Time series forecasting: double exponential smoothing - Revision history

A WASSERMANN at 23:03, 14 July 2010

2010-07-14T23:03:47Z

A WASSERMANN at 17:01, 9 July 2009

2009-07-09T17:01:10Z

← Older revision		Revision as of 17:01, 9 July 2009
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	The data is the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php].		The data is from the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php].

	The dashed curve are the observed values. The blue curve are the predicted values and it is computed by the following rules:		The dashed curve are the observed values. The blue curve are the predicted values and it is computed by the following rules:

A WASSERMANN at 17:00, 9 July 2009

2009-07-09T17:00:48Z

← Older revision		Revision as of 17:00, 9 July 2009
Line 8:		Line 8:

	Then, the values are iteratively computed by		Then, the values are iteratively computed by
	:<math>S_t = \alpha\cdot y_t + (1-\alpha)\cdot(S_{t-1} + b_{t-1});</math>		:<math>S_t = \alpha\cdot y_t + (1-\alpha)\cdot(S_{t-1} + b_{t-1})</math>
	:<math>b_t = \gamma\cdot(S_t - S_{t-1}) + (1-\gamma)\cdot b_{t-1};</math>		:<math>b_t = \gamma\cdot(S_t - S_{t-1}) + (1-\gamma)\cdot b_{t-1}</math>

			Here, the time series <math>y</math> is stored in the array ''data''.
	<jsxgraph width="700" height="500">		<jsxgraph width="700" height="500">
	var data, datax, i, brd;		var data, datax, i, brd;

A WASSERMANN at 16:59, 9 July 2009

2009-07-09T16:59:14Z

← Older revision		Revision as of 16:59, 9 July 2009
Line 1:		Line 1:
	The data is the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php].		The data is the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php].

	The dashed curve are the observed values~~, the~~ blue curve are the predicted values.		The dashed curve are the observed values. The blue curve are the predicted values and it is computed by the following rules:

			Initial values:
			:<math> S_0 = y_0</math>
			:<math> b_0 = y_1-y_0</math>

			Then, the values are iteratively computed by
			:<math>S_t = \alpha\cdot y_t + (1-\alpha)\cdot(S_{t-1} + b_{t-1});</math>
			:<math>b_t = \gamma\cdot(S_t - S_{t-1}) + (1-\gamma)\cdot b_{t-1};</math>

	<jsxgraph width="700" height="500">		<jsxgraph width="700" height="500">
	var data, datax, i, brd;		var data, datax, i, brd;
Line 58:		Line 67:
	//		//
	// global array data		// 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 = "406.60 428.50 ... 521.80 524.40 526.80";
	data = data.split(' ');		data = data.split(' ');
	datax = [];		datax = [];

A WASSERMANN at 16:54, 9 July 2009

2009-07-09T16:54:14Z

@@ Line 52: / Line 52: @@
 ===The JavaScript code===
 <source lang="javascript">
 </source>
 [[Category:Examples]]
 [[Category:Statistics]]

A WASSERMANN at 16:53, 9 July 2009

2009-07-09T16:53:24Z

← Older revision		Revision as of 16:53, 9 July 2009
Line 2:		Line 2:

	The dashed curve are the observed values, the blue curve are the predicted values.		The dashed curve are the observed values, the blue curve are the predicted values.
	<jsxgraph width="~~500~~" height="500">		<jsxgraph width="700" height="500">
	var data, datax, i, brd;		var data, datax, i, brd;

A WASSERMANN: New page: The data is the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php]. The dashed curv...

2009-07-09T16:52:50Z

New page: The data is the file zurich.txt from [http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php http://statistik.mathematik.uni-wuerzburg.de/timeseries/index.php]. The dashed curv...

New page

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

The dashed curve are the observed values, the blue curve are the predicted values.
<jsxgraph width="500" height="500">
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:'α'});
gamma = brd.createElement('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'γ'});

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.
</jsxgraph>

===The JavaScript code===
<source lang="javascript">
</source>

[[Category:Examples]]
[[Category:Statistics]]

← Older revision		Revision as of 23:03, 14 July 2010
Line 29:		Line 29:

	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 550, data.length+2, 380], grid: false});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 550, data.length+2, 380], grid: false});
	brd.~~createElement~~('axis',[[0,0],[0,1]]);		brd.create('axis',[[0,0],[0,1]]);
	brd.~~createElement~~('axis',[[0,400],[1,400]]);		brd.create('axis',[[0,400],[1,400]]);

	brd.~~createElement~~('curve',[datax,data],{strokeColor:'gray',dash:2}); // plot the observed data		brd.create('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:'α'});		alpha = brd.create('slider', [[10,520],[100,520],[0,0.1,1.0]],{name:'α'});
	gamma = brd.~~createElement~~('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'γ'});		gamma = brd.create('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'γ'});

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

	estimate.updateDataArray = function() {		estimate.updateDataArray = function() {
Line 78:		Line 78:

	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 550, data.length+2, 380], grid: false});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 550, data.length+2, 380], grid: false});
	brd.~~createElement~~('axis',[[0,0],[0,1]]);		brd.create('axis',[[0,0],[0,1]]);
	brd.~~createElement~~('axis',[[0,400],[1,400]]);		brd.create('axis',[[0,400],[1,400]]);

	brd.~~createElement~~('curve',[datax,data],{strokeColor:'gray',dash:2}); // plot the observed data		brd.create('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:'α'});		alpha = brd.create('slider', [[10,520],[100,520],[0,0.1,1.0]],{name:'α'});
	gamma = brd.~~createElement~~('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'γ'});		gamma = brd.create('slider', [[10,510],[100,510],[0,0.1,1.0]],{name:'γ'});

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

	estimate.updateDataArray = function() {		estimate.updateDataArray = function() {