KDGP2W102

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:41:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs.htm/, Retrieved Wed, 18 May 2011 16:38:03 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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41 39 50 40 43 38 44 35 39 35 29 49 50 59 63 32 39 47 53 60 57 52 70 90 74 62 55 84 94 70 108 139 120 97 126 149 158 124 140 109 114 77 120 133 110 92 97 78 99 107 112 90 98 125 155 190 236 189 174 178 136 161 171 149 184 155 276 224 213 279 268 287 238 213 257 293 212 246 353 339 308 247 257 322 298 273 312 249 286 279 309 401 309 328 353 354 327 324 285 243 241 287 355 460 364 487 452 391 500 451 375 372 302 316 398 394 431 431

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.213143664571728 beta 0.00645020019309578 gamma 0.424943606209328 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50 47.1054399101549 2.89456008984506 14 59 55.9623334237949 3.03766657620507 15 63 59.6005878986157 3.39941210138434 16 32 30.4393736626745 1.56062633732548 17 39 36.5604009451042 2.43959905489584 18 47 42.8251094355241 4.17489056447594 19 53 56.0035962549115 -3.00359625491154 20 60 43.6874883540302 16.3125116459698 21 57 51.8988510976764 5.10114890232358 22 52 48.2401909021988 3.7598090978012 23 70 41.8819045749854 28.1180954250146 24 90 81.8658655722616 8.13413442773837 25 74 86.9533818199762 -12.9533818199762 26 62 97.59893837588 -35.5989383758799 27 55 94.1112419276597 -39.1112419276597 28 84 42.9292530224352 41.0707469775648 29 94 61.2354810756631 32.7645189243369 30 70 78.9123828735137 -8.91238287351375 31 108 93.1912445312896 14.8087554687104 32 139 85.7451682403308 53.2548317596692 33 120 98.1611181026277 21.8388818973723 34 97 92.3826877848778 4.61731221512221 35 126 92.4133341597528 33.5866658402472 36 149 146.190315323712 2.80968467628821 37 158 139.583025059722 18.4169749402784 38 124 151.406900840488 -27.4069008404876 39 140 147.812296583395 -7.81229658339467 40 109 108.535321209427 0.464678790573487 41 114 117.503833288205 -3.50383328820544 42 77 111.491890235354 -34.4918902353538 43 120 137.39274145732 -17.39274145732 44 133 133.550538091547 -0.55053809154694 45 110 121.870273958662 -11.8702739586622 46 92 101.636565226357 -9.6365652263573 47 97 107.771493254877 -10.7714932548772 48 78 139.961931816656 -61.9619318166555 49 99 124.886206798664 -25.8862067986642 50 107 113.177831745124 -6.1778317451242 51 112 119.061002171178 -7.06100217117785 52 90 89.025113480404 0.974886519596055 53 98 95.4199629759895 2.58003702401052 54 125 82.3202326698113 42.6797673301887 55 155 129.630849234439 25.3691507655606 56 190 140.700154878202 49.2998451217977 57 236 133.529531758246 102.470468241754 58 189 132.209757472178 56.790242527822 59 174 155.570702285706 18.4292977142937 60 178 182.914272374356 -4.91427237435593 61 136 198.150377986194 -62.1503779861937 62 161 185.047759625669 -24.0477596256693 63 171 190.702749040376 -19.7027490403756 64 149 144.299472155167 4.70052784483343 65 184 155.819588965496 28.1804110345041 66 155 158.658606313424 -3.65860631342397 67 276 205.406540582624 70.5934594173757 68 224 239.226122351407 -15.2261223514072 69 213 228.979468223588 -15.9794682235881 70 279 177.769152238656 101.230847761344 71 268 197.045259744193 70.9547402558069 72 287 231.909422911663 55.0905770883368 73 238 237.520355788563 0.479644211436948 74 213 255.630083725713 -42.630083725713 75 257 263.55145139239 -6.5514513923896 76 293 212.264665165241 80.7353348347592 77 212 257.289537670045 -45.289537670045 78 246 227.386238467003 18.6137615329972 79 353 335.435918697595 17.5640813024049 80 339 324.956767280605 14.0432327193946 81 308 317.200424013297 -9.20042401329687 82 247 297.353097436938 -50.3530974369376 83 257 269.048143450591 -12.0481434505908 84 322 281.58562500724 40.41437499276 85 298 263.01824072365 34.9817592763499 86 273 273.783458765984 -0.783458765984278 87 312 307.634036808232 4.36596319176772 88 249 281.39354454695 -32.3935445469503 89 286 258.376361117543 27.6236388824572 90 279 265.247190210507 13.7528097894926 91 309 384.965513568946 -75.9655135689458 92 401 352.066686631739 48.9333133682611 93 309 342.098302816729 -33.0983028167292 94 328 300.232758213022 27.7672417869783 95 353 300.52637748455 52.4736225154502 96 354 349.806600446728 4.19339955327212 97 327 316.668359676069 10.3316403239307 98 324 308.931172358704 15.0688276412964 99 285 352.763567038031 -67.7635670380308 100 243 294.805200411893 -51.8052004118931 101 241 287.646325003512 -46.6463250035125 102 287 273.798827019887 13.2011729801129 103 355 363.304616749659 -8.30461674965943 104 460 387.219805983285 72.7801940167154 105 364 351.471344673296 12.5286553267037 106 487 337.976115293889 149.023884706111 107 452 371.926430917621 80.073569082379 108 391 414.750270368213 -23.7502703682132 109 500 372.294169448289 127.705830551711 110 451 388.943639219658 62.0563607803422 111 375 417.178199639249 -42.1781996392486 112 372 357.815125604945 14.1848743950554 113 302 367.547487313136 -65.5474873131365 114 316 375.106366255874 -59.1063662558744 115 398 464.864989196216 -66.8649891962161 116 394 515.546883764625 -121.546883764625 117 431 407.554042998301 23.4459570016993 118 431 441.367396683969 -10.367396683969 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 119 415.894057518493 370.117254719446 461.67086031754 120 406.642333118478 357.656358905109 455.628307331848 121 416.914953425497 364.473432897251 469.356473953742 122 385.423295300731 331.314231281724 439.532359319739 123 366.87274006942 310.844594442455 422.900885696386 124 337.324017241984 280.33001388933 394.318020594639 125 317.963806162545 259.61746165562 376.310150669471 126 339.857506927664 276.953324752322 402.761689103007 127 437.892047535513 362.264104046423 513.519991024603 128 483.199372564462 400.109727283842 566.289017845081 129 446.77259110999 366.237817302377 527.307364917603 130 465.193408486715 388.409600198748 541.977216774682

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/174i11305729680.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/174i11305729680.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/28j0y1305729680.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/28j0y1305729680.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/3jzk01305729680.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057294802178k5on53126zs/3jzk01305729680.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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