Fourier connoisseurs... - page 3
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I don't believe it!
The picture is so good - no lag, and the ironing is good... Something must be wrong! Must be overdrawing?
What else could it be? - Otherwise, it's just a way to make money.
I also used Fourier lines - slow and fast, only zero bar is redrawn
Here are also the Fourier lines - slow and fast, only zero bar is re-drawn
I believe this one - it won't work as it is thoroughly delayed!
No. It's an elementary approximation of the period by OPT + its error by 2*PI (0th bar). Because if the values at 0 and 2*PI are not equal, the OPF will produce an error on them by equating the values to the 0th harmonic, i.e. the arithmetic mean of the analysed period. You can take a simple moving average and set the number of analyzed bars as an input value, and at the 0-th bar the value of this very moving average will be equal to the value of the FOS by 2*PI.
Oh, Yura, you are so well-read...
Tell me, you simple patsy, "Why is there no FZ in that picture?"
Hi all...
I have a question about the Fourier transform...
After Fourier transform and high pass filtering with reverse transform,
you want to continue calculating the resulting function out of the transform range (if you can give an example)...
The Fourier transform is nothing more than a non-linear regression (fitting) of a trigonometric series. You can of course find the amplitudes, phases and frequencies of the most important trigonometric terms and extrapolate them into the future. For example, in my indicator Extrapolator, the importance of each frequency is determined by the root-mean-square error of the regression, i.e. if a certain trigonometric term fits the data more exactly, it is considered most important. However, note that the extrapolation of trigonometric terms implies that the price movement is indeed described by simple trigonometric functions. In other words, if the price movement is the solution of a homogeneous differential equation, then trigonometric extrapolation will make sense. Otherwise, its success will be the same as extrapolating any other fitting function (a polynomial, for example). I am not convinced that price movements are the solution of a homogeneous differential equation, because it is unlikely that the waves that existed in prices 20 years ago still exist today. You can of course talk about economic cycles with a period of a few years. But these cycles do not influence the price movement within a day or even within a week, i.e. on the time interval interesting to a trader. Notwithstanding the above, I do not deny the existence of faster waves in prices. But they are initiated by certain events at certain moments (important news release for example) and fade out quickly, like earthquake waves. Trigonometric functions fitting and extrapolation makes sense only during these aftershocks and only with fading amplitude. i.e. A*exp(-|lambda|*t)*cos(w*t+a). IMHO
The Fourier transform is nothing more than a non-linear regression (fitting) of a trigonometric series. You can of course find the amplitudes, phases and frequencies of the most important trigonometric terms and extrapolate them into the future. For example, in my indicator Extrapolator, the importance of each frequency is determined by the root-mean-square error of the regression, i.e. if a certain trigonometric term fits the data more exactly, it is considered most important. However, note that the extrapolation of trigonometric terms implies that the price movement is indeed described by simple trigonometric functions. In other words, if the price movement is the solution of a homogeneous differential equation, then trigonometric extrapolation will make sense. Otherwise, its success will be the same as extrapolating any other fitting function (a polynomial, for example). I am not convinced that price movements are the solution of a homogeneous differential equation, because it is unlikely that the waves that existed in prices 20 years ago still exist today. You can of course talk about economic cycles with a period of a few years. But these cycles do not influence the price movement within a day or even within a week, i.e. on the time interval interesting to a trader. Notwithstanding the above, I do not deny the existence of faster waves in prices. But they are initiated by certain events at certain moments (important news release for example) and fade out quickly, like earthquake waves. Trigonometric functions fitting and extrapolation makes sense only during these aftershocks and only with fading amplitude. i.e. A*exp(-|lambda|*t)*cos(w*t+a). IMHO
Note that after the wave has faded, the price often fluctuates in a narrow range and then either continues along the trend or a new shock and a new fading wave occurs. It is possible to predict the fading waves (after one or two bursts) but it is impossible to predict the direction of the shock.
Why?
Shock tends to be counter-directed to outrage. Statistically reliable.
..... I would call it the incomplete wave effect.
I.e. if the wave does not fit into the measuring section, correct Fourier prediction is not possible.
Both straight and long-period harmonics are subject to this effect.
This is not what it is called.
Once again I give you the definition. Any function with a finite spectrum can be represented as a Fourier series (not necessarily periodic by the way http://www.nsu.ru/education/funcan/node35.html#SECTION00330000000000000000 )
Anyone working with PF should understand Kotelnikov's theorem very well.
Those examples you gave y=k*x+c or very large period, this is a non fulfillment of Kotelnikov's theorem, the spectrum is infinite.
I beg to differ, let's assume we are at the end of the movement and in 10 points the trend will change,
I think we should not jump on the bandwagon, especially because the reliability of these 10 points is questionable.
I have often noticed that the first 10 points are not true, but the nearest real quotes are equal to the forecasted ones.
Here the question flows smoothly into "Fourier or last point effect", and on this question it seems to me that the effect
is caused by another effect. Try to set a straight line of the form y = k*x + c, and then extrapolate with Fourier,
and instead of an upward straight line we get a downward curve. I would call it the incomplete wave effect.
I.e. if the wave does not fit in the measurement area then correct prediction by Fourier method is not possible.
Both straight and long-period harmonics are subject to this effect.
But your figure shows a straight line which is related to the formula y=ax+b
I'm showing a function that through a Fourier transform (green line)
has its function based on cosines, i.e. we can observe the continuation of the curve...
after transforming it, we get the pre-curve and after transforming it we get the smoothed
price
That's not what it's called.
Once again, I'll give you a definition. Any function with a finite spectrum can be represented as a Fourier series (not necessarily periodic by the way http://www.nsu.ru/education/funcan/node35.html#SECTION00330000000000000000 )
Anyone working with PF should understand Kotelnikov's theorem very well.
The examples you cited y=k*x+c or very large period, it is a failure of Kotelnikov's theorem, the spectrum is infinite.
this is the principle on which compression in communication systems is built... to transmit not a digitized signal but signal spectra obtained as a result of TF in a window time interval... in this case we have a time interval which is constantly shifting and miming a variable frequency conversion... when frequency deviates insignificantly these changes can be ignored... but at sharp jumps, it demands new recalculation... and it is still important for continuation of a curve of a signal that the wave would be at the beginning of the phase i.e. during growth i.e. at the maximum or minimum of the values... Optimum level in my opinion at level 0.15 from a wave turning point...
Why?
Shock tends to be counter-directed to outrage. It's statistically reliable.
But there are exceptions... when a disturbance passes through, the shock is counter-directional to the directional stress accumulation...
I observed such perturbations last September...