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Fourier series curve fitted to ES data
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Fourier series curve fitted to ES data

  #11 (permalink)
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davidcohenphd View Post
FA is useful in many areas, not just those that are related to cycles. But if you are looking for information about it among traders, then you simply don't know enough about the thing to be able to use it profitably. Spend some time learning more about it and how it can be applied. Then you will not need to ask pseudoexperts who never used it but base ther knowledge of it on Wikipedia articles they just read 10 minutes ago, LOL.



Basically I agree with everything he said.

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  #12 (permalink)
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davidcohenphd View Post
FA is useful in many areas, not just those that are related to cycles. But if you are looking for information about it among traders, then you simply don't know enough about the thing to be able to use it profitably. Spend some time learning more about it and how it can be applied. Then you will not need to ask pseudoexperts who never used it but base ther knowledge of it on Wikipedia articles they just read 10 minutes ago, LOL.

This is a very general statement with no specific information. You could for example replace the word "FA" with the word "lap dance", and the whole thing still would make sense!

Even if we are not experts of Fourier and Hilbert transforms or Goertzel algorithms, there is nothing bad to try to improve our knowledge. I think the question is justified, whether methods developped be physicists and engineers can be easily applied to trading.

It is true that I understand little about the subject, but further learning would certainly overcharge my limited mathematical capabilities, so I am falling back to heuristics, thing most traders do, when faced with a complex situation. And my heuristics tells me that sentiment and correlations might be more important than assumed cycles.

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  #13 (permalink)
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Fat Tails View Post
Not sure that a naked DFT will reveil much of a cycle. You could have a look at the Corona Indicators developped by John F. Ehlers. He detrends the time series before analyzing for cycles. I have put the indicators on a 3 min chart for ES for last Friday.

If you look at the cyclical component, there was a dominant cycle with a period of around 28 in the beginning of the session. The lows were tradeable because of the trend that developped later in the day, the highs predicted were not impressive. The problem here is that the cycle amplitude was too small compared to the noise. The signal-to-noise stayed below 4DB during the first two hours, with a large corona, which means that the cyclical signal was week and the noise dominant.

Also to note that the cyclical component, which can barely be identified within price action, changed its period during noon - increased period - and then again prior to the close of the session. if I take into account the daily volatility smile, it is possible that the cycle analysis works better on range charts than time based charts. This is what the shorter cycle in the beginning and the end and the longer cycle in the middle suggest.

But this is just one day of observation. I do not think that cycle analysis is an easy route to success. But it is the sexiest indicator I have ever seen.

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Alas I think you have convinced me to avoid the stock market, haha. I suppose my dreams of sweeping in on the bottom of supposed cycles and coming out at the crest have been crushed (with good reason.)

Thank you for the technical response - it is nice to hear from an expert and I assure you that experts in this area are far and few in between (at least my limited experience has taught me so.)

Just to clarify for everybody else:
Fourier Series and Fourier Transforms are two totally different things.

A Fourier series is just a function with a collection of these terms:
a1*cos(n*x) + b1*sin(n*x)

where if you keep going, my 8 part Fourier series would look something like this:
a1*cos(n*x) + b1*sin(n*x) + .... a8*cos(n*x) + b8*sin(n*x)

Now Fourier Transforms are ugly sons of bitches. I still don't completely understand them and I honestly don't think most people do. I know in about 3 lines of code, we used them to reconstruct raw MRI data from an MRI machine to the nice pictures you're used to seeing from MRI's but other than that it's kind of a mystery to me. I can tell you that if you have a sound signal, a Fourier Transform will show you the frequencies that are in the signal and their prominence.

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  #14 (permalink)
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tantrev View Post
Thank you for the technical response - it is nice to hear from an expert and I assure you that experts in this area are far and few in between (at least my limited experience has taught me so.)

I am certainly not an expert. I am just suspicious. It is easy to give a meaning to any random set of data. If you flip a coin a thousand times, you will find cycles and trends, and it is all smoke and mirrors. Of course, there are real cycles that exist. The daily cycle that repeats itself, which affects volatility in the first place. There is a seasonal cycle, which is obvious for agriculturals and some energy products. Also there is a weekly cycle, which affects the behaviour of trades. The Monday night session typically has a higher volatility than the Tuesday night session, as the news of the weekend need to be digested. If there are cyclical patterns, you also may find them in high frequency analysis of trades.

But then I think that markets are less cyclical and more driven by non-linear dynamics. So the model that I have in mind is not the model of a pendulum, but a multi-agent model, where the agent's behaviour relies on feedback. Such a model can produce temporary oscillations (such as the hog or cattle cycle), but they are instable and dissolve. Timeseries of market data are non-stationary, probability distribution shift from Gaussian to non-Gaussian, when feedback reinforces.

I do not remember, where I have seen this model of a planetary motion with only three or four planets that looked cyclical but then suddenly one of the planets disappeared in outer space... the cyclical behaviour was just an illusion. I also like the Sugarscape simulation, it also shows pseudo-cyclical behaviour, before it drifts away.

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