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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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