Time series forecasting: double exponential smoothing

The data is the file zurich.txt from http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php.

The dashed curve are the observed values, the blue curve are the predicted values.

The JavaScript code

    var data, datax, i, brd;
    
    //
    // zurich.txt from http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php
    //
    // global array data
    data = "406.60 428.50 429.30 426.30 434.70 415.90 419.00 408.80 410.10 408.30 420.40 415.20 409.70 408.90 411.00 410.60 409.60 409.50 409.80 413.00 417.90 415.80 415.50 421.30 423.50 426.80 426.60 427.20 433.30 435.00 442.50 447.00 450.60 448.90 446.20 443.60 446.30 448.20 452.40 451.30 451.80 459.90 464.70 467.30 463.50 466.60 461.10 464.90 467.30 458.40 458.80 463.20 462.40 461.10 465.50 461.50 458.20 460.80 459.30 445.70 425.10 437.60 438.00 436.60 437.60 437.60 438.60 443.10 446.40 445.90 450.80 451.60 457.30 456.70 455.60 454.75 453.90 451.20 450.70 446.80 443.40 448.40 451.80 449.80 449.10 447.60 448.40 450.00 443.00 440.60 437.40 435.40 432.00 430.80 429.60 437.10 440.00 438.30 435.20 436.60 435.25 433.90 436.50 436.30 437.40 441.00 445.40 450.10 449.20 450.50 455.60 452.00 451.80 456.80 455.30 457.40 457.40 461.10 459.60 462.40 463.40 464.60 469.00 472.20 471.80 470.10 465.20 470.40 468.50 468.70 469.70 472.50 474.70 472.40 475.00 476.10 473.20 471.50 472.20 471.10 472.80 470.40 470.50 472.10 471.10 468.50 465.50 465.70 465.40 466.90 468.85 470.80 474.00 478.10 480.50 481.00 479.10 476.40 469.80 471.60 470.60 467.20 473.10 471.70 474.80 477.20 474.60 475.10 475.90 475.80 472.00 470.80 469.10 464.30 463.70 467.20 467.30 467.10 465.60 462.70 449.45 436.20 466.00 467.40 467.00 471.50 469.80 474.20 476.10 477.10 480.30 478.70 478.80 479.30 479.30 478.30 477.20 480.20 484.10 488.70 492.70 492.60 491.90 491.90 495.10 494.50 494.50 496.90 496.20 498.40 498.00 496.00 497.90 495.40 497.30 495.20 499.20 500.60 497.90 499.60 497.00 498.10 496.70 491.40 487.60 486.70 487.40 489.30 485.30 501.80 485.40 491.30 495.50 501.80 504.50 502.50 505.80 510.30 511.90 509.90 508.70 510.70 512.90 512.90 513.80 516.10 512.10 511.10 505.30 505.10 505.20 508.40 510.70 511.30 514.90 517.30 519.70 521.80 524.40 526.80";
    data = data.split(' ');
    datax = [];
    for (i = 0; i < data.length; i++)  { 
        data[i] = parseFloat(data[i]); 
        datax[i] = i;
        }
    
    
    brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 550, data.length+2, 380], grid: false});
    brd.createElement('axis',[[0,0],[0,1]]);
    brd.createElement('axis',[[0,400],[1,400]]);

    brd.createElement('curve',[datax,data],{strokeColor:'gray',dash:2});                    // plot the observed data

    alpha = brd.createElement('slider', [[10,520],[100,520],[0,0.1,1.0]],{name:'&alpha;'});   
    gamma = brd.createElement('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'&gamma;'});

    estimate = brd.createElement('curve',[[0],[0]]);                                        // The filtered curve

    estimate.updateDataArray = function() { 
            var t,
                alphalocal = alpha.Value(),  // Read the slider value of alpha
                gammalocal = gamma.Value(),  // Read the slider value of gamma 
                S = data[0],                 // Set the inital values for S and b
                b = data[1]-data[0],
                Snew;
                
            this.dataX[0] = 0;
            this.dataY[0] = S;
            for (t=1; t<data.length; t++) {
                Snew = alphalocal*data[t] + (1-alphalocal)*(S + b);
                b    = gammalocal*(Snew - S) + (1-gammalocal)*b;
                this.dataX[t] = t;
                this.dataY[t] = Snew;
                S = Snew;
            }
        }
     brd.update(); // first computation of the filtered curve.