Shari Van Elsen-Exponential Smoothing-niet werkzoekende werklozen

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 12:32:54 -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/May/28/t1211999665cz381a4e8h64249.htm/, Retrieved Wed, 28 May 2008 20:34:29 +0200

User-defined keywords:

Dataseries X:

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516.922 514.258 509.846 527.070 541.657 564.591 555.362 498.662 511.038 525.919 531.673 548.854 560.576 557.274 565.742 587.625 619.916 625.809 619.567 572.942 572.775 574.205 579.799 590.072 593.408 597.141 595.404 612.117 628.232 628.884 620.735 569.028 567.456 573.100 584.428 589.379 590.865 595.454 594.167 611.324 612.613 610.763 593.530 542.722 536.662 543.599 555.332 560.854 562.325 554.788 547.344 565.464 577.992 579.714 569.323 506.971 500.857 509.127 509.933 517.009 519.164 512.238 509.239 518.585 522.975 525.192 516.847 455.626 454.724 461.251 470.439 474.605 476.049 471.067 470.984 502.831 512.927 509.673 484.015 431.328 436.087 442.867 447.988 460.070 467.037 460.170 464.196 485.025 501.492 520.564 488.180 439.148 441.977 456.608 461.935 480.961 492.865

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.888914021311308 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 560.576 535.631623943236 24.9443760567635 14 557.274 548.732821239622 8.54117876037787 15 565.742 559.125819798248 6.6161802017516 16 587.625 582.305743480441 5.31925651955896 17 619.916 615.307938516962 4.60806148303811 18 625.809 621.574442313632 4.23455768636757 19 619.567 616.011183348429 3.55581665157058 20 572.942 569.517873627223 3.42412637277732 21 572.775 569.49758590406 3.27741409594034 22 574.205 571.584508580918 2.62049141908244 23 579.799 578.140900146066 1.65809985393400 24 590.072 589.413183354962 0.65881664503786 25 593.408 600.145118468587 -6.73711846858725 26 597.141 583.262025839998 13.8789741600016 27 595.404 598.186025223382 -2.78202522338177 28 612.117 612.867682291489 -0.750682291488602 29 628.232 640.395219813697 -12.1632198136972 30 628.884 631.712005475546 -2.82800547554643 31 620.735 619.795336477195 0.939663522805176 32 569.028 570.961862614428 -1.93386261442754 33 567.456 566.162485677649 1.29351432235148 34 573.1 566.412917130405 6.68708286959463 35 584.428 576.477250645962 7.9507493540375 36 589.379 593.232151873451 -3.853151873451 37 590.865 599.131750216861 -8.26675021686117 38 595.454 583.179105306172 12.2748946938277 39 594.167 594.826412538341 -0.659412538341257 40 611.324 611.620543501636 -0.296543501635597 41 612.613 638.28399846179 -25.6709984617898 42 610.763 618.630541707602 -7.86754170760219 43 593.53 602.652693489727 -9.12269348972688 44 542.722 544.555440927838 -1.83344092783761 45 536.662 540.203846561932 -3.54184656193149 46 543.599 536.755207767244 6.84379223275607 47 555.332 547.099218061146 8.23278193885358 48 560.854 562.793574087544 -1.93957408754432 49 562.325 569.9038896642 -7.57888966420023 50 554.788 556.844582372258 -2.05658237225805 51 547.344 554.315618516736 -6.97161851673627 52 565.464 565.539050742508 -0.0750507425084379 53 577.992 589.580647558929 -11.5886475589292 54 579.714 584.422904392901 -4.70890439290088 55 569.323 571.113383408181 -1.79038340818056 56 506.971 520.343657841127 -13.3726578411266 57 500.857 505.544911854185 -4.68791185418473 58 509.127 502.23121840169 6.89578159830972 59 509.933 512.775740052483 -2.84274005248290 60 517.009 517.494903162678 -0.485903162677914 61 519.164 525.270958316853 -6.10695831685291 62 512.238 514.13352234812 -1.89552234812038 63 509.239 511.201735405928 -1.96273540592773 64 518.585 527.6437460408 -9.05874604079986 65 522.975 542.420610972802 -19.4456109728018 66 525.192 531.042945865977 -5.85094586597734 67 516.847 517.042454962831 -0.195454962831377 68 455.626 466.403855363012 -10.7778553630118 69 454.724 454.876419189022 -0.152419189021543 70 461.251 456.881174684145 4.36982531585477 71 470.439 464.098525169685 6.3404748303152 72 474.605 477.242588282427 -2.63758828242732 73 476.049 482.481559951146 -6.4325599511456 74 471.067 471.5225236106 -0.455523610599926 75 470.984 469.863305308553 1.12069469144740 76 502.831 488.257952904555 14.5730470954454 77 512.927 522.887615047615 -9.96061504761451 78 509.673 521.451472489106 -11.7784724891062 79 484.015 502.810165800906 -18.7951658009059 80 431.328 434.462466139456 -3.13446613945638 81 436.087 430.909682793006 5.17731720699373 82 442.867 438.154473657135 4.71252634286515 83 447.988 445.895367420668 2.09263257933196 84 460.07 454.266127068585 5.80387293141496 85 467.037 466.587263828728 0.44973617127215 86 460.17 462.409961941763 -2.23996194176311 87 464.196 459.339627139689 4.85637286031056 88 485.025 482.549339171564 2.47566082843611 89 501.492 503.700119170681 -2.20811917068079 90 520.564 508.953340424332 11.6106595756676 91 488.18 510.323504931112 -22.1435049311117 92 439.148 440.739103817559 -1.59110381755869 93 441.977 439.481559466696 2.49544053330413 94 456.608 444.290760804127 12.3172391958732 95 461.935 458.500556987963 3.43444301203732 96 480.961 468.476337510113 12.4846624898867 97 492.865 486.141352260178 6.72364773982179 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 98 487.242230587701 471.034855510506 503.449605664895 99 486.951332659455 465.266324278711 508.6363410402 100 505.579683037047 479.545087398684 531.61427867541 101 524.009511128592 494.254498918324 553.764523338859 102 532.760633035108 499.701272284887 565.819993785329 103 520.06030504935 483.998109958183 556.122500140516 104 472.442659542139 433.609136699453 511.276182384826 105 473.053427462737 431.63358827964 514.473266645833 106 476.73546083768 432.881570935715 520.589350739645 107 479.009536288885 432.849767646552 525.169304931219 108 486.937744750286 438.581929973841 535.293559526731 109 492.865 442.408628704851 543.321371295149

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/1ndn01211999567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/1ndn01211999567.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/2fvwe1211999567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/2fvwe1211999567.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/380581211999567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211999665cz381a4e8h64249/380581211999567.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

Copyright

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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