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<FONT face=Arial color=#0000ff
size=2>Corey,
<FONT face=Arial color=#0000ff
size=2>
FWIW,
your T3 version of Hilbert cycle finder is working best for me. Of
course, that doesn't mean that it is the best. It is working best in
combination with my systems.
<FONT face=Arial color=#0000ff
size=2>
If you
are interest in how I am using it...
<FONT face=Arial color=#0000ff
size=2>
This
particular system had an optimised lookback of 10 days. Using your
version of the Hilbert Cycle finder, I ended up by saying something like
this:
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial
color=#0000ff size=2>lookback = IIF(HilbertPeriod() > 30, 12,
8)
<FONT face=Arial color=#0000ff
size=2>
These
values (30,12,8) were all optimised, but made logical sense to me and actually
were my initial defaults.
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>Ten-year CAR on 19,000 stocks, 1% slippage, taking 35 positions at a
time, shorting against an up-trend went from 50% to 60% and max drawdown went
from 40% to 20%.
<FONT face=Arial color=#0000ff
size=2>
Thanks
for prompting me to have another look at dynamically adjusting lookback
periods.
<BLOCKQUOTE
>
<FONT face="Times New Roman"
size=2>-----Original Message-----From: Corey Saxe
[mailto:res1wgwl@xxxxxxxxxxx]Sent: Monday, February 09, 2004 12:04
AMTo: amibroker@xxxxxxxxxxxxxxxSubject: Re: [amibroker]
Re: Determining cycles
Anthony,
That's correct. Just something that i was working with.
Smoothperiod is the resulting output from the Hilbert cycle period, and the
input for the RSI.
Try plotting this and adjust "RSI Lookback".
T=Param<FONT
size=2>("RSI
Periods",<FONT
color=#4b0082>1<FONT face=Verdana
color=#4b0082>4,<FONT face=Verdana
color=#4b0082>2,<FONT face=Verdana
color=#4b0082>100,<FONT face=Verdana
color=#4b0082>1);
T2=<FONT
color=#b300b3>Param("RSI
Lookback",1<FONT
size=2>,1,<FONT
color=#4b0082>15,<FONT face=Verdana
color=#4b0082>1);
mo = C<FONT
size=2>-Ref(<FONT
color=#ff0000>C,-T2);
Up = <FONT
color=#b300b3>IIf( mo><FONT
color=#4b0082>0, mo, <FONT
color=#4b0082>0);
Dn = <FONT
color=#b300b3>IIf( mo<<FONT
color=#4b0082>0, -mo, <FONT
color=#4b0082>0);
Ut = <FONT
color=#b300b3>AMA(Up,<FONT
color=#4b0082> 1/T<FONT
size=2>);
Dt = <FONT
color=#b300b3>AMA(Dn,<FONT
color=#4b0082> 1/T<FONT
size=2>);
RSIt=<FONT
color=#4b0082>100<FONT
size=2>*(Ut/(Ut+Dt));
Plot<FONT
size=2>(RSIt,"RSIt",1,1);<FONT color=#b300b3
size=1>
Plot<FONT
size=2>(RSI(14),"RSI",0,1);// Regular RSI
-CS
<BLOCKQUOTE dir=ltr
>
----- Original Message -----
<DIV
>From:
Anthony
Faragasso
To: <A title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, February 08, 2004 2:31
PM
Subject: Re: [amibroker] Re:
Determining cycles
Corey,
Thank you for sharing....
I notice at the bottom of the formula....you
have a Param() for RSI lookback Divisor....since it is not assigned, I do
not believe it serves any purpose at this time...is this correct
?
T=SmoothPeriod/Param<FONT
size=2>("SmoothPeriod
Divisor",<FONT color=#ff00ff
size=2>1,<FONT color=#ff00ff
size=2>1,<FONT color=#ff00ff
size=2>5,<FONT color=#ff00ff
size=2>0.1);
T2=T/4<FONT
size=2>;
Param("RSI
Lookback Divisor",<FONT color=#ff00ff
size=2>4,<FONT color=#ff00ff
size=2>1,<FONT color=#ff00ff
size=2>15,<FONT color=#ff00ff
size=2>0.1);// Not assigned
Anthony
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Corey
Saxe
To: <A
title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, February 08, 2004 5:03
PM
Subject: Re: [amibroker] Re:
Determining cycles
Anthony,
Here (attachment and below) is an example of RSI driven
by Hilbert cycle periods. As you can tell, I'm not done with this formula
either.
Note that the Hilbert transform part of the cycle period
formula is different. I have found that over time Ehlers has made
different versions. I collect them like beer bottles and test them for
accuracy and response... like beer.
-CS
/*
----------------------------------------------------------
Adaptive RSI w/Hilbert Cycle
Period
AFL conversion by Corey Saxe
<FONT color=#000000
size=2>----------------------------------------------------------
*/
SetBarsRequired<FONT
size=2>( 100000, 0 );
Prices =(<FONT
color=#ff0000>H+<FONT
color=#ff0000>L)/<FONT
color=#4b0082>2;
Smoother = <FONT
color=#4b0082>0; Detrender = <FONT
color=#4b0082>0;
I1 = <FONT
color=#4b0082>0; I2 = <FONT
color=#4b0082>0;
Q1 = <FONT
color=#4b0082>0; Q2 = <FONT
color=#4b0082>0;
jI = <FONT
color=#4b0082>0; jQ = <FONT
color=#4b0082>0;
X1 = <FONT
color=#4b0082>0; X2 = <FONT
color=#4b0082>0;
Y1 = <FONT
color=#4b0082>0; Y2 = <FONT
color=#4b0082>0;
Re = <FONT
color=#4b0082>0; Im = <FONT
color=#4b0082>0;
Period = <FONT
color=#4b0082>0;SmoothPeriod=<FONT
color=#4b0082>1;
CU=<FONT
color=#4b0082>0; CD=<FONT
color=#4b0082>0;
pi = <FONT
color=#4b0082>4 * <FONT
color=#b300b3>atan(<FONT
color=#4b0082>1)
;
for (i = 6;
i<BarCount; i++)
{
Smoother[i] = (<FONT
color=#4b0082>4*Prices[i] + <FONT
color=#4b0082>3*Prices[i-<FONT
color=#4b0082>1]+ <FONT
color=#4b0082>2*Prices[i-<FONT
color=#4b0082>2]+ Prices[i-<FONT
color=#4b0082>3])/<FONT
color=#4b0082>10;
Detrender[i] = (<FONT
color=#4b0082>0.0962*Smoother[i] + <FONT
color=#4b0082>0.5769*Smoother[i-<FONT
color=#4b0082>2] - <FONT
color=#4b0082>0.5769*Smoother[i-<FONT
color=#4b0082>4] - <FONT
color=#4b0082>0.0962*Smoother[i-<FONT
color=#4b0082>6]) * (<FONT
color=#4b0082>0.075*Period[i-<FONT
color=#4b0082>1] + <FONT
color=#4b0082>0.54<FONT
size=2>);
//{Compute InPhase AND Quadrature
components}
Q1[i] = (<FONT
color=#4b0082>0.0962*Detrender[i] +
0.5769<FONT
size=2>*Detrender[i-2<FONT
size=2>] - 0.5769<FONT
size=2>*Detrender[i-4<FONT
size=2>] - 0.0962<FONT
size=2>*Detrender[i-6<FONT
size=2>])*(0.075<FONT
size=2>*Period[i-1]
+ 0.54<FONT
size=2>);
I1[i] = Detrender[i-<FONT
color=#4b0082>3<FONT
size=2>];
//{advance the phase of I1 AND Q1 by 90
degrees}
jI[i] = <FONT
color=#4b0082>0.0962*I1[i] + <FONT
color=#4b0082>0.5769*I1[i-<FONT
color=#4b0082>2] - <FONT
color=#4b0082>0.5769*I1[i-<FONT
color=#4b0082>4] - <FONT
color=#4b0082>0.0962*I1[i-<FONT
color=#4b0082>6] * (<FONT
color=#4b0082>0.075*Period[i-<FONT
color=#4b0082>1] + <FONT
color=#4b0082>0.54<FONT
size=2>);
jQ[i] = <FONT
color=#4b0082>0.0962*Q1[i] + <FONT
color=#4b0082>0.5769*Q1[i-<FONT
color=#4b0082>2] - <FONT
color=#4b0082>0.5769*Q1[i-<FONT
color=#4b0082>4] - <FONT
color=#4b0082>0.0962*Q1[i-<FONT
color=#4b0082>6] * (<FONT
color=#4b0082>0.075*Period[i-<FONT
color=#4b0082>1] + <FONT
color=#4b0082>0.54<FONT
size=2>);
//{Phasor addition to equalize amplitude
due to quadrature calculations (AND 3 bar
averaging)}
I2[i] = I1[i] - jQ[i];
Q2[i] = Q1[i] + jI[i];<FONT
color=#008000 size=1>
//{Smooth the I AND Q components before
applying the discriminator}
I2[i] = <FONT
color=#4b0082>0.2*I2[i] + <FONT
color=#4b0082>0.8*I2[i-<FONT
color=#4b0082>1];
Q2[i] = <FONT
color=#4b0082>0.2*Q2[i] + <FONT
color=#4b0082>0.8*Q2[i-<FONT
color=#4b0082>1<FONT
size=2>];
//{Homodyne
Discriminator}
//{Complex Conjugate
Multiply}
X1[i] = I2[i]*I2[i-<FONT
color=#4b0082>1];
X2[i] = I2[i]*Q2[i-<FONT
color=#4b0082>1];
Y1[i] = Q2[i]*Q2[i-<FONT
color=#4b0082>1];
Y2[i] = Q2[i]*I2[i-<FONT
color=#4b0082>1];
Re[i] = X1[i] + Y1[i];
Im[i] = X2[i] - Y2[i];<FONT
color=#008000 size=1>
//{Smooth to remove undesired Cross
products}
Re[i] = <FONT
color=#4b0082>0.2*Re[i] + <FONT
color=#4b0082>0.8*Re[i-<FONT
color=#4b0082>1];
Im[i] = <FONT
color=#4b0082>0.2*Im[i] + <FONT
color=#4b0082>0.8*Im[i-<FONT
color=#4b0082>1<FONT
size=2>];
//{Compute Cycle
Period}
if<FONT
size=2> (Im[i] != 0
AND Re[i] !=
0) Period[i] =
(2*pi)/<FONT
color=#b300b3>atan<FONT
size=2>(Im[i]/Re[i]);
if<FONT
size=2> (Period[i] > 1.5<FONT
size=2>*Period[i-1])
Period[i] = 1.5<FONT
size=2>*Period[i-1<FONT
size=1>];
if<FONT
size=2> (Period[i] < 0.67<FONT
size=2>*Period[i-1])
Period[i] = 0.67<FONT
size=2>*Period[i-1<FONT
size=1>];
if<FONT
size=2> (Period[i] < 6<FONT
size=2>) Period[i] = 6<FONT
size=1>;
if<FONT
size=2> (Period[i] > 50<FONT
size=2>) Period[i] = 50<FONT
size=1>;
Period[i] = <FONT
color=#4b0082>0.2*Period[i] + <FONT
color=#4b0082>0.8*Period[i-<FONT
color=#4b0082>1<FONT
size=2>];
//End Hilbert Cycle
Period-----------------------------------------------<FONT
size=1>
SmoothPeriod[i] = <FONT
color=#4b0082>0.33 * Period[i] + <FONT
color=#4b0082>0.67 *
SmoothPeriod[i-1<FONT
size=1>];
}
/*
'x=int(0.5 * SmoothPeriod(i))
' for n = 1 To int(0.5 *
SmoothPeriod(i))
' if Close(n) > Close(n-1)
then
' CU(n) = CU(n-1) + ( Close(n) -
Close(n-1) )
' End if
'if Close(n) < Close(n-1)
then
' CD(n) = CD(n-1) + ( Close(n-1) -
Close(n) )
'End if
'if (CU(n) + CD(n)) <> 0
then
' RSIh(n) = (100 * ( CU(n)) /( CU(n) +
CD(n) ) )
' End if
'Next
*/
T=SmoothPeriod/<FONT
color=#b300b3>Param(<FONT
color=#0000ff>"SmoothPeriod Divisor",<FONT
color=#4b0082>1,<FONT
color=#4b0082>1,<FONT
color=#4b0082>5,<FONT
color=#4b0082>0.1<FONT
size=2>);
T2=T/<FONT
color=#4b0082>4;<FONT
color=#b300b3>Param(<FONT
color=#0000ff>"RSI Lookback Divisor",<FONT
color=#4b0082>4,<FONT
color=#4b0082>1,<FONT
color=#4b0082>15,<FONT
color=#4b0082>0.1<FONT
size=2>);
mo = Prices-<FONT
color=#b300b3>Ref<FONT
size=2>(Prices,-T2);
Up = <FONT
color=#b300b3>IIf( mo><FONT
color=#4b0082>0, mo, <FONT
color=#4b0082>0);
Dn = <FONT
color=#b300b3>IIf( mo<<FONT
color=#4b0082>0, -mo, <FONT
color=#4b0082>0);
Ut = <FONT
color=#b300b3>AMA(Up,<FONT
color=#4b0082>2/(<FONT
color=#4b0082>2<FONT
size=2>*T));
Dt = <FONT
color=#b300b3>AMA(Dn,<FONT
color=#4b0082>2/(<FONT
color=#4b0082>2<FONT
size=2>*T));
RSIt=<FONT
color=#4b0082>100<FONT
size=2>*(Ut/(Ut+Dt));
GraphXSpace<FONT
size=2>=5;
Plot<FONT
size=2>(RSIt,"RSI-Hilbert",0,1);<FONT
face=Verdana color=#b300b3 size=1>
Plot<FONT
face=Verdana>(RSI<FONT
face=Verdana>(LastValue<FONT
face=Verdana>(Smoothperiod)),"LastValue
RSI",1<FONT
face=Verdana>,1<FONT face=Verdana
size=1>);
Plot<FONT
size=2>(T,"Smoothed Cycle Period",2,1|<FONT
face=Verdana>styleOwnScale);
UT=<FONT
color=#b300b3>Param(<FONT
color=#0000ff>"Threshold",<FONT
color=#4b0082>70,<FONT
color=#4b0082>50,<FONT
color=#4b0082>100,<FONT
color=#4b0082>1<FONT
size=2>);
PlotGrid<FONT
size=2>(UT,0);
PlotGrid<FONT
size=2>(100-UT,0);
<BLOCKQUOTE dir=ltr
>
----- Original Message -----
<DIV
>From:
Anthony
Faragasso
To: <A
title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, February 08, 2004
4:28 AM
Subject: Re: [amibroker] Re:
Determining cycles
Corey,
How do you use this formula with other
indicators....could you give us an example.....
Thank you
Anthony
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Corey
Saxe
To: <A
title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, February 08, 2004
6:24 AM
Subject: Re: [amibroker] Re:
Determining cycles
Chuck,
One of the things that I was working on is an
improved "smoother" (Smoother2) for the input data to the Hilbert
transform (TASC v18:11) rather that Ehlers smoother (Smoother1). As
you can see I was trying out Tillson's T3 smoother, and "Periods2" is
just the amount of periods of smoothing that T3 is using. "Smoother2"
is the T3 output for use in the rest of the formula. "a" is simply the
"Hot" input parameter for use in T3. Note that I am using TEMA and not
EMA as the original T3 suggests. (BTW, I tripped over a TASC V19:6
article by Steve Burns that describes an adaptive T3 to
boot.)
Yes, I undestand that the formula should be able to
accurately find cycles down to a period of 6 days but using a
quick and dirty test using a synthetic waveform (Sine Wave Test in the
formula), I found odd fluctuations in cycle period output below 9
days. I am still working on a resolution for it.
Smoother1 is the native smoother from Ehlers
original formula. Smoother2 is my replacement of it by
T3.
The formula that I sent for Ara is just one of many
rough test examples, not yet ready for prime time. Ara and
everyone are free to twist and tweak it as they please. When I am
confident of the accuracy of its output (and the accuracy of my
translation and AFL coding), I would be happy to share.
Below is the EasyLanguage (Ha!) formula I derived
from.
<FONT
face=Arial size=1>
{
—————————————————————————————
HilbertPeriod
(Function) by John Ehlers (7/22/00)
This is the
Hilbert Cycle Period Function used by the Hilbert Channel
Breakout
System.
<FONT face=Verdana color=#000080
size=2>————————————————————————————— }
Inputs:
Price(numeric);
Vars:
Smoother(0), Detrender(0), I1(0), Q1(0), jI(0), jQ(0),
I2(0),Q2(0),
X1(0), X2(0), Y1(0), Y2(0), Re(0), Im(0), Period(0);
If CurrentBar
>5 then begin
Smoother =
(4*Price + 3*Price[1] + 2*Price[2] + Price[3])/10;
Detrender =
(.25*Smoother + .75*Smoother[2] - .75*Smoother[4]
-
.25*Smoother[6])*(.046*Period[1] + .332);
{Compute
InPhase and Quadrature components}
Q1 =
(.25*Detrender + .75*Detrender[2] - .75*Detrender[4] -
<FONT face=Verdana color=#000080
size=2>.25*Detrender[6])*(.046*Period[1] + .332);
I1 =
Detrender[3];
{advance the
phase of I1 and Q1 by 90 degrees}
jI = .25*I1 +
.75*I1[2] - .75*I1[4] - .25*I1[6];
jQ = .25*Q1 +
.75*Q1[2] - .75*Q1[4] - .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}
I2 = .15*I2 +
.85*I2[1];
Q2 = .15*Q2 +
.85*Q2[1];
{Homodyne
Discriminator}
{Complex
Conjugate Multiply}
X1 =
I2*I2[1];
X2 =
I2*Q2[1];
Y1 =
Q2*Q2[1];
Y2 =
Q2*I2[1];
Re = X1 +
Y1;
Im = X2 -
Y2;
{Smooth to
remove undesired cross products}
Re = .2*Re +
.8*Re[1];
Im = .2*Im +
.8*Im[1];
{Compute Cycle
Period}
If Im <>
0 and Re <> 0 then Period = 360/ArcTangent(Im/Re);
If Period >
1.5*Period[1] then Period = 1.5*Period[1];
If Period <
.67*Period[1] then Period = .67*Period[1];
If Period
<6 then Period = 6;
If Period
>50 then Period = 50;
Period =
.2*Period + .8*Period[1];
{END CORE
CODE}
HilbertPeriod
= Period;
<FONT face=Verdana color=#000080
size=2>end;
-CS
----- Original Message -----
<BLOCKQUOTE dir=ltr
>
<DIV
>From:
<A title=chuck_rademacher@xxxxxxxxxx
href="">Chuck Rademacher
To: <A
title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Saturday, February 07,
2004 7:47 PM
Subject: RE: [amibroker] Re:
Determining cycles
<FONT face=Arial color=#0000ff
size=2>Thanks, Phsst.
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>I am using Corey's code with great success and I was a bit
concerned about "future leak". I couldn't see where it
was happening and didn't really take the time to
investigate. I just liked the results I was
getting.
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>Corey, I'm hoping that you see this email as I have a couple
of questions for you.
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>1. Can you tell me what is going on with "Periods2" and
"a"? I see you have them as Param statements, but can
you recommend defaults. If I do understand what you are
doing with Periods2, your default of "5" seems a bit
low. Espeicially in light of your comment about "Periods
< 9 are NOT reliable". Or is that referring to some
other variable?
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>2. You seem to have built-in two smoothing techniques
(Smoother1 and Smoother2). Can you tell me more about the
logic behind these?
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>
<FONT face=Arial color=#0000ff
size=2>Thanks.
<BLOCKQUOTE
>
<FONT face="Times New Roman"
size=2>-----Original Message-----From: Phsst
[mailto:phsst@xxxxxxxxx]Sent: Saturday, February 07,
2004 10:00 PMTo:
amibroker@xxxxxxxxxxxxxxxSubject: [amibroker] Re:
Determining cyclesChuck and
Corey,The offending line of code
is:SetBarsRequired( 1000000, 1000000 );The above
line caused the 'Check' feature to issue a warning
aboutreferencing 'future
quotes'.Regards,Phsst--- In
amibroker@xxxxxxxxxxxxxxx, "Chuck
Rademacher"<chuck_rademacher@x> wrote:>
Corey,> > When I used your code (or mine) for the
HilbertPeriod thingie, AB thinks> that we are looking into
the future. Any idea where to look for the>
problem?> -----Original
Message-----> From: Corey Saxe
[mailto:res1wgwl@xxxx]> Sent: Saturday,
February 07, 2004 5:30 AM> To:
amibroker@xxxxxxxxxxxxxxx> Subject: Re:
[amibroker] Determining cycles> >
> Ara,> > I use
dynamic periods for nearly everything. To suppose that amarket
is> always and forever going to cycle at say, 21 days is
absurd.> > Hence, why I supported
dynamic parameter input for variousfunctions and>
indicators.> > Something I've been
tweaking is included.> > Note that each
indicator or metric that you desire to measure hasits
own> sweet-spot which will be a multiple (or fraction) of
the resulting cycle> frequency.> For
instance, If you want to use cycle period input to the
MACD,you may> find that it works best if the input
periods are multiplied by 0.67, but> maybe RSI works best
if the cycle periods are multiplied by 0.5.>
> Don't bother with FFT. The deficiencies are
vast. Dennis Meyers did a> series of articles a few years
ago in Futures mag, and describedmany of the> failures
of FFT to work on market prices because of the
constantvariability> of the current cycle
periods.> >
-CS> ----- Original Message
-----> From: Ara
Kaloustian> To:
Ami-Main> Sent: Friday, February
06, 2004 11:43 AM> Subject:
[amibroker] Determining cycles> >
> Has anyone used cycle length
determined dynamically and used to set> parameters for each
run?> > I considered using
Fast Fourier Transform... am open to any other>
suggestions> > If it works
one can produce constantly optimzed system ...geting
close> to the"holly grail">
>
Thanks> Ara> >
> Send BUG REPORTS to
bugs@xxxx> Send SUGGESTIONS to
suggest@xxxx>
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