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### Least Squares Polynomial Fit Pattern Detection for Amibroker (AFL) newman over 6 years ago Amibroker (AFL)

Rating:
Tags:
amibroker, polynomial

I found this indicator here it is written by E.M.Pottasch it attempts to find the best fitting polynomial to the selected point on the price chart. This formula requires a recent version of Amibroker as it uses the new matrix functions.

### Indicator / Formula

SetBarsRequired( sbrall, sbrall );
s1 = GetChartID() + StrToNum( Name() );

order = Param( "n-th Order", 2, 1, 10, 1 );
nbar = Param( "Lookback nbars", 30, 10, 2000, 1 );
clevel = Param( "Confidence Level", 2, 1, 3, 0.1 );
extend = Param( "Extend Fit (Bars)", 10, 0, 20, 1 );
trig = ParamTrigger( "Force Calculation", "Press Here" );
lengthDev = Param( "Pattern Deviation Length (%)", 100, 0, 200, 1 );
cofDev = Param( "Coefficient Deviation (%)", 5, 0, 10, 0.5 );
clr = ParamTrigger( "Clear Patterns", "Press Here" );

aa = 0;// declare coefficient matrix as global

x = BarIndex();
sv = selectedvalue( x );

eb1 = sv; // endbar of pattern to look for
bars1 = nbar;
prc = C;

SetChartOptions( 0, chartShowDates );
SetChartBkColor( ColorRGB( 0, 0, 0 ) );
SetBarFillColor( IIf( C > O, ColorRGB( 0, 75, 0 ), IIf( C <= O, ColorRGB( 75, 0, 0 ), colorLightGrey ) ) );
Plot( C, "", IIf( C > O, ColorRGB( 0, 255, 0 ), IIf( C <= O, ColorRGB( 255, 0, 0 ), colorLightGrey ) ), styleCandle, Null, Null, 0, 0, 1 );

function get_y( eb, bars )
{
fb = eb - bars;
yy = Matrix( bars + 1, 1, 0 );

yy = MxSetBlock( yy, 0, bars, 0, 0, Ref( prc, fb ) );

return yy;
}
function get_x( eb, bars )
{
xx = Matrix( bars + 1, order + 1, 1 );
x = BarIndex() - bars / 2;

for( j = 1; j <= order; j++ )
{
xx = MxSetBlock( xx, 0, bars, j, j, x ^ j );
}

return xx;
}
function calculateCoefficients( eb, bars )
{
xx = get_x( eb, bars );
yy = get_y( eb, bars );
xxt = MxTranspose( xx );
aa = MxSolve( xxt @ xx, xxt ) @ yy;

return aa;
}
function calculateFit( eb, bars )
{
global rr;
global xxa;
global zza;
global rrext;
global rrextxxa;
global rrextzza;

rr = rrext = Null; // store the fit in rr
lb = eb;
fb = eb - bars;

x = BarIndex() - bars / 2;

// calculate coefficients
aa = calculateCoefficients( eb, bars );

// store the fit in rr
for( i = fb; i <= lb; i++ )
{
rr[i] = aa[0][0];

for( j = 1; j <= order; j++ )
{
rr[i] += aa[j][0] * x[ i - fb ] ^ j;
}
}

// extended fit (only when channel is active at last bar)
if( lb == eb )
{
for( i = lb + 1; i <= lb + extend; i++ )
{
rrext[i - extend] = aa[0][0];

for( j = 1; j <= order; j++ )
{
rrext[i - extend] += aa[j][0] * x[ i - fb ] ^ j;
}
}
}

// calculate standard deviation
sdp = 0;

for( i = fb; i <= lb; i++ )
{
sdp = sdp + ( prc[i] - rr[i] ) ^ 2;
}

sd = sqrt( sdp / ( bars - 2 ) ); // devide by ( bars - 2 ) corresponding to StdErr function

xxa = rr + sd * clevel;
zza = rr - sd * clevel;
rrextxxa = rrext + sd * clevel;
rrextzza = rrext - sd * clevel;
}

calculateFit( eb1, bars1 );

Plot( rr, "", colorYellow, styleLine, Null, Null, 0, 0, 1 );
Plot( xxa, "", colorYellow, styleline, null, null, 0, 0, 1 );
Plot( zza, "", colorYellow, styleline, null, null, 0, 0, 1 );
Plot( rrext, "", colorYellow, styleDashed | styleNoLabel | styleNoRescale, Null, Null, extend, 0, 1 );
Plot( rrextxxa, "", colorYellow, styleDashed | styleNoLabel | styleNoRescale, Null, Null, extend, 0, 1 );
Plot( rrextzza, "", colorYellow, styleDashed | styleNoLabel | styleNoRescale, Null, Null, extend, 0, 1 );
lastBarOfFit = eb1 == BarIndex();
Plot( lastbarOfFit, "", ColorRGB( 100, 100, 100 ), styleHistogram | styleThick | styleOwnScale | styleNoLabel, 0, 1, 0, 0, 1 );

str = "ORDER: " + order + "\n" + "POLYNOMIAL COEFFICIENTS:\n";

for( i = 0; i <= order; i++ )
{
str = str + "aa[" + i + "][0]" + ":  " + aa[i][0] + "\n";
}

Title = EncodeColor( colorYellow ) + str + EncodeColor( colorBlack ) ;

minLength = round( bars1 - bars1 * ( 0.5 * lengthDev / 100 ) );
maxLength = round( bars1 + bars1 * ( 0.5 * lengthDev / 100 ) );

aap = aa; // coefficients of pattern to search for

// trigger to search for mathing patterns in the entire data array
if( trig )
{
storeEndBar = 0;
storeBars = 0;
Say( "Calculation Started" );
cnt = 0;

for( i = maxlength + 1; i < barcount; i++ )
{
for( j = minlength; j < maxlength; j++ )
{
calculateFit( i, j );
cnt2 = 0;

for( k = 1; k <= order; k++ )
{
if( aa[k][0] > aap[k][0] - cofDev * aap[k][0] / 100 AND aa[k][0] < aap[k][0] + cofDev * aap[k][0] / 100 )
{
cnt2 = cnt2 + 1;

//if( C[i] < zza[i] AND C[i - 1] > zza[i - 1] AND cnt2 == order )
if( cnt2 == order )
{
storeEndBar[ cnt ] = i;
storeBars[ cnt ] = j;
cnt = cnt + 1;
}
}
else
if( aa[k][0] < aap[k][0] - cofDev * aap[k][0] / 100 AND aa[k][0] > aap[k][0] + cofDev * aap[k][0] / 100 )
{
cnt2 = cnt2 + 1;

//if( C[i] > xxa[i] AND C[i - 1] < xxa[i - 1] AND cnt2 == order )
if( cnt2 == order )
{
storeEndBar[ cnt ] = i;
storeBars[ cnt ] = j;
cnt = cnt + 1;
}
}
}
}
}

StaticVarSet( "storeEndBar" + s1, storeEndBar );
StaticVarSet( "storeBars" + s1, storeBars );
Say( "Finished" );
}

storeEndBar1 = StaticVarGet( "storeEndBar" + s1 );
storeBars1 =   StaticVarGet( "storeBars" + s1 );

// avoid plot called too often in loop
lv = LastValue( ValueWhen( storeBars1 != 0, BarIndex() ) );
fv = Max( 0, lv - 160 );

for( i = lv; i > fv; i-- )
{
if( IsEmpty( storeBars1[i] ) )
{
break;
}
else
if( !IsEmpty( storeBars1[i] ) AND storeBars1[i] >= minlength )
{
a = storeEndBar1[ i ];
b = storeBars1[ i ];
calculateFit( a, b );

Plot( rr, "", colorBlue, styleLine | stylenolabel, Null, Null, 0, 0, 2 );
Plot( zza, "", colorBlue, styleLine | stylenolabel, Null, Null, 0, 0, 2 );
Plot( xxa, "", colorBlue, styleLine | stylenolabel, Null, Null, 0, 0, 2 );
}
}

if( clr )
{
StaticVarSet( "storeEndBar" + s1, Null );
StaticVarSet( "storeBars" + s1, Null );
}

1.

12 errors coming in this code….i am using ami 6.0

2.

Looking at the formula it uses the new matrix functions. I believe they are only available in Amibroker 6.10 and newer.

3.