please help me..

yoza

New Member
#1
"I found the AFL from somewhere but I can not use it because there are some errors, for the senior and masters please help me correct it."

"I am very happy with this website, really really helped me in learning and I always read every review of the senior, for that I say many thanks. "

"Sorry if my language is not good." :cool:


_SECTION_BEGIN("tomy_frenchy");
//------------------------------------------------------------------------------
//
// Formula Name: tomy_frenchy
// Author/Uploader: tomy_frenchy - tom_borgo [at] hotmail.com
// E-mail:
// Date/Time Added: 2006-11-07 22:00:53
// Origin:
// Keywords: prediction ar auto regressive regression
// Level: semi-advanced
// Flags: indicator,function
// Formula URL: http://www.amibroker.com/library/formula.php?id=757
// Details URL: http://www.amibroker.com/library/detail.php?id=757
//
//------------------------------------------------------------------------------
//
// Prediction AR (Auto-regressive)
//
// - With Least Square / Durbin-Levinson / Gaussian Elimination
//
// - Autocorrelation function estimator biased and not biased
//
// - Denoising by centered T3 moving average
//
// - Detrending by derivation
//
// TO DO:
//
// - some problem of stability
//
// - check optimum order for AR
//
// - check correlation of residual to confirm the model
//
// - PFE, Ramset, etc test for AR modeling efficiency
//
// - maybe ARMA will be better ?
//
//------------------------------------------------------------------------------


// *********************************************************
// *
// * Prediction with model AR by Least Square / Autocorrelation
// * - Native AFL and VBS (for Gaussian Elimination if selected)
// * - biased or not biased estimator depending volatility
// * - averaging by T3 zerolag
// * - detrend by derivation
// *
// * - tomy_frenchy, v0.1
// * - fred for VBS Gaussian Elimination. Thanks a lot.
// *
// *********************************************************

// *********************************************************
// *
// * Price field = Data to predict
// * Periods = Periods for T3 filtering
// * Slope = Slope for T3 filtering (0.7 to 0.83 for usual value)
// * Methode = 0: Durbin-Levinson, 1: Gaussian Elimination
// * Order = Order of AR model
// * ExtraF = Number of Bars to Extrapolate Forward
// *
// *********************************************************

// *********************************************************
// *
// * Plotting :
// * The bar position on the graphics separe in/out samples
// * Green: computed from current data (centered T3 moving average)
// * Blue: predicted, in-sample (AR, for the bar delayed because of T3 MA)
// * Red: predicted, out-sample (AR, pure prediction)
// *
// *********************************************************


// For a resolution with Gaussian Elimination (more stable than Levinson-Durbin but slower)
EnableScript("VBScript");
<%
function Gaussian_Elimination (OrderAR, Autocorr)
Dim b(200, 200)
Dim w(200)
Dim Coeff(200)

for i = 1 To 200
Coeff(i) = 0
next

n = OrderAR

for i = 1 to n
for j = 1 to n
b(i, j) = cDbl(Autocorr(abs(j - i)))
next
w(i) = cDbl(Autocorr(i))
next

n1 = n - 1
for i = 1 to n1
big = cDbl(abs(b(i, i)))
q = i
i1 = i + 1

for j = i1 to n
ab = cDbl(abs(b(j, i)))
if (ab >= big) then
big = ab
q = j
end if
next

if (big <> 0.0) then
if (q <> i) then
for j = 1 to n
Temp = cDbl(b(q, j))
b(q, j) = b(i, j)
b(i, j) = Temp
next
Temp = w(i)
w(i) = w(q)
w(q) = Temp
end if
end if

for j = i1 to n
t = cDbl(b(j, i) / b(i, i))
for k = i1 to n
b(j, k) = b(j, k) - t * b(i, k)
next
w(j) = w(j) - t * w(i)
next
next

if (b(n, n) <> 0.0) then

Coeff(n) = w(n) / b(n, n)
i = n - 1

while i > 0
SumY = cDbl(0)
i1 = i + 1
for j = i1 to n
SumY = SumY + b(i, j) * Coeff(j)
next
Coeff(i) = (w(i) - SumY) / b(i, i)
i = i - 1
wend

Gaussian_Elimination = Coeff

end if
end function
%>

function T3(price,periods,s) {
e1=EMA(price,periods);
e2=EMA(e1,Periods);
e3=EMA(e2,Periods);
e4=EMA(e3,Periods);
e5=EMA(e4,Periods);
e6=EMA(e5,Periods);
c1=-s*s*s;
c2=3*s*s+3*s*s*s;
c3=-6*s*s-3*s-3*s*s*s;
c4=1+3*s+s*s*s+3*s*s;
Ti3=c1*e6+c2*e5+c3*e4+c4*e3;
return ti3;
}

function f_centeredT3(data) {
global slide;
periods = Param("Periods", 5, 1, 200, 1);
slope = Param("Slope", 0.7, 0, 3, 0.01);
slide = floor(periods/2);
centeredT3 = data;
centeredT3 = Ref(T3(data,periods,slope),slide);
centeredT3 = IIf( IsNan(centeredT3) OR !IsFinite(centeredT3) OR IsNull(centeredT3), data, centeredT3);
return centeredT3;
}

function f_detrend(data) {
detrended[0]=0;
for (i = 1; i < BarCount; i++) detrended = data - data[i-1];
return detrended;
}

function f_retrend(data, first_value, first_index, last_index) {
for (i = 0; i < first_index; i++) retrended = -1e10;
retrended[first_index]=first_value;
for (i = first_index + 1; i < last_index + 1; i++) retrended = data + retrended[i-1];
for (i = last_index + 1; i < BarCount; i++) retrended = -1e10;
return retrended;
}

function AR(Data, BegBar, EndBar, OrderAR, ExtraF, Methode) {
BI = BarIndex();
Data_all = Data;
Data = IIf(BI < BegBar, 0, IIf(BI > EndBar, 0, Data));

LongBar = EndBar - BegBar + 1;


// Calcul for autocorrelation function
temp = MA(Data,LongBar);
moy_data = temp[EndBar];
data_centred = Data - moy_data;

for (i = 0; i < OrderAR + 1; i++) {
temp = 0;
for (j = BegBar; j < EndBar + 1 - i; j++) {
temp = temp + data_centred[j]*data_centred[j+i];
}
//Autocorr=(1/(LongBar))*temp; //biased estimator, small variance
Autocorr=(1/(LongBar-i))*temp; //not biased estimator, strong variance
}
Autocorr=Autocorr/Autocorr[0];


Gaussian_Elimination = Methode; // 0: Durbin-Levison, 1: Gaussian Elimination

if ( Gaussian_Elimination == 1 ) {
// Calcul AR parameters with Gaussian Elimination (vbs, more stable and precise, but slower)
VBS = GetScriptObject();
AR_Coeff = VBS.Gaussian_Elimination(OrderAR, Autocorr);
}

else {
// Calcul AR parameters with Durbin-Levison algorythm for Toeplitz matrix

// initialisation :
AR_Coeff = 0;
alpha[1] = Autocorr[0];
beta[1] = Autocorr[1];
k[1] = Autocorr[1] / Autocorr[0];
AR_Coeff[1] = k[1];

// itertive calcul :
for (n = 1; n < OrderAR; n++) {

// Last coefficient calcul
// Step 1 : invert Coeff array
for (i = 1; i < n + 1; i++) AR_Coeff_inv[n+1-i] = AR_Coeff;

// Step 2
temp = 0;
for (i = 1; i < n + 1; i++) temp = temp + Autocorr * AR_Coeff_inv;
beta[n+1] = Autocorr[n+1] - temp;

// Step 3
alpha[n+1] = alpha[n] * (1 - k[n]*k[n]);

// Step 4
k[n+1] = beta[n+1] / alpha[n+1];
AR_Coeff[n+1] = k[n+1];

// Other older coefficients calcul
// Step 5
for (i = 1; i < n + 1; i++) New_AR_Coeff = AR_Coeff - k[n+1] * AR_Coeff_inv;

// Step 6
New_AR_Coeff[n+1] = AR_Coeff[n+1];

// Update
AR_Coeff = New_AR_Coeff;
}
}



// Prediction to +1 :
//Data = Data * Data_max;
AR_data = 0;
for (i = 1; i < OrderAR + 1; i++) {
AR_data = AR_data + AR_Coeff * Ref(Data,-i);
printf("Coeff AR " + NumToStr(i, 1.0) + " = " + NumToStr(AR_Coeff, 1.9) + "\n");
}
AR_data = IIf(BI < BegBar, -1e10, IIf(BI > EndBar, -1e10, AR_data));


// Prdiction to +Forward
AR_data_pred = IIf(BI > EndBar, -1e10, Data); // to be sure not to compute future value
for (i = EndBar + 1; i < EndBar + 1 + ExtraF; i++) {
temp = 0;
for (j = 1; j < OrderAR + 1; j++) {
temp = temp + AR_Coeff[j] * AR_data_pred[i-j];
}
AR_data_pred = temp;
}
for (i = EndBar + 1; i < EndBar + 1 + ExtraF; i++) {
AR_data = AR_data_pred;
}


// End
return AR_data;
}


// *********************************************************
// *
// * Demo AFL to use AR Prediction
// *
// *********************************************************

SetBarsRequired(20000,20000);

BI = BarIndex();
current_pos = SelectedValue( BI ) - BI[ 0 ];
printf( "Position: " + WriteVal(current_pos) + "\n" );


// Denoising and detrending for stationnarity
data_source = ParamField("Price field",-1);
centeredT3 = f_centeredT3(data_source);
data = f_detrend(centeredT3);


// Choice of parameters
Methode = Param("Methode 0:DL, 1:GE", 0, 0, 1, 1);
longueur = Param("Longueur", 200, 1, 5000, 1);
OrderAR = Param("nth Order AR", 2, 1, 50, 1);
ExtraF = Param("Extrapolate Forwards", 0, 0, 50, 1);


BegBar = current_pos - longueur - slide;
EndBar = current_pos - slide;


// Prediction calcul
AR_pred = AR(data, BegBar, EndBar, OrderAR, ExtraF, Methode);
AR_pred = f_retrend(AR_pred, centeredT3[EndBar], EndBar, EndBar + slide + ExtraF);


// Reconstruct data + prediction
Data_reconstruct = -1e10;
Data_reconstruct = IIf( BI <= EndBar AND BI >= BegBar, centeredT3, AR_pred);


// Plot result
Plot(Data_reconstruct, "AR Prediction - " + NumToStr(OrderAR, 1.0), IIf(BI > EndBar + slide, colorRed, IIf(BI > EndBar AND BI <= EndBar + slide, colorBlue, colorBrightGreen)), styleThick, Null, Null, 0);
_SECTION_END();
 

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