// Downloaded From https://www.WiseStockTrader.com _SECTION_BEGIN("tomy_frenchy"); //------------------------------------------------------------------------------ // // Author/Uploader: tomy_frenchy - tom_borgo [at] hotmail.com //------------------------------------------------------------------------------ // // 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[i] = data[i] - data[i-1]; return detrended; } function f_retrend(data, first_value, first_index, last_index) { for (i = 0; i < first_index; i++) retrended[i] = -1e10; retrended[first_index]=first_value; for (i = first_index + 1; i < last_index + 1; i++) retrended[i] = data[i] + retrended[i-1]; for (i = last_index + 1; i < BarCount; i++) retrended[i] = -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[i]=(1/(LongBar))*temp; //biased estimator, small variance Autocorr[i]=(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[i]; // Step 2 temp = 0; for (i = 1; i < n + 1; i++) temp = temp + Autocorr[i] * AR_Coeff_inv[i]; 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[i] = AR_Coeff[i] - k[n+1] * AR_Coeff_inv[i]; // 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[i] * Ref(Data,-i); printf("Coeff AR " + NumToStr(i, 1.0) + " = " + NumToStr(AR_Coeff[i], 1.9) + "\n"); } AR_data = IIf(BI < BegBar, -1e10, IIf(BI > EndBar, -1e10, AR_data)); // PrÃ©diction 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[i] = temp; } for (i = EndBar + 1; i < EndBar + 1 + ExtraF; i++) { AR_data[i] = AR_data_pred[i]; } // 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();