Re: [amibroker] Re: Hurst Channels

[Rakesh Sahgal]

Thank you very much. This gives me the justification to renew my
subscription.  I only wish the two other things I had requested
you to consider had also found favour with you similarly.

Best Regards


ROn 10/11/06, Tomasz Janeczko <[EMAIL PROTECTED]> wrote:









Hello,
 
Because of so much talk about FFT I decided to release 4.86.0 
to "cool down" discussion 
even considering the fact that account manager part 
which is big thing is not yet complete and therefore has been 
hidden/disabled in this beta.
 
The example formula that uses AB 4.86 FFT 
includes de-trending which is of course straightforward (calculate 
linear regression
and subtract regression line from the data - look at 
"de-trending" comment inside formula in the read-me). 
Best 
regards,Tomasz Janeczkoamibroker.com


  ----- Original Message ----- 
  
From: 
  Rakesh 
  Sahgal 
  To: 
amibroker@yahoogroups.com 
  Sent: Wednesday, October 11, 2006 7:57 
  AM
  Subject: Re: [amibroker] Re: Hurst 
  Channels
  FredSo in essence are you saying that to get a 
  meaningful response from a FFT it is essential that the data series be 
  de-trended? Also since TJ had in response to your query indicated that the FFT 
  implementation he was going to include in AB was not going to be constrained 
  by ^2 limitation requiring data padding/windowing(?),  the problem of 
  ascertaining cycles should be resolved if the data is detrended and then run 
  through the FFT function in AB?Rakesh
  On 10/11/06, Fred 
  Tonetti <[EMAIL PROTECTED]> wrote:
  
    
    
    Bill,
     
    As a follow up to 
    my last …
     
    Lets use the wave 
    generator ( below in AFL )  to manufacture some synthetic data 
    …
     
    You can see that I 
    purposely picked wave lengths that are powers of two … The reason is that 
    FFT's will of course resolve these quite well as long as you have the sample 
    size set to be a power of 2 which is larger then the longest wavelength. 
     The amplitudes and phase offsets are pretty much random.  
    
     
    See the attachments 
    …
     
    #1 The individual 
    and composite ( DATA ) waves we generated
    #2 The histogram or 
    periodogram for the FFT … Notice how it picked all wave lengths out with 
    very little trouble.
    #3 The output 
    cycles which are a result of the individual cycle lengths, amplitudes and 
    phase offsets that the FFT detected.  Notice how this is almost a 
    perfect match of the input.  The individual waves can of course be 
    easily extrapolated and combined to present a picture of where the data 
    should go in the future.
     
    #4 Another 
    generated wave this time with trend added in … Notice the effect on the 
    white composite line.  
    #5 The resulting 
    histogram from the FFT WITHOUT detrending the data first.  Notice how 
    it has become "confused".
    #6 The resulting 
    output waves now don't look much like the inputs.
     
    #7 Same histogram 
    as in #5 but with detrending the data prior to invoking the FFT.  
    Notice how now we are back to where we should be.
    #8 The resulting 
    output waves as we would expect them to be …
     
    #9 Another 
    generated wave this time with a very high noise level ( the grey histogram 
    ).  You can see the effect it has had on the data we 
    manufactured.
    #10 The histogram 
    from FFT.  Notice how even though the noise levels have gone up here, 
    the FFT still had no real problems finding the cycles.
    #11 The resulting 
    output waves which now look very much like the input … WITHOUT the 
    noise.
     
    #12 Here I have 
    purposely changed the wave lengths from being powers of 2 to 7, 17, 27, 37 
    & 47…. Notice the effect it has had in the histogram … I had to increase 
    the data sample to 512 to get this resolution which is still somewhat 
    "muddy" … but all in all the FFT did a good job of finding the 
    cycles.
     
    The other thing to 
    keep in mind here with this particular wave generator is that I have not 
    introduced any variation in wave length, amplitude or phase offset over the 
    life of the data sample … which in my opinion … does happen … For the 
    purists that don't think this happens, then I would think that they would at 
    least admit that non cyclic events can make it appear to DSP algorithms as 
    if this were the case.
     
    rTrend   =  
    0
;
    
rNoise   
    =  0
 
    ;
    dFactor  =  
    1
;
     
    rCyc1Amp =  
3;
    rCyc2Amp =  
5;
    rCyc3Amp =  
7;
    rCyc4Amp =  
9;
    rCyc5Amp = 
11;
     
    rCyc1Len =  
4;
    rCyc2Len =  
8;
    rCyc3Len = 
16;
    rCyc4Len = 
32;
    rCyc5Len = 
64;
     
    rCyc1Phase = 
72;
    rCyc2Phase = 
144;
    rCyc3Phase = 
216;
    rCyc4Phase = 
288;
    rCyc5Phase = 
360;
     
    if
 (Source == "Generator"
 )
    {
        pi = 
    4
 * atan (
1 );

     
        StartX = 
    1000
;
     
        Trend = (BI + 
    1
) * rTrend * dFactor * (rCyc1Amp + 
    rCyc2Amp + rCyc3Amp + rCyc4Amp + rCyc5Amp) / 5
 ;
     
        Noise = (
Random
 () - 0.5
 ) * 2
 * rNoise * dFactor * (rCyc1Amp + 
    rCyc2Amp + rCyc3Amp + rCyc4Amp + rCyc5Amp) / 5
 ;
     
    
    
    
Cycle1 
    = 
cos
 
    ((BI / rCyc1Len + rCyc1Phase / 
360
 
    ) * 
2
 
    * pi) * (rCyc1Amp * dFactor) + Trend * 
0.2
 
    ;
        Cycle2 = 
    cos((BI / rCyc2Len + rCyc2Phase / 
    360
 ) * 2
 * pi) * (rCyc2Amp * dFactor) + Trend * 
    0.2
 ;
        Cycle3 = 
    cos((BI / rCyc3Len + rCyc3Phase / 
    360
 ) * 2
 * pi) * (rCyc3Amp * dFactor) + Trend * 
    0.2
 ;
        Cycle4 = 
    cos((BI / rCyc4Len + rCyc4Phase / 
    360
 ) * 2
 * pi) * (rCyc4Amp * dFactor) + Trend * 
    0.2
 ;
        Cycle5 = 
    cos((BI / rCyc5Len + rCyc5Phase / 
    360
 ) * 2
 * pi) * (rCyc5Amp * dFactor) + Trend * 
    0.2
 ;
     
        CycleX = Cycle1 + Cycle2 + Cycle3 + 
    Cycle4 + Cycle5 + Noise;
     
        
    if
 (PlotIt == "IP Cycles"
)
        {
            
    Plot (Cycle1, 
"C1"
, colorRed);
            
    Plot (Cycle2, 
"C2"
, colorOrange);
            
    Plot (Cycle3, 
"C3"
, colorYellow);
            
    Plot (Cycle4, 
"C4"
, colorBrightGreen);
            
    Plot (Cycle5, 
"C5"
, colorBlue);
            
    Plot (CycleX, 
"Cx"
, colorWhite, styleThick );
            
    Plot (Noise,  
"n"
,  colorLightGrey, styleThick | styleHistogram);
        }
     
    
    
    Data   = StartX + CycleX;
    }
     
     
     
    
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