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The final form could be
in =ln(Close/Ref(Close,-1));
BarsToEnd = LastValue( BarIndex() ) - BarIndex();
Z=LastValue(Cum(1))-Cum(1);
for(i=3;i<=8;i++)
{
VarSet("mean"+i,ValueWhen( BarsToEnd % 2^i == 0, MA( in, 2^i ), 0 ));
VarSet("dist"+i,Cum( in - VarGet("mean"+i) ) - ValueWhen( BarsToEnd %
2^i == 0, in-VarGet("mean"+i) ));
VarSet("RS"+i,( HHV( VarGet("dist"+i), 2^i ) - LLV( VarGet("dist"+i),
2^i ) ) / StDev( in , 2^i ));
VarSet("ARS"+i,(257-2^i)*MA(VarGet("RS"+i)*(Z%(2^i)==0),257-2^i)/2^(8-
i));
VarSet("Y"+i,log(VarGet("ARS"+i))/log(2));
}
Y8=VarGet("Y8");Y7=VarGet("Y7");Y6=VarGet("Y6");
Y5=VarGet("Y5");Y4=VarGet("Y4");Y3=VarGet("Y3");
Sumx = 3+4+5+6+7+8;
Sumy = Y8 + Y7 + Y6 + Y5 + Y4 + Y3;
sumxy = 8*Y8 + 7*Y7 + 6*Y6 + 5*Y5 + 4*Y4 + 3*Y3;
Sumx2 = 3*3 + 4*4 + 5*5 + 6*6 + 7*7 + 8*8;
b=( 6 * sumxy - sumx*sumy )/( 6 * sumx2 - sumx*sumx);
Filter = BarsToEnd == 0;
AddColumn( Close, "Close", 1.5 );
AddColumn( b, "Hurst Exponent", 1.5);
AddColumn( 2-b, "Fractal Dim", 1.5 );
Dimitris
--- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS" <TSOKAKIS@xxxx>
wrote:
>
> The part
>
> ARS8 = RS8;
> ARS7 = ( RS7 + Ref( RS7, -128 ) ) / 2;
> ARS6 = ( RS6 + Ref( RS6, -64 ) + Ref( RS6, -128 ) +
> Ref( RS6, -192) ) / 4;
> ARS5 = ( RS5 + Ref( RS5, -32 ) + Ref( RS5, -64 ) +
> Ref( RS5, -96 ) + Ref( RS5, -128 ) +Ref( RS5, -160 ) +
> Ref( RS5, -192 ) +Ref( RS5, -224 ) ) / 8;
> ARS4 = ( RS4 + Ref( RS4, -16 ) + Ref( RS4, -32 ) +
> Ref( RS4, -48 ) + Ref( RS4, -64 ) + Ref( RS4, -80 ) +
> Ref( RS4, -96 ) +Ref( RS4, -112 ) + Ref( RS4, -128 ) +
> Ref( RS4, -144 ) + Ref( RS4, -160 ) +Ref( RS4, -176 ) +
> Ref( RS4, -192 ) +Ref( RS4, -208 ) + Ref( RS4, -224 ) +
> Ref( RS4, -240 ) ) / 16;
> ARS3 = ( RS3 +
> Ref( RS3, -8 ) + Ref( RS3, -16 ) +
> Ref( RS3, -24 ) + Ref( RS3, -32 ) +
> Ref( RS3, -40 ) + Ref( RS3, -48 ) +
> Ref( RS3, -56 ) + Ref( RS3, -64 ) +
> Ref( RS3, -72 ) + Ref( RS3, -80 ) +
> Ref( RS3, -88 ) + Ref( RS3, -96 ) +
> Ref( RS3, -104 ) + Ref( RS3, -112 ) +
> Ref( RS3, -120 ) + Ref( RS3, -128 ) +
> Ref( RS3, -136 ) + Ref( RS3, -144 ) +
> Ref( RS3, -152 ) + Ref( RS3, -160 ) +
> Ref( RS3, -168 ) + Ref( RS3, -176 ) +
> Ref( RS3, -184 ) + Ref( RS3, -192 ) +
> Ref( RS3, -200 ) + Ref( RS3, -208 ) +
> Ref( RS3, -216 ) + Ref( RS3, -224 ) +
> Ref( RS3, -232 ) + Ref( RS3, -240 ) +
> Ref( RS3, -248 ) ) / 32;
>
> may be replaced by
>
> Y=LastValue(Cum(1))-Cum(1);
> ARS8 = RS8;
> ARS7=129*MA(RS7*(Y%128==0),129)/2;
> ARS6=193*MA(RS6*(Y%64==0),193)/4;
> ARS5=225*MA(RS5*(Y%32==0),225)/8;
> ARS4=241*MA(RS4*(Y%16==0),241)/16;
> ARS3=249*MA(RS3*(Y%8==0),249)/32;
>
> Dimitris
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
<TSOKAKIS@xxxx>
> wrote:
> >
> > Hans,
> > Thank you for your reply and the ref you posted in other messages.
> > Here is some notes:
> >
> > 1.
> > The formula references FUTURE quotes.
> > If you read for ^NDX Oct1 Hurst=0.58, ten days later the value
for
> > the same date Oct1 WILL NOT BE 0.58 !!
> > We have discussed the topic many times in the past, a "HURST"
> > research of this list archives will give more than 50 messages.
> >
> > 1a.
> > How do you use this code ?
> >
> > 2.
> > If you still want to use it, the code may be substantially
shorter .
> > Example :
> > The part
> >
> > mean8 = ValueWhen( BarsToEnd % 256 == 0, MA( in, 256 ), 0 );
> > mean7 = ValueWhen( BarsToEnd % 128 == 0, MA( in, 128 ), 0 );
> > mean6 = ValueWhen( BarsToEnd % 64 == 0, MA( in, 64 ), 0 );
> > mean5 = ValueWhen( BarsToEnd % 32 == 0, MA( in, 32 ), 0 );
> > mean4 = ValueWhen( BarsToEnd % 16 == 0, MA( in, 16 ), 0 );
> > mean3 = ValueWhen( BarsToEnd % 8 == 0, MA( in, 8 ), 0 );
> > dist8 = Cum( in - mean8 ) - ValueWhen( BarsToEnd % 256 == 0, in-
> > mean8 );
> > dist7 = Cum( in - mean7 ) - ValueWhen( BarsToEnd % 128 == 0, in-
> > mean7 );
> > dist6 = Cum( in - mean6 ) - ValueWhen( BarsToEnd % 64 == 0, in-
> > mean6 );
> > dist5 = Cum( in - mean5 ) - ValueWhen( BarsToEnd % 32 == 0, in-
> > mean5 );
> > dist4 = Cum( in - mean4 ) - ValueWhen( BarsToEnd % 16 == 0, in-
> > mean4 );
> > dist3 = Cum( in - mean3 ) - ValueWhen( BarsToEnd % 8 == 0, in-
> mean3 );
> > RS8 = ( HHV( dist8, 256 ) - LLV( dist8, 256 ) ) / StDev( in ,
256 );
> > RS7 = ( HHV( dist7, 128 ) - LLV( dist7, 128 )) / StDev( in ,
128 );
> > RS6 = ( HHV( dist6, 64 ) - LLV( dist6, 64 )) / StDev( in , 64 );
> > RS5 = ( HHV( dist5, 32 ) - LLV( dist5, 32 )) / StDev( in , 32 );
> > RS4 = ( HHV( dist4, 16 ) - LLV( dist4, 16 )) / StDev( in , 16 );
> > RS3 = ( HHV( dist3, 8 ) - LLV( dist3, 8 )) / StDev( in , 8 );
> >
> > may be written
> >
> > for(i=3;i<=8;i++)
> > {
> > VarSet("mean"+i,ValueWhen( BarsToEnd % 2^i == 0, MA( in, 2^i ),
> 0 ));
> > VarSet("dist"+i,Cum( in - VarGet("mean"+i) ) - ValueWhen(
BarsToEnd
> %
> > 2^i == 0, in-VarGet("mean"+i) ));
> > VarSet("RS"+i,( HHV( VarGet("dist"+i), 2^i ) - LLV( VarGet
> ("dist"+i),
> > 2^i ) ) / StDev( in , 2^i ));
> > }
> > RS8=VarGet("RS8");
> > RS7=VarGet("RS7");
> > RS6=VarGet("RS6");
> > RS5=VarGet("RS5");
> > RS4=VarGet("RS4");
> > RS3=VarGet("RS3");
> >
> > You may continue for the rest of the code in this way.
> > It is always interesting to see 10 code lines instead of an A4
page.
> > [ If you are interested, I will do the rest of the code for you
> some
> > other time ]
> > 3.
> > The "Chaos Hypertextbook" is interesting. I will translate it in
> AFL
> > someday. I hope Glenn Elert will be also happy, since the fair
use
> is
> > encouraged [in one way or the other I will ask his
> opinion/permission]
> >
> > Dimitris
> >
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "Hans" <hansib@xxxx> wrote:
> > >
> > > Hello Dimitris,
> > >
> > > here is the code for the exploration of Hurst Exponent:
> > >
> > > // we use logarithmic returns
> > > in =ln(Close/Ref(Close,-1));
> > >
> > > BarsToEnd = LastValue( BarIndex() ) - BarIndex();
> > >
> > > // calculate R/S statistics
> > > // for last 256 bars. We divide this period into
> > > // 1 region of 256 bars
> > > // 2 regions of 128 bars
> > > // 4 regions of 64 bars
> > > // 8 regions of 32 bars
> > > // 16 regions of 16 bars
> > > // 32 regions of 8 bars
> > > // (63 regions in total)
> > >
> > > mean8 = ValueWhen( BarsToEnd % 256 == 0, MA( in, 256 ), 0 );
> > > mean7 = ValueWhen( BarsToEnd % 128 == 0, MA( in, 128 ), 0 );
> > > mean6 = ValueWhen( BarsToEnd % 64 == 0, MA( in, 64 ), 0 );
> > > mean5 = ValueWhen( BarsToEnd % 32 == 0, MA( in, 32 ), 0 );
> > > mean4 = ValueWhen( BarsToEnd % 16 == 0, MA( in, 16 ), 0 );
> > > mean3 = ValueWhen( BarsToEnd % 8 == 0, MA( in, 8 ), 0 );
> > >
> > > dist8 = Cum( in - mean8 ) - ValueWhen( BarsToEnd % 256 == 0, in-
> > > mean8 );
> > > dist7 = Cum( in - mean7 ) - ValueWhen( BarsToEnd % 128 == 0, in-
> > > mean7 );
> > > dist6 = Cum( in - mean6 ) - ValueWhen( BarsToEnd % 64 == 0, in-
> > > mean6 );
> > > dist5 = Cum( in - mean5 ) - ValueWhen( BarsToEnd % 32 == 0, in-
> > > mean5 );
> > > dist4 = Cum( in - mean4 ) - ValueWhen( BarsToEnd % 16 == 0, in-
> > > mean4 );
> > > dist3 = Cum( in - mean3 ) - ValueWhen( BarsToEnd % 8 == 0, in-
> > mean3 );
> > >
> > > // calculate RS statistics for all regions
> > >
> > > RS8 = ( HHV( dist8, 256 ) - LLV( dist8, 256 ) ) / StDev( in ,
> 256 );
> > > RS7 = ( HHV( dist7, 128 ) - LLV( dist7, 128 )) / StDev( in ,
> 128 );
> > > RS6 = ( HHV( dist6, 64 ) - LLV( dist6, 64 )) / StDev( in , 64 );
> > > RS5 = ( HHV( dist5, 32 ) - LLV( dist5, 32 )) / StDev( in , 32 );
> > > RS4 = ( HHV( dist4, 16 ) - LLV( dist4, 16 )) / StDev( in , 16 );
> > > RS3 = ( HHV( dist3, 8 ) - LLV( dist3, 8 )) / StDev( in , 8 );
> > >
> > > // calculate average RS is corresponding regions
> > >
> > > ARS8 = RS8;
> > > ARS7 = ( RS7 + Ref( RS7, -128 ) ) / 2;
> > > ARS6 = ( RS6 +
> > > Ref( RS6, -64 ) + Ref( RS6, -128 ) +
> > > Ref( RS6, -192) ) / 4;
> > > ARS5 = ( RS5 +
> > > Ref( RS5, -32 ) + Ref( RS5, -64 ) +
> > > Ref( RS5, -96 ) + Ref( RS5, -128 ) +
> > > Ref( RS5, -160 ) + Ref( RS5, -192 ) +
> > > Ref( RS5, -224 ) ) / 8;
> > > ARS4 = ( RS4 +
> > > Ref( RS4, -16 ) + Ref( RS4, -32 ) +
> > > Ref( RS4, -48 ) + Ref( RS4, -64 ) +
> > > Ref( RS4, -80 ) + Ref( RS4, -96 ) +
> > > Ref( RS4, -112 ) + Ref( RS4, -128 ) +
> > > Ref( RS4, -144 ) + Ref( RS4, -160 ) +
> > > Ref( RS4, -176 ) + Ref( RS4, -192 ) +
> > > Ref( RS4, -208 ) + Ref( RS4, -224 ) +
> > > Ref( RS4, -240 ) ) / 16;
> > >
> > > ARS3 = ( RS3 +
> > > Ref( RS3, -8 ) + Ref( RS3, -16 ) +
> > > Ref( RS3, -24 ) + Ref( RS3, -32 ) +
> > > Ref( RS3, -40 ) + Ref( RS3, -48 ) +
> > > Ref( RS3, -56 ) + Ref( RS3, -64 ) +
> > > Ref( RS3, -72 ) + Ref( RS3, -80 ) +
> > > Ref( RS3, -88 ) + Ref( RS3, -96 ) +
> > > Ref( RS3, -104 ) + Ref( RS3, -112 ) +
> > > Ref( RS3, -120 ) + Ref( RS3, -128 ) +
> > > Ref( RS3, -136 ) + Ref( RS3, -144 ) +
> > > Ref( RS3, -152 ) + Ref( RS3, -160 ) +
> > > Ref( RS3, -168 ) + Ref( RS3, -176 ) +
> > > Ref( RS3, -184 ) + Ref( RS3, -192 ) +
> > > Ref( RS3, -200 ) + Ref( RS3, -208 ) +
> > > Ref( RS3, -216 ) + Ref( RS3, -224 ) +
> > > Ref( RS3, -232 ) + Ref( RS3, -240 ) +
> > > Ref( RS3, -248 ) ) / 32;
> > >
> > > // calculate Hurst exponent as a linear regression slope
> > > // of Log2( AvgRS )/ Log2( region size )
> > >
> > > Y8 = log( ARS8 )/log( 2 );
> > > Y7 = log( ARS7 )/log( 2 );
> > > Y6 = log( ARS6 )/log( 2 );
> > > Y5 = log( ARS5 )/log( 2 );
> > > Y4 = log( ARS4 )/log( 2 );
> > > Y3 = log( ARS3 )/log( 2 );
> > >
> > > Sumx = 3+4+5+6+7+8; // sum of log2( region size )
> > > Sumy = Y8 + Y7 + Y6 + Y5 + Y4 + Y3; // sum of log2( AvgRS )
> > > sumxy = 8*Y8 + 7*Y7 + 6*Y6 + 5*Y5 + 4*Y4 + 3*Y3;
> > > Sumx2 = 3*3 + 4*4 + 5*5 + 6*6 + 7*7 + 8*8;
> > >
> > > // the slope of linear regression from R/S
> > > // is the estimate of Hurst exponent
> > > b=( 6 * sumxy - sumx*sumy )/( 6 * sumx2 - sumx*sumx);
> > > Hurst = b;
> > > Filter = BarsToEnd == 0;
> > > AddColumn( Close, "Close", 1.5 );
> > > AddColumn( Hurst, "Hurst Exponent", 1.5);
> > > AddColumn( 2-Hurst, "Fractal Dim", 1.5 );
> > > /*
> > > there is also another aersion of hurst calculation at
> > > http://www.amibroker.com/library/detail.php?id=65
> > >
> > > I hope this could be a good start
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
> > <TSOKAKIS@xxxx>
> > > wrote:
> > > >
> > > > ...
> > > > Aleksandr Mikhailovich Lyapunov
> > > > He was born 6 June 1857 in Yaroslavl (Russia) and died 3
> November
> > > > 1918 in Odessa (he committed suicide three days after the
death
> > of
> > > > his wife).
> > > > ...
> > > > This would probably be a start for this interesting
discussion.
> > The
> > > > topic is fairly advanced and I do not know if it is
interesting
> > for
> > > > the readers of this list.
> > > > Hans,
> > > > Since you already have the AFL code for Hurst Exponent, post
it
> > > > together with a short description for the use to begin with.
> > > > Dimitris
> > > > --- In amibroker@xxxxxxxxxxxxxxx, "Hans" <hansib@xxxx> wrote:
> > > > > Dear group members,
> > > > >
> > > > > I would like to calculate Lyapunov exponent as exploration.
> > > > >
> > > > > Please find in this page some reference and formula:
> > > > > http://www.iqnet.cz/dostal/CHA1.htm
> > > > >
> > > > > Is anyone of you able (and so kind) to build the code for
> > > Amibroker
> > > > > starting from the linked formula?
> > > > > (NOTE: I have already the code for Hurst Exponent).
> > > > >
> > > > > many thanks!
> > > > >
> > > > > PS maybe Dimitri has already some code. ;)
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