Even / Odd decomposition

• 08/13/2021 at 1:42 PM #175235
  JS

  I continue to promote Digital Signal Processing (DSP) on this forum because I think it has a lot to offer us…

  DSP is all about signals, in our case the (input)signal is the share price or the price of the Dow Jones Index, etc.

  An important part of DSP is the decomposition of the input signal.

  Decomposition is to decompose the input signal into two or more components.

  The purpose of decomposition is to break up a complicated input signal into several simpler components.

  The opposite of decomposition is superposition, where you add the different components back together and thus get the original input signal back.

  A decomposition is valid when the components form the original signal after the superposition (summation).

   

  There are several strategies to dissect signals (the most important are the impulse decomposition and the Fourier decomposition) and Even-Odd decomposition is one of them.

  When we look in the x-y plane, a signal has an “Even symmetry” when it can be mirrored around the y-axis and an “odd symmetry” when it can be mirrored around the y-axis AND its values is opposite to the original signal.

  You can also view this as a rotation around point zero (decomposition is part of the concept of circular symmetry).

  Of course most signals neither have a even- or odd symmetry but the beauty of it is that it works for all signals.

   

  Equations (discreet):

   

  Xe[n] = (x[n] + x[N-n]) / 2 (even signal)

  Xo[n] = (x[n] – x[N-n]) / 2 (odd signal)

   

  Xsp[n]  = Xe[n] + Xo[n] (Superpositie)

   

  The most important point here is that you can dissect a signal into components and this decomposition is valid when the addition (superposition) of the components forms the original signal.

  Even / Odd decomposition

  N = 10000 Xe = (Close + Close[N]) / 2 Xo = (Close - Close[N]) / 2 Xsp = Xe + Xo Return Xe as "Even", Xo as "Odd", Xsp as "Superposition"

  1 2 3 4 5 6 7 8

  N = 10000   Xe = (Close + Close[N]) / 2 Xo = (Close - Close[N]) / 2   Xsp = Xe + Xo   Return Xe as "Even", Xo as "Odd", Xsp as "Superposition"

   

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  GraHal

  

  JS

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  08/14/2021 at 10:00 AM #175293
  JS

  How you can use this in practice depends on yourself and your imagination.

  Apply a few technical rules and you have a perfect system, without delay and directly linked to the input signal.

  

  JS

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  08/14/2021 at 10:40 AM #175301
  JS

  And you can apply it to all markets, no exceptions.

  

  JS

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  08/14/2021 at 2:20 PM #175339
  snucke

  I think you will have to explain a bit more since i believe most people here are not supergood at math and have not studied it as deep.

  Why i say that is because we use this platform PRT which is superlimited for a person that know how to code math and such.

  my understand of DSP is that you use it to dissect lets say a signal from which it is built from the begining to give you the end result that you get from the dissected value

  i dont really see how it can be used as such a great tool, please enlight me though since my math aswell is limited which is the reason i use PRT.

   

  maybe you can share an example of code that dissect a signal and you manipulate it in a way, where it takes a trade and so on, a more hands on example

  

  snucke

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  08/14/2021 at 3:23 PM #175340
  JS

  Sorry, I can’t explain it any easier but the difference with a regular indicator is that here you break down the signal itself into simpler parts (the even signal and the odd signal) and then you start using it in your system.

  You can then draw up trading rules based on these signals (even and odd signal).

  For example:

  • When the odd signal goes through zero (0) I go short…

  Or

  • When the current price rises above the even signal I go long…

  When you draw up such rules and use them at your own discretion, you have a (trading) system.

  The special thing about these signals is that they have no delay and that together they form the original signal again, so they have a “direct link” with the price action.

  If there are any more questions, I would like to answer them.

  

  JS

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  08/14/2021 at 10:58 PM #175364
  JS

  Example of a trading system based on Even / Odd decomposition

  This is one of the many possible trading systems based on the Even / Odd decomposition

  In this case I only used the Odd-signal to form a kind of trend following system, only long without money management (1 contract)

  When Xo (Odd-signal) crosses over 5 then go long

  When Xo crosses under -10 then Sell

  This very simple system makes money in all (time)periods N (see optimalisation report)

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  GraHal, PeterSt

  

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  08/14/2021 at 11:50 PM #175372
  JS

  All possible systems based on the even/odd decomposition are lineair, which means that you can use many contract as you can afford, because the characteristics of  the system don’t change.

  

  JS

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  08/16/2021 at 8:15 AM #175427
  snucke

  you said there ar several stra0241tegies to dissect a signal, how would i go about if i would want to use the “Fourier” to break down a signal, lets say close as u earlier showed

  or am i missunderstanding what u meant?

  

  snucke

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  08/16/2021 at 8:46 AM #175428
  JS

  Hi Snucke,

  You are right, with the Fourier Decomposition you can also dissect the input signal.

  To do this you must first code the Fourier Decomposition in PRT which is not so simple…

  

  JS

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  08/16/2021 at 9:57 AM #175444
  snucke

  ok, are you able to help in doing so?

  or maybe you can point me in a direction where i can learn and do it myself

  

  snucke

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  08/16/2021 at 10:14 AM #175446
  JS

  I am busy solving the problem and code it in PRT… (this will take some time)

  To do it yourself, read and study, read about Fourier and the equations (see internet) and try to master the language in PRT (including arrays)…

  This is not simple and can take a while…

   

  

  JS

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  08/16/2021 at 10:38 AM #175450
  snucke

  okay!

  this is very interesting, i’ve been looking at supertrend and there seems to be some interesting signals like odd crosses over/under superposition.

  as you said the possibilites of dissecting is almost endless, but at firsta glance i like what i see

   

  

  snucke

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  08/25/2021 at 10:31 AM #176179
  snucke

  i’ve been dabbling with this back and forth now and the signals which are prodused with even/odd decomposition is weirdly good.

  i’ve put som strategies live on the demo account and i will have to see if they perform as good as they did with WF testing.

   

  I have one question about this though, what do you mean by the characteristics do not change?

  All possible systems based on the even/odd decomposition are lineair, which means that you can use many contract as you can afford, because the characteristics of  the system don’t change.

   

  

  snucke

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  08/25/2021 at 12:05 PM #176192
  JS

  Good to hear that the system works (weirdly) good…

  The most important characteristic of a system is the combination of edge (profit /loss ratio) with %Profit trades.

  When this combination is good you have a winning system  (all the casino’s in the world are build on this combination).

  Your system is lineair because there are no “weird” calculations with squares, roots, etc…and because your system is lineair the characteristics don’t change when  you vary your input.

  So if you use 1 contract or a hundred contracts the characteristics (edge and %Profit trades) of the system don’t change.

  See the contracts as visitors in your casino, more visitors means more money, because the characteristics don’t change.

  

  JS

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  08/25/2021 at 1:39 PM #176207
  snucke

  I do not underatand how this is any different from any other sttategies that do not operate with momeymanagement?

  If you do not have momeymanagement in your system then it is also linear?

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  GraHal

  

  snucke

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