Fast Fourier Transform - Cycle Extraction - page 111
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https://substackcdn.com/image/fetch/w_1272,h_764,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd6a8ca0-2eeb-4930-a88f-83dead4d5740_3376x3357.jpeg
What this chart!?? This look like charts from hurst's book.
It's from https://www.sigma-l.net/
He mentioned the MA method in free article, It have lag, But this one looks not?
I think we need a good filter which output will as much as the price it self. But it should be smoothed. Like hull ma.
Maybe We should need ask some engineer? They should know more about the filter.
Must know the filter's math relation with output.
e.g What parameter will cause output act like a 25 and 50 ma line.
1.Some filter might not have the linar output.
2.Their input might not be integer but a fraction.
What we need.
Use many way to Extract cycle. And find a best one or the most simple and effective one.
I know hurst use periodogram.
And I see that corona period chart look like spectrum, we can modify it's output to make it become a kind of periodogram.
We use the accumulative of a same number on the X asix of corona period chart. (Firstly, round it to integer numbers, number > 0.5 should round higher and <0.4 should round to lower number)
In this way, we can transform any spect chart into periodogram.
If corona chart behaves like spectrum chart. Our periodogram will extract any noticeable cycles from a range of bars. (usually 180bars of daily chart & weekly chart)
(You must limit the data input to a small range bars, Too long it not recommanded. This limit should be set as a parameter and can be easily changed by user)
E.g X=cycle's length Y=cycle's amplitude
The Y asix need not to be number it self, It can be bars. But their length should be correct.
And the end product should have 3 or 4 biggest amplitude plot out by text.
Or just plot the amp on the peak of every waves.
The text chart is format of periodogram.
We can see the There is TWO noticeable cycle. The exactly cycle might be slight bigger or smaller than that number. (2 & 4 days is the cycle found out)
I'm back.
My math is very bad. Can any explain the Goertzel's calculation.
Can you show a example?
I heard it from somewhere that they said the k should be calculated.
Well I learnt the DFT's calculation. The K is a int number and it don't need to be calculated.
I'v been fooled by those guys. They just know to copy paste articles.
There is a article in medium.com and it's code is just to fool people around.
And on mathlab's support page their mentioned the " round(f/Fs*N) + 1;"
This is to convert the Frequency to nearest K value.
But well. It's just because they want to see which K-bar contains the frequency which they need.
In price analyze we don't need it because the frequencys are unknown.
So what you need is a loop of K. (In original DFT calculation if you carefully selected the parameters. To stop the unnecessary calculation. I think it not that slow.)
Here is why. Because in 60 bars of input (N=60) the valid output will only be 30bar of frequency series.
The N/2 is caused frequency series have a mirror structure so the other half is useless.
And the PWD spect chart is not the MAG spect chart!!!
What you need is a MAG type output not the power dense type thing.
Only when it convered to mag chart then you have the real amplitude of price.
Well all of those is empty telling
Without price model. The correct calculation.
All those thing is useless.
Unless your price model need the information of frequency domain.
Then those chart is useful to you.
Hi I think the Goertzel is no more than a selective dft.
And thos real value version is not tested. I can't say it's won't have bugs. Who knows!!!
In dft you calcute cos(xxx) - jsin(xxx)
But this real value version of Goertzel don't have substraction.
And have anyone tested the formula by using a simple wave?
I created a group on keybase
It's called "price_research"
Careful- I hope no ones brain pops...
Sorry about all the cut and paste—another vague idea, but we need chaos cycles right?
If anyone has interest "Order Out OF Chaos" by Ilya Prigogine will give you some amazing thoughts and then I could just say what about this page- lol, so many ideas.
I seriously suggest checking out this PDF- but I am not a math head, I hope this is all as helpful as it looks.
A Random-Walk or Color-Chaos
on the Stock Market?
-Time-Frequency Analysis of S&P Indexes
Ping Chen
Ilya Prigogine Center for Studies in Statistical Mechanics & Complex Systems
The University of Texas, Austin, Texas 78712
http://pchen.ccer.edu.cn/homepage/Major%20papers%20by%20Chenping/SNDE96p.PDF
Chaos theory - Wikipedia, the free encyclopedia
In common usage, "chaos" means "a state of disorder".[23] However, in chaos theory, the term is defined more precisely. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[24]
it must be sensitive to initial conditions;
it must be topologically mixing; and
its periodic orbits must be dense.
The requirement for sensitive dependence on initial conditions implies that there is a set of initial conditions of positive measure which do not converge to a cycle of any length.
...
It is interesting that the most practically significant condition, that of sensitivity to initial conditions, is actually redundant in the definition, being implied by two (or for intervals, one) purely topological conditions, which are therefore of greater interest to mathematicians.
Sensitivity to initial conditions is popularly known as the "butterfly effect", so called because of the title of a paper given by Edward Lorenz
...
A consequence of sensitivity to initial conditions is that if we start with only a finite amount of information about the system (as is usually the case in practice), then beyond a certain time the system will no longer be predictable. This is most familiar in the case of weather, which is generally predictable only about a week ahead.[29]
The Lyapunov exponent characteristics the extent of the sensitivity to initial conditions. Quantitatively, two trajectories in phase space with initial separation diverge
where λ is the Lyapunov exponent. The rate of separation can be different for different orientations of the initial separation vector. Thus, there is a whole spectrum of Lyapunov exponents — the number of them is equal to the number of dimensions of the phase space. It is common to just refer to the largest one, ie to the Maximal Lyapunov exponent (MLE), because it determines the overall predictability of the system. A positive MLE is usually taken as an indication that the system is chaotic.
There are also measure-theoretic mathematical conditions (discussed in ergodic theory) such as mixing or being a K-system which relate to sensitivity of initial conditions and chaos.[4]
...
Distinguishing random from chaotic data It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness.[62][63]
All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[62][64] Thus, given a time series to test for determinism, one can:
pick a test state;
search the time series for a similar or 'nearby' state;
compare their respective time evolutions.
Define the error as the difference between the time evolution of the 'test' state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos) .A stochastic system will have a randomly distributed error.[65]
Essentially all measures of determinism taken from time series rely upon finding the closest states to a given 'test' state (eg, correlation dimension, Lyapunov exponents, etc.). To define the state of a system one typically relies on phase space embedding methods .[66] Typically one chooses an embedding dimension, and investigates the propagation of the error between two nearby states. If the error looks random, one increases the dimension. If you can increase the dimension to obtain a deterministic looking error, then you are done. Though it may sound simple it is not really. One complication is that as the dimension increases the search for a nearby state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension) to find a suitably close candidate. If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory There is no problem choosing the dimension too large – the method will work.
When a non-linear deterministic system is attended by external fluctuations, its trajectories present serious and permanent distortions. Furthermore, the noise is amplified due to the inherent non-linearity and reveals totally new dynamical properties. The Statistical tests attempt to separate minimal no skeleton or inversely isolate the deterministic part risk failure. Things become worse when the deterministic component is a non-linear feedback system.[67] In presence of interactions between nonlinear deterministic components and noise, the resulting nonlinear series can display dynamics that tradition nonlinearity are sometimes not able to capture.[68]
What kind of thing are you? The paper is so complicated. How do you use it!??
What about this?
I don't know if I get this at all or how to do anything, but I think there are many valuable clues for people smarter than me- I was trying not to scream, just some stuff I can tell is important
http://pchen.ccer.edu.cn/homepage/Major%20papers%20by%20Chenping/SNDE96p.PDF
In spectral representation, a plane wave has an infinite time-span but a zero-width in
frequency domain. In a correlation representation, a pulse has a zero-width time-span but a full
window in frequency space. To overcome their shortcomings, the wavelet representation with a
finite span both in time and frequency (or scale) can be constructed for an evolutionary time series.
The simplest time-frequency distribution is the short-time Fourier transform (STFT) by imposing a
shifting finite time-window in the conventional Fourier spectrum.
The concepts of instantaneous auto-correlation and instantaneous frequency are important in
developing generalized spectral analysis. A symmetric window in a localized time interval is
introduced in the instantaneous autocorrelation function in the bilinear Wigner distribution (WD),
the corresponding time-dependent frequency or simply time-frequency can be defined by the
Fourier spectrum of its autocorrelations [Wigner1932]:
WD t w S t t S t t)exp( iwt)dt
2
) * (
2
( , ) = ò ( + - - (4.1)
Continuous time-frequency representation can be approximated by a discretized twodimensional
time-frequency lattice. An important development in time-frequency analysis is the
linear Gabor transform which maps the time series into the discretized two-dimensional timefrequency
space [Gabor 1946]. According to the uncertainty principle in quantum mechanics and
information theory, the minimum uncertainty only occurs for the Gaussian function.
4p
1 Dt Df ³ (4.2)
where Dt measures the time uncertainty, Df the frequency uncertainty (angular frequency:
w= 2p f ).
Gabor introduced the Gaussian window in non-orthogonal base function h(t).
( ) ( ) ,
,
, S t C h t m n
m n
m n =å (4.3)
]*exp( )
(2 )
( )
( ) * exp[ 2
2
, - Dw
- D
= - i nt
L
t m t
h t a m n (4.4)
where Dt is the sample time-interval, Dw the sample frequency-interval, L the normalized Gaussian
window-size, m and n the time and frequency coordinate in discretized time-frequency space [Qian
and Chen 1994a].
edit: those eqations didn't copy right also-
- pg 23 starts getting very interesting- oops, shall we delete all our posts?
People may ask what will happen once the market knows about the limited predictability of
color chaos in the stock market? At this stage, we can only speculate the outcome under complex
dynamics and market uncertainty. We believe that the profit opportunities associated with color
chaos are limited and temporary, but the nonlinear pattern of persistent cycles will remain in
existence and perhaps evolve over time.
Hybrid Superheterodyne-FFT
https://en.wikipedia.org/wiki/Spectrum_analyzer
https://en.wikipedia.org/wiki/Frequency_domain
https://en.wikipedia.org/wiki/Spectral_theory
The wave vector gives us insight into physically meaningful properties of the electromagnetic wave such as its spatial extent and coupling requirements for wave vector matching...
Rough surfaces can be thought of as the superposition of many gratings of different periodicities. Kretschmann proposed[7] that a statistical correlation function be defined for a rough surface... equations follow
...
then the Fourier transform of the correlation function is...
https://en.wikipedia.org/wiki/Surface_plasmons
http://theresonanceproject.org/pdf/quaternions_spinors_twistors_paper.pdf
His thesis is also quite watery. I glanced at it and saw the integral symbol.
Generally, that is used to calculate continuous signals. Computers don’t use that formula.
Then the spectrogram has been here for more than 10 years, and no one has done a good job of indicators. It’s a shame. I guess this format is not very easy to use.
How are you doing research now?
他论文也挺水的 我瞟了一眼看见了积分符号
一般那个是算连续信号用的. 计算机不用那种公式的.
然后谱图这边是10多年了也没人做好指标 真是丢大人了 估计是这个格式不太好用
你现在咋样 现在还搞研究不?
Write in English please.
Well, from the glance this is a kind of automatically cycle pick method.
And from the start of the paper they mentioned something related to the analog system
Maybe they altered it to adapt to digital signal. But well my math is bad.
Whatever such paper might be useful. Because I find they mentioned the detrend.
Those skill is required for frequency analyze and must be studied.
Well I glanced it again and their way seems need to analyze a 2d chart.
It's too complicated.
Hello everyone!
It is more convenient to investigate the fast Fourier transform.
For MT5
It says "2023.05.17 11:37:20.349 MQL5 'fFourier.ex5' version is too old, it should be recompiled"