First Difference and Running Sum

• 08/04/2021 at 7:27 AM #174646
  JS

  In DSP (Digital Signal Processing) there are processes that can change signals in ways that resemble differentiation and integration.

  Only the terms differentiation and integration refers to actions on continuous signals.

  For actions on discreet signals these terms are given other names:

  First Derivative (continuous signals) = First Difference (discreet signals)

  Integration (continuous signals) = Running Sum (discreet signals)

  The relation (equation) for the First Difference is: y[n] = x[n] – x[n-1]

  The relation(equation) for the Running Sum is: y[n] = x[n] + y[n-1]

  This kind of equation is also called, Difference Equation or Recursion Equation.

  In code:

  //Calculation of the First Difference

  y=0

  For i = 1 to N-1

  y = Close[i] – Close[i-1]

  Next

  Return y

  //Calculation of the Running Sum

  y=Close

  For i = 1 to N-1

  y = Close[i] + y[i-1]

  Next

  Return y

   

  

  JS

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  08/04/2021 at 7:47 AM #174649
  robertogozzi

  The first FOR…NEXT is useless, since Y will be assigned only the last value of all iterations, the same as:

  y = Close[N-1] – Close[N-2]

  1	y = Close[N-1] – Close[N-2]

  Did you mean:

  For i = 1 to N-1 y = Close[i] – y[i+1] Next

  1 2 3

  For i = 1 to N-1    y = Close[i] – y[i+1] Next

  ?
  Moreover, is it correct N-1 as last iteration?

  

  robertogozzi

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  08/04/2021 at 11:34 AM #174661
  JS

  Thanks Roberto,

  Indeed sloppy coding, properly I must use arrays.

  The last iteration must be N instead of N-1

  (when i start at 0 then i=0 to N-1)

  

  JS

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  08/04/2021 at 1:56 PM #174663
  JS

  @Roberto, can you give me some help with the coding…?

  (The equitations are correct)

  

  JS

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  08/04/2021 at 2:46 PM #174667
  robertogozzi

  I’ll try asap.

   

  1 user thanked author for this post.

  JS

  

  robertogozzi

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  08/10/2021 at 11:28 AM #175005
  robertogozzi

  I think the First Difference should be (see attached pic):

  y[n] = x[n + 1] – x[n]

  If this is the case, then the code to get Ys is:

  //Calculation of the First Difference y = Close – Close[1] Return y

  1 2 3

  //Calculation of the First Difference y = Close – Close[1] Return y

  FOR…NEXT is useless, as you only return the value calculated by the LAST iteration.
  What exactly do you want to calculate?
  As you have put it, it’s just a momentum indicator over the last 2 candles.

  

  robertogozzi

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  08/10/2021 at 4:41 PM #175031
  JS

  Thanks Roberto for the effort, I will give it a thought …

  

  JS

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  06/17/2022 at 2:12 PM #195487
  JS

  First Difference

  DefParam DrawOnLastBarOnly = True UnSet($y) $y[0]=0 DrawHLine(0) Coloured(0,0,255) N=2000 For i = 1 to N-1 $y[lastset($y)+1] = close[i] - close[i-1] DrawPoint(BarIndex[i],$y[i],2) DrawSegment(BarIndex[i-1],$y[i-1],BarIndex[i],$y[i]) Next Return

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

  DefParam DrawOnLastBarOnly = True   UnSet($y) $y[0]=0   DrawHLine(0) Coloured(0,0,255)   N=2000   For i = 1 to N-1 $y[lastset($y)+1] = close[i] - close[i-1] DrawPoint(BarIndex[i],$y[i],2) DrawSegment(BarIndex[i-1],$y[i-1],BarIndex[i],$y[i]) Next   Return

  Running Sum

  DefParam DrawOnLastBarOnly = True UnSet($y) $y[0]=0 UnSet($x) $x[0]=0 N=2000 For i = 1 to N-1 $x[LastSet($x)+1] = Close[i] - Close[i-1] Next For i = 1 to N-1 $y[lastset($y)+1] = $y[i-1] + $x[i] DrawPoint(BarIndex[i],$y[i],2) DrawSegment(BarIndex[i-1],$y[i-1],BarIndex[i],$y[i]) Next Return

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

  DefParam DrawOnLastBarOnly = True   UnSet($y) $y[0]=0 UnSet($x) $x[0]=0   N=2000   For i = 1 to N-1 $x[LastSet($x)+1] = Close[i] - Close[i-1] Next   For i = 1 to N-1 $y[lastset($y)+1] = $y[i-1] + $x[i] DrawPoint(BarIndex[i],$y[i],2) DrawSegment(BarIndex[i-1],$y[i-1],BarIndex[i],$y[i]) Next   Return

  I’ve become a little wiser 😉 partly thanks to the forum…

  The theory of the “first difference” and the “running sum” is correct but the execution was not correct, I had to use arrays…

  The “first difference” is the discrete version of the first derivative or the slope of the input signal (close).

  The “running sum” is the discrete version of the integral or when you integrate the first derivative you get the original signal (close).

  

  JS

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