Fourier-based hypothesis - page 4
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By shifting the phase.
What I was doing was very, very different.
>> you got to go? >> well, bye, then.
hopefully there'll be more time.
>> hopefully there will be more time.
>> Ok. Communication other than the forum? I have Skype, if you can see it on the net. I also have MSN but I don't use it much.
Ok. Is there any communication other than the forum? I have Skype, if you can see it on the net. I also have MSN but I don't use it much.
>> get in touch.
Get in touch...
Write something I'll see.
2 forte928: I've looked through the FFT forum carefully, I haven't seen the idea of testing on previous data (where the same model/market parameters seem to still be valid) yet.
I think a limited prediction process is possible based on the assumption that the market has been subject to a particular model for some time. And if we are lucky and all three segments are in this "stability range", then all is well.
2 neoclassic: Thanks for the pictures and for the code of AdaptiveExtrapolator indicator, I am trying to modify your code trying to check the hypothesis. Actually this very post and attempts to predict using FFT indicator has generated the hypothesis.
By the way, you can combine the idea about choosing the segment length for testing and the hypothesis. For example, if you make the test segment equal to 25% of the FFT segment. Then if on the FFT cutoff the result is the best, and on the previous 20% it gives a strong discrepancy, then there is a high probability that the model is wrong, as it poorly describes the near past (when the same market model is valid), and therefore is poorly applicable.
2 VladislavVG: Thanks for the questions and clarifications about PF. Attempted answers:
1. FFT can extrapolate the future for a period from zero (if the market model has changed dramatically or harmonics have been incorrectly allocated) to infinity (if the market is still cyclic to infinity and we can represent using at most N/2 harmonics, where N is the length of the test segment).
2. Plus or minus the sum of all amplitudes, as this series converges. If we do a slope before the FFT and back at the end, it is plus or minus infinity within the channel.
3. About periodic function - see Wikipedia(https://ru.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B8%D0%BE%D0%B4%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F). Thanks for the reminder.
Regarding the constancy of the money supply - you're right, of course, if you play "as a grown-up", then you need to make a correction for the volume of money supply (and for the time during the day - at different times of day trading is done differently). Although, I don't think there is a linear dependence of the price change intensity diagram (I don't know how to calculate it) on the "money supply release", most likely it is less significant compared to other factors.
Clearly, it is impossible to solve the market in analytical form (except to repeat the success of LTCM http://murphy.wallst.ru/ltcm.htm) . But it is probably possible to approximate it. The essence of the assumption, on which the entire thechanalysis is based, is the following: if an analytical model of market behavior can be built for a certain period of time, then this model can be successfully applied for some time. And may be without success (((
Reshetov: Quote: "If you obtain a Fourier series expansion in BP of 1000 bars, then for the next 1000 bars you get an exact copy of the previous 1000-bar period" - it seems to me that this is not quite true, because the harmonics are not multiples of each other and are still shifted relative to each other. But through a period T, which is equal to the product of all the periods of the harmonics - we will definitely get a repeat.
Quote: "All you can do to extrapolate is for example to decompose the previous two periods by N bars into a spectral analysis. Then to extrapolate the next (not yet existing) N bars, take the arithmetic mean of the harmonic amplitudes and shift the phases of each harmonic by exactly as many radians as the difference in the corresponding harmonics in the two previous periods under study." - This rule is valid assuming that there is such a model that the periods of the basic harmonics vary continuously, and their variation can be extrapolated by linear approximation (sorry for the complicated construction). This may or may not be the case. We need to conduct an experiment. Also, the amplitudes of the harmonics must also change over time, so it is not necessarily the case that the top three harmonics of one period, will not be replaced by others with those that have increased amplitudes. Thanks for the detailed breakdown of inertia!
YUBA The rocket example is very revealing. So if you imagine a model of a changing market as two missiles flying at the same speed: a ballistic missile (like a bull) and an anti-aircraft missile (like a bear). If they fly along the same trajectory, the distance is maintained (like a flat). If the distance increases, the price goes up, if it decreases, it goes down. Both missiles know that there is a preemptive pattern, according to which the second missile can get close to the first. But at some point, the first missile makes a movement that changes its initial trajectory, and the second missile has to adjust its flight path and pre-emptive tactics (something like changing market parameters) as a delay. I'll have to think at my leisure, maybe I can do something with this market model )))
If you are able to post something from your archive about this algorithm, it will be very interesting to read.
By the way, another idea - can't you do an FFT on a very large segment, isolate the main harmonic of the market. Then take a smaller segment and normalise it relative to this large harmonic, highlight the next harmonic, etc. Based on the idea that large market harmonics are more inertial than small ones, do you think there will be a better result than just PF on a fixed segment?
Clearly, it would only be possible to predict the maximum length of the smallest segment with such a procedure.
Hypothesis #3: While experimenting with different FFT indicator parameters, it occurred to me that if you put them all on the chart at once, the price is most likely to follow the path where the curves will clump the tightest))) It turned out to be something of a probability distribution field, where FFT is used for the prediction function.
Not quite sure what the best FFT result means? the minimum RMS between the approximation and the price?
equantis wrote >>
By the way, another idea - can't we do an FFT on a very large segment, isolate the main harmonic of the market. Then take a smaller segment and normalise relative to that large harmonic, isolate the next harmonic, etc. Based on the idea that large market harmonics are more inertial than small ones, do you think there will be a better result than just PF on a fixed segment?
Clearly, it will only be possible to predict the maximum length of the smallest segment using such a procedure.
I believe this is the only way to predict with FFT. In essence we get an all scales forecast for the period of maximum harmonic with gradually fading details of the forecast
Hypothesis #3: While experimenting with different FFT indicator parameters, it occurred to me that if you put them all on the chart at once, the price is most likely to follow the path where the curves will clump the tightest))) I got something of a probability distribution field where FFT is used for the prediction function.
there is already an implementation of this idea, "bpf by montecarlo"