simple model

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 16 Jul 2008 04:09:55 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u.htm/, Retrieved Wed, 16 Jul 2008 10:10:53 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

385.34 438.82 317.22 505.15 513.57 515.48 519.31 524.42 430.38 527.86 467.25 547.68 428.1 519.38 404.74 377.95 439.9 434.65 472.25 434.87 468.36 486 476.66 422.87 321.15 360.79 435.66 493.59 472.93 469.13 608.37 562.38 525.81 415.59 398.06 436.89 434.64 432.37 436.46 454.18 353.71 486.32 397.47 340.25 427.57 472.29 466.95 463.79 332.87 396.88 400.09 513.36 559.07 602.5 436.19 309.19 443.44 429.61 669.12 441.38 440.42 471.11 372.26 308.55 330.52 439.67 442.34 434.54 490.87 343.64 343.52 338.43 424.45 358.84 341.53 330.08 497.54 333.63 362.37 398.84 471.53 289.33 351.94 510.98 461.96 347.99 436.01 499.4 516.88 421.33 291.39 374.25 398.23 365.47 399.48 356.31 355.06 389.09 285.71 392 456.03 421.94 403.81 396.69 502.69 358.37 521.93 463.62 426.42 485.72 401.01 531.99 430.61 343.58 315.35 307.93 443.44 424.78 409.02 396.94 337.55 403.86 393.54 330.8 269.71 297.89 416.37 532.98 427.62 260.76 299.12 339.37 409.16 416.12 388.47 374.89 430.87 494 477.09 458.11 404.04 327.33 308.86 354.6 345.44 490.86 558.26 372.58 380.16 367.25 321.93 303.8 411.05 501.1 376.05 593.39 378.92 544.44 436.73 325.05 350.66 366.97 316.25 332.28 354.6 567.46 464.75 418.27 370.65 500.3 435.1 414.71 470.8 475.48 589.4 769.36 437.62 337.55 383.22 328.85 330.94 370.53 536.53 484.39 410.36 429.9 420.29 487.75 542.87 478.49 393.81 332.17 437.82 433.74 473.94 492.12 429.77 486.14 523.94 400.85 365.03 309.43 340.65 400.06 407.61 427.46 512.95 457.17 438.17 339.29 326.9 405.07 518.25 512.58 606.84 551.57 460.45 410.94 478.4 516.75 460.18 434.73 425.87 416.21 400.46 408.78 450.6 352.62 519.44 294.28 344.59 438.06 350.12 437.82 428.98 446.66 409.37 463.74 560.29 572.95 477.94 394.91 370.99 446.05 448.95 341.22 235.96 334.07 457.87 614.63 414.79 403.8 501.73 386.21 448.13 374.19 423.79 454.79 390.3 358.65 335.02 321.85 329.94 342.15 584.59 451.13 423.44 442.77 370.56 383.49 428.35 432.89 508.39 554.24 415.83 383.48 287.35 280.27 424.89 376.05 421.94 382.62 508.37 290.79 206.38 308.37 505.04 511.66 596.84 330.39 293.53 560.72 482.61 563.69 295.73 295.19 338.19 407.33 477.14 428.89 614.89 628.98 786.59 472.22 319.54 331.44 317.86 300.61 373.81 401 569.96 349.32 417.3 495.64 465.46 431.26 415.03 466.93 506.33 478.2 486.57 450.41 713.47 754.51 375.6 343.75 551.51 447.13 396.4 474.09 525.82 591.87 654.39 668.46 732.83 531.97 471.77 525.22 415.67 483.73 533.49 534.96 479.64 573.62 599.54 768.71 566.73 570.12 574.29 617.31 638.5 507.23 493.42 642.42 697.01 535.03 432.21 446.66 631.22 703.81 561.97 652.98 709.05 539 458.89 523.21 573.84 766.18 571.81 677.8 580.64 565.14 611.92 569.39 547.63 525.8 523.33 607.71 526.63 515.49 514.28 493.1 495.36 629.82 657.57 669.76 632.46 636.75 610.52 474.27 376.1 330.56 480.97 491.44 582.88 670.05 616.88 645.68 854.13 559.46 603.91 511.72 480.74 397.82 441.76 558.62 484.92 527.55 520.59 550.67 797.42 697.64 504.57 470.89 711.13 757.07 563.3 600.92 546.61 532.03 571.56 683.56 415.58 542.94 458.98 454.34 498.52 470.67 633.98 791.3 905.45 523.65 707.17 720.68 835.48 741.77 671.46 540.95 459.91 512.47 693.51 526.15 389.69 462.1 516.48 798.05 1006.19 588.32 713.47 641.86 838.13 528.2 776.93 707.6 663.77 455.82 546.17 557.09 495.37 570.79 525.78 658.06 659.04 543.52 791.38 750.78 561.69 540.96 451.16 476.54 495.21 617.02 673.62 510.93 503.34 525.76 642.56 820.75 475.15 392.97 381.11 385.35 497.83 549.93 506.81 525.68 497.76 541.69 663.2 678.64 651.17 497.86 583.47 808.68 701.64 551.62 522.52 537.05 537.05 539.26 656.62 651.66 632.86 835.9 841.35 741.25 618.01 777.69 764.89 756.84 801.02 755.34 590.96 744.05 633.14 534.92 572.22 685.11 727.19 720.3 684.2 614.93 575.72 620.94 655.86 772.21 756.25 687.71 603.68 653.91 658.03 875.81 874 622.04 599.86 738.64 919.68 897.71 687.41 645.95 662.24 822.04 736.15 693.71 682.87 786.37 880.52 791.95 914.2 773.57 609.17 588.11 781.7 878.29 761.48 664.59 717.18 691.07 610.89 713.66 787.88 719.53 652.11 695.46 739.78 819.39 824.47 774.19 739.28 710.02 671.53 562.67 625.09 702.37 806.92 822.81 758.54 753.24 725.16 715.06 732.43 692.81 716.5 860.77 714.09 645.9 581.26 555.99 576.22 669.32 854.82 889.11 823.62 653.6 565.62 549.91 639.7 670.66 665.73 528.24 474.14 502.55 594.4 767.06 765.84 589.06 578.99 680.74 644.8 652.78 658.08 552.37 569.73 700.34 605.86 589.14 573.16 597.47 600 553.42 499.14 489.79 472.83 501.34 491.06 453.77 484.71 566.38 457.66 403.04 365 379.49 426.48 479.02 523.12 406.11 399.38 403.81 425.48 399.38 416.23 437.43 410.49 438.55 468.95 531.23 449.37 444.73 470.4 422.93 475.12 578.56 555.82 583.9 494.33 455.6 441.78 430.74 354.89 326.81 382.2 402.06 419.86 399.31 350.37 348.73 294.49 226.73 238.97 221.57 199.37 210.14 283.55 352.49 251.66 180.66 323.39 429.25 435.36 424.63 389.79 362.98 365.56 388.13 447.39 481.22 519.89 525.06 497.16 508.05 451.48 352.42 371.14 302.85 296.23 284.45 286.1 266.88 271.51 256.11 259.78 243.45 236.43 232.8 226.41 222.4 241.52 205.09 227.62 360.59 378.85 289.3 321.45 298.97 296.12 291.2 246.31 247.13 237.6 249.05 218.01 201.32 192.78 184.83 166.84 154.3 147.24 139.44 124.68 113.2 119.97 128.81 128.21

Text written by user:

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.454679807742351 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 317.22 438.82 -121.6 4 505.15 383.53093537853 121.61906462147 5 513.57 438.828668298425 74.7413317015754 6 515.48 472.812042626904 42.6679573730958 7 519.31 492.212301282062 27.0976987179376 8 524.42 504.533077725394 19.8869222746056 9 430.38 513.575259721799 -83.195259721799 10 527.86 475.748055026416 52.1119449735835 11 467.25 499.442304148085 -32.1923041480854 12 547.68 484.805113487251 62.8748865127493 13 428.1 513.39305479869 -85.2930547986896 14 519.38 474.612025041064 44.7679749589364 15 404.74 494.967119288407 -90.2271192884072 16 377.95 453.942670037208 -75.992670037208 17 439.9 419.390337434862 20.5096625651377 18 434.65 428.715666866840 5.93433313316041 19 472.25 431.413888314904 40.836111685096 20 434.87 449.981243724829 -15.1112437248286 21 468.36 443.110466333276 25.2495336667243 22 486 454.590919446446 31.409080553554 23 476.66 468.8719941539 7.78800584610008 24 422.87 472.413043154701 -49.543043154701 25 321.15 449.886821818151 -128.736821818151 26 360.79 391.352788424512 -30.5627884245125 27 435.66 377.456505659585 58.203494340415 28 493.59 403.920459276218 89.669540723782 29 472.93 444.691388812852 28.2386111871479 30 469.13 457.530915118336 11.5990848816645 31 608.37 462.804784802318 145.565215197682 32 562.38 528.990348862374 33.3896511376259 33 525.81 544.171949022214 -18.3619490222140 34 415.59 535.823141571019 -120.233141571019 35 398.06 481.155559877249 -83.095559877249 36 436.89 443.373686688018 -6.48368668801845 37 434.64 440.425685271249 -5.78568527124855 38 432.37 437.795051004459 -5.42505100445948 39 436.46 435.328389856759 1.13161014324061 40 454.18 435.842910139127 18.3370898608727 41 353.71 444.180414631623 -90.4704146316231 42 486.32 403.045343900546 83.2746560994541 43 397.47 440.908648525656 -43.438648525656 44 340.25 421.157972165423 -80.9079721654232 45 427.57 384.370750936425 43.1992490635749 46 472.29 404.012577195265 68.2774228047347 47 466.95 435.056942669265 31.8930573307346 48 463.79 449.558071844720 14.2319281552804 49 332.87 456.029042202165 -123.159042202165 50 396.88 400.031112571953 -3.15111257195269 51 400.09 398.598365313563 1.49163468643724 52 513.36 399.276581486014 114.083418513986 53 559.07 451.148008282543 107.921991717457 54 602.5 500.217958727808 102.282041272192 55 436.19 546.723537588944 -110.533537588944 56 309.19 496.466169968921 -187.276169968921 57 443.44 411.315477012728 32.124522987272 58 429.61 425.921848948396 3.68815105160445 59 669.12 427.598776759464 241.521223240536 60 441.38 537.413600108168 -96.0336001081683 61 440.42 493.74906127418 -53.3290612741804 62 471.11 469.501413946956 1.60858605304395 63 372.26 470.232805544291 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478.702246901806 -72.5922469018061 637 399.38 445.696018036908 -46.3160180369076 638 403.81 424.637059860495 -20.8270598604952 639 425.48 415.167416287287 10.3125837127133 640 399.38 419.85633986711 -20.4763398671101 641 416.23 410.546161593065 5.68383840693457 642 437.43 413.130488147169 24.2995118528310 643 410.49 424.178985524647 -13.6889855246472 644 438.55 417.954880218113 20.5951197818873 645 468.95 427.319065320972 41.630934679028 646 531.23 446.247810696967 84.9821893030332 647 449.37 484.887496190794 -35.5174961907941 648 444.73 468.738407851274 -24.0084078512741 649 470.4 457.822269585257 12.5777304147431 650 422.93 463.541109632067 -40.6111096320673 651 475.12 445.076058112355 30.0439418876446 652 578.56 458.736431833652 119.823568166348 653 555.82 513.21778877053 42.6022112294704 654 583.9 532.588153981744 51.3118460182557 655 494.33 555.91861426423 -61.58861426423 656 455.6 527.915514971452 -72.315514971452 657 441.78 495.035110527443 -53.2551105274431 658 430.74 470.821087111528 -40.0810871115276 659 354.89 452.597026129554 -97.7070261295538 660 326.81 408.171614273891 -81.3616142738913 661 382.2 371.178131138231 11.0218688617690 662 402.06 376.189552353262 25.8704476467385 663 419.86 387.952322515489 31.9076774845109 664 399.31 402.460099179651 -3.15009917965148 665 350.37 401.027812690278 -50.6578126902782 666 348.73 377.994728155614 -29.2647281556144 667 294.49 364.688647184188 -70.1986471841875 668 226.73 332.770739778708 -106.040739778708 669 238.97 284.556156603268 -45.5861566032683 670 221.57 263.829051683182 -42.2590516831816 671 199.37 244.614714188498 -45.2447141884984 672 210.14 224.042856239914 -13.9028562399144 673 283.55 217.721508237681 65.8284917623195 674 352.49 247.652394216141 104.837605783859 675 251.66 295.319936658114 -43.6599366581144 676 180.66 275.468645052360 -94.8086450523597 677 323.39 232.36106854764 91.02893145236 678 429.25 273.750085599391 155.499914400609 679 435.36 344.452756783012 90.9072432169881 680 424.63 385.786444651299 38.8435553487008 681 389.79 403.447824929276 -13.6578249292759 682 362.98 397.237887716254 -34.257887716254 683 365.56 381.661517915769 -16.1015179157686 684 388.13 374.340482845467 13.7895171545331 685 447.39 380.61029785415 66.7797021458501 686 481.22 410.973679986916 70.2463200130836 687 519.89 442.913263265073 76.976736734927 688 525.06 477.913031124343 47.1469688756567 689 497.16 499.349805868361 -2.18980586836142 690 508.05 498.354145357142 9.6958546428582 691 451.48 502.762654682054 -51.2826546820544 692 352.42 479.445467110701 -127.025467110701 693 371.14 421.689552146425 -50.5495521464248 694 302.85 398.705691495026 -95.8556914950264 695 296.23 355.122044115058 -58.8920441150576 696 284.45 328.345020819269 -43.8950208192692 697 286.1 308.386841192317 -22.2868411923173 698 266.88 298.25346452381 -31.3734645238102 699 271.51 283.988583705913 -12.4785837059127 700 256.11 278.314823665611 -22.2048236656115 701 259.78 268.218738710378 -8.43873871037846 702 243.45 264.381814615956 -20.9318146159556 703 236.43 254.864541170674 -18.4345411706744 704 232.8 246.482727535374 -13.6827275353737 705 226.41 240.261467610199 -13.851467610199 706 222.4 233.963484980244 -11.5634849802443 707 241.52 228.705801852595 12.8141981474048 708 205.09 234.532159002630 -29.4421590026296 709 227.62 221.145403807794 6.47459619220575 710 360.59 224.089271959676 136.500728040324 711 378.85 286.153396741741 92.6966032582587 712 289.3 328.300670489575 -39.0006704895754 713 321.45 310.567853129552 10.8821468704475 714 298.97 315.515745576432 -16.5457455764316 715 296.12 307.992729158786 -11.8727291587858 716 291.2 302.594438947492 -11.3944389474921 717 246.31 297.413617637514 -51.1036176375144 718 247.13 274.177834595151 -27.0478345951507 719 237.6 261.879730361581 -24.2797303615806 720 249.05 250.840227228741 -1.79022722874100 721 218.01 250.026247056562 -32.0162470565620 722 201.32 235.469106000253 -34.1491060002527 723 192.78 219.942197049485 -27.1621970494847 724 184.83 207.592094517165 -22.7620945171651 725 166.84 197.242629758287 -30.4026297582872 726 154.3 183.419167904927 -29.1191679049273 727 147.24 170.179270240298 -22.9392702402977 728 139.44 159.749247257689 -20.3092472576893 729 124.68 150.515042619171 -25.8350426191712 730 113.2 138.768370408071 -25.568370408071 731 119.97 127.142948666644 -7.17294866664406 732 128.81 123.881553745949 4.92844625405142 733 128.21 126.122418741209 2.08758125879081 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 734 127.071599786603 -55.7914234089559 309.934622982161

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/124o41216202985.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/124o41216202985.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/2qkda1216202985.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/2qkda1216202985.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/3rb0a1216202985.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t1216203048pur9i914il4dk9u/3rb0a1216202985.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 1 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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