Steve,
Are your math skills strong enough to implement what's in Appendix 6
of Hurst's book ?
--- In amibroker@yahoogroups.com, "Steve Dugas" <[EMAIL PROTECTED]> wrote:
>
> OK, thanks Andy! I will do something else for a few days and wait
for Cybernetics to arrive ( I also got the MESA book, but had to
wait while they backordered both. ) I have had Hurst's book on my
shelf for a couple of months now, waiting patiently for a little
attention - I will look that over in the meantime. Thanks very much
and good luck with your move - maybe we can pick this up again a
little way down the road...
>
> Steve
>
> ----- Original Message -----
> From: Andy Davidson
> To: amibroker@yahoogroups.com
> Sent: Friday, October 06, 2006 4:27 AM
> Subject: Re: [amibroker] Ehlers Dominant Cycle
>
>
> Steve,
>
> I think Ehler believes that the Cyber Cycle method is better...I
remember that being my impression when I read the books. Certainly
both approaches use the Hilbert Transform but I think the difference
lies in the method of extracting the Quadrature and In-Phase
components. Difficult to say exactly without the book to hand to
double check what I'm saying!
>
> As for the differences between approaches, try playing around
with the alpha parameter (which determines the smoothing and
therefore low-end cut-off level for the measured cycles). You will
probably see some very large shifts in the period for even a 0.01
change in alpha. This tells me something.
>
> I do use Ehler's cycle measurements in some of my indicators as
an adaptive input to the period function. He talks about this
approach in the Cybernetic book. The reason I do this is because my
feeling is that something which at least attempts to measure a cycle
period is probably better than than some arbitrary optimised number.
I say 'probably' as I can't prove this to be the case - it's just a
matter of what makes more logical sense to me.
>
> To my mind though there's one pretty big hole in Ehler's
approach. Basically he states that although there are multiple
cycles at play in the market at any one time there is only one that
is "dominant" and thus tradeable. So you are only taking into
account and trying to measure one specific cycle at any one time.
One way he achieves this is through limiting the parameters to
specific wavelength ranges. Therefore you might be assuming that you
are (a) going to ignore cycles less than 6-bars in period as noise
and (b) going to ignore cycles of more than, say, 60 bars as too
long to trade (or too prone to margins of error) and then measuring
*the* cycle in that range. Well what if there is a 20-bar and a 45-
bar cycle at play at the same time and the noise sometimes exceeds 6-
bars? My experience is that Ehler's method is not good at coping
with this. I'm no engineer and so my theorising might be flawed, but
my experience of engineering tells me that you get to work with much
bigger margins of error than we can tolerate as traders. For
example, you might be able to use Hilbert Transforms in electronic
engineering to extract a person's voice from a 'noisy'
waveform...but I would say that there is still too much noise in the
output signal to transfer the analogy to the trading world. We can
make sense of the extracted voice but this is because our human
brains are good at that sort of thing, not because the modified
signal is particularly clear in a real sense. Our trading capital is
not so good at dealing with the remnant noise!!
>
> As far as measuring cycles goes, I have had much more success
and have much more confidence in the approach outlined by Hurst in
his "Profit Magic of Stock Transaction Timing". An old book which
uses centred MAs and assumes there are many cycles to be
measured...centred MAs are much more low-tech than Hilbert
Transforms I know, but there's beauty in the simplicity if you can
get away from the idea that your indicators must tell you
the "answer" right up to the right edge of the chart. Of course, the
fact that centred MAs *don't* go the right-edge makes backtesting
very difficult. Well, there's flaws with everything of course...
>
> Anyway, let me know how you get on and I'll help more if I can.
I'm in the process of moving house at the moment so can't do much
more until I get set-up again. Good luck.
>
> Andy
>
>
> Steve Dugas wrote:
> Hi Andy,
>
> In Rocket Science, Ehlers shows 3 methods to compute the cycle
period. Then he tests them against each other and determines that
the Homodyne Discriminator method had the the best characteristics
of the 3, so he uses that code as a basis for the indicators that
follow. The 3 yeilded fairly similar results, so when my graph
looked wrong, I figured the code from the library should give me a
rough idea of what mine should look like even though it is created
through a different technique. I still think there is something
wrong with mine, it should look much more like the other one. Maybe
I will be able to just substitute your code for mine and build from
there. Is the one in Cybernetics supposed to be better? I ordered
that book too, but it got delayed and I just found out that it
shipped today. Thanks for the code!
>
> Steve
> ----- Original Message -----
> From: Andy Davidson
> To: amibroker@yahoogroups.com
> Sent: Thursday, October 05, 2006 1:46 PM
> Subject: Re: [amibroker] Ehlers Dominant Cycle
>
>
> Steve,
> I think you're getting confused between Ehler's two books.
As far as I recall (books not to hand right now) he makes the
confusion easy as there is a "Dominant Cycle" indicator in
both 'Rocket Science' and 'Cybernetic', which are based on different
methods. Looks to me like the top one on your plot is the former and
the bottom is the latter. I personally have used the latter...the
code is copied below, which is probably nearly identical to the
posted AFL library version as I used that as a starting point when I
worked through it myself.
> Can't help you with the 'Rocket Science' version I'm afraid.
> Andy
>
>
> // Ehler's Dominant Cycle Period
> // Cybernetic Analysis for Stocks and Futures
> // Chapter 9, p. 107. Code on p. 111.
>
> //Global Parameters
> X = Param("MP[1] Close[2]",1,1,2,1);
> Z1 = IIf(X==1, (H+L)/2 , C);
> Z2 = Param("Alpha", .07, .01, 1, .01);
>
> function CyclePeriod(price, alpha)
> {
> instperiod = deltaphase = cycle = period = 0;
> Cycle = ( price[2] - 2*price[1] + price
[0] )/4; //initialise arrays
> smooth = ( price + 2*Ref(price,-1) + 2*Ref(price,-2) + Ref
(price,-3) )/6;
>
> for (i=6 ; i<BarCount ; i++)
> {
> Cycle[i] = (1-alpha/2)^2 * ( smooth[i] - 2*smooth[i-1] +
smooth[i-2] ) +
> 2*(1-alpha)*Cycle[i-1] - (1-alpha)^2*Cycle[i-
2];
>
> Q1[i] = (.0962*cycle[i] + .5769*cycle[i-2] -.5769*cycle[i-
4] - .0962*cycle[i-6])*(.5 + .08*InstPeriod[i-1]);
> I1[i] = cycle[i-3];
>
> if(Q1[i] != 0 AND Q1[i-1] != 0)
> DeltaPhase[i] = (I1[i]/Q1[i] - I1[i-1]/Q1[i-1])/(1 + I1[i]
*I1[i-1]/(Q1[i]*Q1[i-1]));
> //limit Delta Phase High/Low (0.09rads = 69bars, 1.1rads
= 6bars...per page 117)
> if(DeltaPhase[i] < 0.09)
> DeltaPhase[i] = 0.09;
> if(DeltaPhase[i] > 1.1)
> DeltaPhase[i] = 1.1;
>
> //---Begin median calculation (placed inline for speed).
> //Hardcoded as length=5 as higher values would be out of
range due to start-up period in main loop
> for(k=4; k>=0; k--)
> { temparray[k] = DeltaPhase[i-k]; } //create new array
with last 5 values of DeltaPhase
> temp = 0;
> for(k=4; k>0; k--) //this series of loops re-organises
temparray into ascending order
> { for (j=4; j>0; j--)
> { if (temparray[j-1] > temparray[j]) //swap values in
array if previous value is greater
> { temp = temparray[j-1];
> temparray[j-1] = temparray[j];
> temparray[j] = temp;
> }}}
> MedianDelta[i] = temparray[2]; //returns the middle
(third) element of temparray
> //---End median calculation
>
> DC[i] = Nz( 6.28318 / MedianDelta[i] + .5, 15 );
>
> InstPeriod[i] = .33*DC[i] + .67*InstPeriod[i-1];
> Period[i] = .15*InstPeriod[i] + .85*Period[i-1];
> }
> for (i=0; i<7; i++)
> { Period[i] = 1; }
> return Period;
> }
>
> Plot( CyclePeriod(Z1,Z2) , "CyberCycle", colorRed );
>
>
>
> Steve Dugas wrote:
> Hi All,
>
> I wonder if anyone has ever tried to code Ehlers Dominant
Cycle - the one based on the Homodyne Discriminator, pp. 68-69 in
Rocket Science. I have never used TradeStation and this is my first
shot at translating EasyLanguage. As far as I can see the code looks
OK to me but what do I know? Anyway, the graph it produces ( middle
one ) looks pretty bad. For comparison, I plotted the Dominant Cycle
code from the AFL library on the bottom ( but I believe this uses a
different method ). I would like to go on and code the rest of the
indicators in the book but many are built on this so I need to get
this right first. Any thoughts or working code would be greatly
appreciated. I have enclosed my code below.Thank you!
>
> Steve
>
> // Dominant Cycle
>
> SetBarsRequired( 10000, 10000 );
>
> // USER DEFINED PARAMS
>
> Price = ( High + Low ) / 2;
>
> // FORMULA
>
> // initialize variables
>
> Smooth = Detrender = I1 = Q1 = jI = jQ = I2 = Q2 = Re = Im
= Period = SmoothPeriod = 0;
>
> // calculate dominant cycle period
>
> for ( i = 6; i < BarCount; i++ )
>
> {
>
> // smooth price data with 4-bar WMA
>
> Smooth[i] = ( 4 * Price[i] + 3 * Price[i-1] + 2 * Price[i-
2] + Price[i-3] ) / 10;
>
> // compute amplitude correction
>
> AmpCorr[i] = 0.075 * Period[i-1] + 0.54;
>
> // compute detrended price data and Quadrature component
with 7-bar Hilbert Transform
>
> Detrender[i] = ( 0.0962 * Smooth[i] + 0.5769 * Smooth[i-
2] - 0.5769 * Smooth[i-4] - 0.0962 * Smooth[i-6] ) * AmpCorr[i];
>
> Q1[i] = ( 0.0962 * Detrender[i] + 0.5769 * Detrender[i-2] -
0.5769 * Detrender[i-4] - 0.0962 * Detrender[i-6] ) * AmpCorr[i];
>
> // compute InPhase component by referencing center bar of
Hilbert Transformer ( 3 bars ago )
>
> I1[i] = Detrender[i-3];
>
> // advance the phase of I1 and Q1 by 90 degrees with 7-bar
Hilbert Transform
>
> jI[i] = ( 0.0962 * I1[i] + 0.5769 * I1[i-2] - 0.5769 * I1
[i-4] - 0.0962 * I1[i-6] ) * AmpCorr[i];
>
> jQ[i] = ( 0.0962 * Q1[i] + 0.5769 * Q1[i-2] - 0.5769 * Q1
[i-4] - 0.0962 * Q1[i-6] ) * AmpCorr[i];
>
> // perform Phasor addition for 3-bar averaging
>
> I2[i] = I1[i] - jQ[i];
>
> Q2[i] = Q1[i] + jI[i];
>
> // smooth the I and Q components
>
> I2[i] = 0.2 * I2[i] + 0.8 * I2[i-1];
>
> Q2[i] = 0.2 * Q2[i] + 0.8 * Q2[i-1];
>
> // apply the Homodyne Discriminator
>
> Re[i] = I2[i] * I2[i-1] + Q2[i] * Q2[i-1];
>
> Im[i] = I2[i] * Q2[i-1] - Q2[i] * I2[i-1];
>
> // smooth the Re and Im components
>
> Re[i] = 0.2 * Re[i] + 0.8 * Re[i-1];
>
> Im[i] = 0.2 * Im[i] + 0.8 * Im[i-1];
>
> // compute Dominant Cycle period
>
> if ( Im[i] != 0 AND Re[i] != 0 )
>
> Period[i] = 360 / atan( Im[i] / Re[i] );
>
> // limit ROC of the cycle period to +/- 50% of previous
cycle period
>
> if ( Period[i] > 1.5 * Period[i-1] )
>
> Period[i] = 1.5 * Period[i-1];
>
> if ( Period[i] < 0.67 * Period[i-1] )
>
> Period[i] = 0.67 * Period[i-1];
>
> // limit the cycle period to be > 6 or < 50
>
> if ( Period[i] < 6 )
>
> Period[i] = 6;
>
> if ( Period[i] > 50 )
>
> Period[i] = 50;
>
> // smooth the cycle period
>
> Period[i] = 0.2 * Period[i] + 0.8 * Period[i-1];
>
> SmoothPeriod[i] = 0.33 * Period[i] + 0.67 * SmoothPeriod[i-
1];
>
> }
>
> Plot( SmoothPeriod, "Dominant Cycle", colorWhite,
styleLine|styleOwnScale );
>
> //Plot( Re, "Re", colorBlue, styleLine|styleOwnScale );
>
> //Plot( Im, "Im", colorSkyblue, styleLine|styleOwnScale );
>
> //Plot( Im/Re, "Im/Re", colorDarkGreen,
styleLine|styleOwnScale );
>
> //Plot( atan(Im/Re), "atan(Im/Re)", colorBrightGreen,
styleLine|styleOwnScale );
>
> //Plot( Period, "Period", colorYellow,
styleLine|styleOwnScale );
>
>
>
> -------------------------------------------------------------------
-----
>
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