Fourier connoisseurs... - page 10
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Mathematics has created structures and operations on them that sometimes correspond very precisely to real causal and spatial relationships between real objects.
But the knockout to everyday consciousness was not done by mathematics, but by physics - together with quantum mechanics and STO/OTO.
There is a story about Heisenberg (he is one of the creators of quantum mechanics). When he was inventing his version of quantum mechanics (matrix mechanics), he urgently needed to invent non-commutative multiplication to explain the Heisenberg uncertainty principle in particular. And he invented it himself, only to find out later that he had invented matrix multiplication, which had been invented in mathematics long ago. And he apparently slept well in his lectures on linear algebra...
In nature, many things happen according to sines, cosines and exponents, or rather, approximately according to them. And mathematics is not the determining factor here: the phenomenon is just a reflection of the fact that in many physical phenomena there are dependencies such as, roughly speaking, "acceleration is approximately proportional to displacement" and "acceleration is approximately proportional to speed". Approximately - because in the vast majority of processes we can isolate the "first approximation", linear, and ignore non-linearities for the time being. Hence the sines.
In noise, Brownian motion and random walk, there are no sines and cosines. The latter are mathematical abstractions that make analysis easier. You might as well use any of the orthogonal functions listed below:
We can talk about sines and cosines if there are oscillatory processes. Describing the market as an oscillating system is as successful as applying the famous formula (18).
there is even a picture on the last page, but you keep denying it. it's an alternative to AlexeyFX filters, he also said that Fourier is not applicable..... although the essence is the same.
If you take two cacti and try to touch them with their needle surfaces, the needles themselves will not do it, and the useful component is in the analysis of these surfaces, Fourier is already applicable to them, we only need to remove the needles, not apply sines to them.
Fourier is applicable to any series. That means you can fit sines and cosines into any data, even random rambling. You have shown a picture of decaying fluctuations in prices in a particular segment of the AUDUSD. But that does not mean that these fluctuations are present everywhere. I can show you a hundred pictures of the same quotation, where there are no fluctuations. That way you can look at clouds, see an elephant (removing the roughness) and claim all clouds are elephants or a combination of elephants.
This whole argument is pointless. If fitting sinusoids into a price chart gives you profitable trading, then good luck to you.
I understand that you can plug a Fourier into anything, but the point is to stick it in the places it's designed for...
In noise, Brownian motion and random walks there are no sines and cosines. The latter are mathematical abstractions that facilitate analysis. You might as well use any of the orthogonal functions listed below:
We can talk about sines and cosines if there are oscillatory processes. Describing the market as an oscillatory system is as successful as using the famous formula (18).
In noise, Brownian motion and random walks there are no sines and cosines. The latter are mathematical abstractions which facilitate analysis.
This is not always the case, in some cases easy-to-analyse abstractions just arise when analysing problems with simple linear dependencies, i.e. they are a consequence, not a simplification. For example, if we pass white noise through a linear bandpass filter or LPF, the output, of course, will not be any sine (but will be in the ACF of the output process!). But if the input is a sum of white noise and some "jump stream", e.g. Poisson's, the output will give us sines/exponents - albeit random, noisy, but still they are. Because the system itself is linear, and thus in principle capable of generating these exponents, and the ease of analysis, again, results from the simplicity of the generating system itself, rather than being an abstract invention.
About other orthogonal sets - they of course can also be solutions of some equations, and thus represent an abstract description of real systems, but the point is that one can hardly think of anything simpler than mx''=-kx, and here the solution, sorry, is sine.
Of course the anticipation will not always be present on one pair, that's what the multi currency is for. At times when there are no such manifestations on a pair, they may occur on another pair, the master and the slave are not constant either, they change, we cannot predict who will be the master and who the slave, and it is not necessary, the master will show himself and will take the lead))))
but it will be too late to enter...
that's because the notion of "leading" I know it sounds crazy, but it looks like this, if you look at a fan of spectral lines, then some line of the fan will be taken from one pair, some from another one, etc., and so on in each count, not the absolute values of the spectral components, it is another concept in index construction, there is no averaging, something akin to a hedge type of analysis.But it's not the same.
It's not about linear price anticipation and stupid static arbitrage, private traders do not have the power in terms of capacity or ping capabilities.
it's the method itself, it doesn't matter if you take data series, like ticks, months or hours ..... the method doesn't change, or you don't even have enough time on the clock to realize the anticipation?
when assembling a single whole, there will be some factors in it that affect the "advance"...
And since they will be constantly changing (in this case, fans of spectral lines, etc.), all this stuff will have to be done by a sliding window...
with all that it implies... this is exactly what I was doing (and it's more complicated - I had to put all sorts of things on the net)... ran it on a long story... no fish there ))))
As for linearity - we'll get there later anyway... and we just want to know the short-long (flip) and that's it...
If you manage to get something, let me know later... but not on two or three years of history of course, but on the entire available history... the smaller the timeframe the better...
a picture even a man has posted (forte) and you can't have it all...
it won't be so pretty on the other sites...
forte928
Eugene - show me if it's not difficult...