with the real data.
Right, that's why I'm talking about cooking skills. Extrapolation is based on a hypothesis about the likely movement(s). And you can draw a curve in the future in all sorts of ways. You can do it with Fourier, you can do it with polynomials, and you can do it with your hands.
Therefore, a person (algorithm), when selecting these or those spectral components from the spectrum and predicting them in the future, gives them (these components) preference, as it believes it will determine the further movement. But is he right? On the basis of what research he has chosen the 1, 3 and 5 garnictics, each of which has its own frequency, amplitude and phase. Or maybe he should have chosen 2, 4 and 6 and phase tweaked ? or taken 256 spectrum components etc.
The primary hypothesis (idea) that gives a statistic about the probable motion. If you can use Fourier to calculate the probability of further movement, you'll be golden, and if not, you'll be out of luck.
Z.U. Fourier works everywhere works, cops radar you light and fine, receivers all listen, cell phone use, etc.
>> what kind of education are you, may I ask, technical or liberal arts?
Should I also tell you who I sleep with and what kind of beer I prefer?
What's your problem?
Sart_repair писал(а) >>
People got carried away with the medium and forgot about the goal.
What a waste of energy and time !
Can you also tell me who I sleep with and what kind of beer I prefer ?
drink more beer, rest, sleep