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I've been meaning to reply to this.
Peter (phoon@xxxxxxxxxxxxx) wrote:
>Does anyone have an EL function to calculate a cycle algorithm? Hopefully,
>this EL cycle algorithm would capture important information about the
>cyclicity of a set of raw price bars, that is different from moving average
>and momentum indicators.
Here's my ELA for the Cycle period, which I adapted from a VBA macro I
wrote, which in turn was written from an article by John Ehlers in TASC.
{----------------------------------------------------------------------
HilbertPeriod by John Ehlers (7/22/00)
ELA adapted from VBA macro by Alex Matulich (8/27/2001)
Calculate the dominant cycle period.
}
Variables: smoother(0), detrender(0), Q1(0), I1(0), pd(14), Q2(0),
I2(0), jI(0), jQ(0), Re(0), Im(0);
If currentbar < 4 Then
smoother = (H+L+C)/3
Else
begin
{ smoothed price has a lag of 1 bar }
smoother = (4*(H+L+C) + 3*(H[1]+L[1]+C[1]) + 2*(H[2]+L[2]+C[2]) +
H[3]+L[3]+C[3]) / 30;
{ Detrend the signal and correct for the amplitude distortion
introduced by the differenceing process used to detrend. }
detrender = (0.25*smoother[0] + 0.75*smoother[2] - 0.75*smoother[4] -
0.25*smoother[6]) * (0.046*pd[1] + 0.332);
{ Compute amplitude-compensated InPhase and Quadrature components.
Quadrature is a difference, so we can apply the detrending computation
again to the detrender signal to get quadrature Q1. The Q1
computation has a 3 bar lag, so we use bar 3 of the original
detrended signal for the in-phase component I1. }
Q1 = (0.25*detrender[0] + 0.75*detrender[2] - 0.75*detrender[4] -
0.25*detrender[6]) * (0.046*pd[1] + 0.332);
I1 = detrender[3];
{ That's it, the Hilbert transform is complete.
We accomplish the first smoothing step without introducing phase
error by advancing the phase of I1 and Q1 by 90 degrees. }
jI = 0.25 * I1 + 0.75 * I1[2] - 0.75 * I1[4] - 0.25 * I1[6];
jQ = 0.25 * Q1 + 0.75 * Q1[2] - 0.75 * Q1[4] - 0.25 * Q1[6];
{ Phasor addition to equalize amplitude due to quadrature calculations
(and 3 bar averaging) }
I2 = I1 - jQ;
Q2 = Q1 + jI;
{ Smooth the I and Q components before applying the discriminator.
This is a fairly strong exponential moving average (EMA). We can
use it because we are only interested in the RELATIVE phase distortion
between two components (yesterday's and today's phase), not the
absolute distortion which the EMA would destroy. }
I2 = 0.15 * I2 + 0.85 * I2[1];
Q2 = 0.15 * Q2 + 0.85 * Q2[1];
{ Smoothing was crucial because the next step involves multiplication
and it is imperative to remove any noise component before performing
the multiplication. We do a complex multiplication of the complex
conjugate of the current signal with the signal delayed one bar.
Apply a homodyne discriminator (which works well in low signal-to-noise
environments. Homodyne means use the signal multiplied by itself one
bar ago to produce a zero-frequency beat note, which carries the phase
angle of the one-bar change. This one-bar rate of change in phase is
exactly the cycle period. }
{ complex conjugate multiplication:
(I2(0) - i*Q2(0)) * (I2(1) + i*Q2(1)) }
Re = I2 * I2[1] + Q2 * Q2[1];
Im = I2 * Q2[1] - Q2 * I2[1];
{ Smooth to remove undesired cross products. }
Re = 0.2 * Re + 0.8 * Re[1];
Im = 0.2 * Im + 0.8 * Im[1];
{ Compute Cycle Period. }
If Im <> 0 And Re <> 0 Then pd = 360 / ArcTangent(Im / Re);
If pd > 1.5 * pd[1] Then pd = 1.5 * pd[1];
If pd < 0.6666667 * pd[1] Then pd = 0.6666667 * pd[1];
If pd < 6 Then pd = 6;
If pd > 50 Then pd = 50;
pd = 0.2 * pd + 0.8 * pd[1]; { smooth yet again }
end;
HilbertCycle = pd;
{----------------------------------------------------------------------}
Enjoy. I have noticed that the Cycle length makes a pretty good
approximation of the ADX -- the longer the cycle length, the more the
market is in a trend.
--
,|___ Alex Matulich -- alex@xxxxxxxxxxxxxx
// +__> Director of Research and Development
// \
//___) Unicorn Research Corporation -- http://unicorn.us.com
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