*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, 29 Dec 2010 22:33:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp.htm/, Retrieved Wed, 29 Dec 2010 23:31:59 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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206010 198112 194519 185705 180173 176142 203401 221902 197378 185001 176356 180449 180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 etc...

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 1 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.786721671208313 beta 0.155737227444672 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 180144 192256.77590812 -12112.7759081197 14 173666 174646.428106398 -980.428106397972 15 165688 164180.807371189 1507.19262881079 16 161570 159602.165810085 1967.83418991519 17 156145 154188.606970165 1956.39302983464 18 153730 152119.123018618 1610.876981382 19 182698 179952.348401522 2745.65159847779 20 200765 200442.561219332 322.43878066825 21 176512 176164.427462601 347.572537398606 22 166618 164082.693874569 2535.30612543123 23 158644 157564.603112553 1079.39688744742 24 159585 162699.575040561 -3114.57504056091 25 163095 157033.520593309 6061.47940669145 26 159044 158060.686855114 983.31314488608 27 155511 151876.285741273 3634.7142587268 28 153745 151536.070533914 2208.92946608641 29 150569 148805.699979991 1763.30002000884 30 150605 148982.909933437 1622.09006656322 31 179612 179540.649021071 71.3509789286763 32 194690 199556.121835498 -4866.12183549814 33 189917 172711.692459614 17205.307540386 34 184128 177934.638374218 6193.36162578195 35 175335 178007.834878517 -2672.83487851685 36 179566 182860.56067138 -3294.56067137973 37 181140 182552.108246814 -1412.10824681402 38 177876 179243.047588603 -1367.04758860334 39 175041 174113.551861832 927.448138168431 40 169292 173346.182184128 -4054.18218412847 41 166070 166832.87427879 -762.874278789735 42 166972 165922.491006595 1049.50899340483 43 206348 196558.795284389 9789.20471561115 44 215706 225216.873886494 -9510.87388649379 45 202108 200907.0069691 1200.99303089993 46 195411 190710.856136706 4700.14386329381 47 193111 187055.840220639 6055.15977936087 48 195198 199049.339913742 -3851.33991374171 49 198770 199042.997871195 -272.997871194704 50 194163 197117.930776858 -2954.93077685832 51 190420 191512.249043426 -1092.24904342552 52 189733 188129.678889893 1603.32111010666 53 186029 187498.596717085 -1469.59671708476 54 191531 187061.553357131 4469.44664286863 55 232571 223314.193184278 9256.80681572173 56 243477 248433.712722975 -4956.71272297547 57 227247 231545.874832777 -4298.8748327769 58 217859 218649.86048071 -790.860480710166 59 208679 211171.888635608 -2492.88863560779 60 213188 213488.229628964 -300.229628963629 61 216234 216634.512356744 -400.512356744439 62 213586 213617.211916038 -31.2119160378934 63 209465 210647.255498067 -1182.25549806724 64 204045 207696.056936062 -3651.05693606209 65 200237 201559.353700862 -1322.35370086171 66 203666 201806.358136104 1859.64186389593 67 241476 236008.629329494 5467.3706705058 68 260307 253632.974070164 6674.02592983609 69 243324 245978.104966728 -2654.10496672837 70 244460 235268.282471264 9191.71752873648 71 233575 236647.931624633 -3072.93162463326 72 237217 240271.635200018 -3054.63520001838 73 235243 242188.15269305 -6945.15269304995 74 230354 234257.517648547 -3903.51764854678 75 227184 227677.911670693 -493.911670693138 76 221678 224508.313359515 -2830.31335951484 77 217142 219381.134929036 -2239.13492903588 78 219452 219340.37877907 111.621220930218 79 256446 252477.564273767 3968.43572623306 80 265845 268537.035194257 -2692.03519425693 81 248624 249733.664875926 -1109.66487592596 82 241114 241164.041968422 -50.0419684217777 83 229245 229923.595156388 -678.595156388124 84 231805 232994.616274153 -1189.61627415262 85 219277 233336.866000632 -14059.866000632 86 219313 217374.183298221 1938.81670177865 87 212610 213750.413699221 -1140.41369922119 88 214771 207127.034028598 7643.96597140183 89 211142 209202.751430529 1939.24856947092 90 211457 212298.996501291 -841.996501291229 91 240048 244740.097239513 -4692.09723951275 92 240636 250736.072567318 -10100.072567318 93 230580 223704.94502859 6875.05497141043 94 208795 219884.192553618 -11089.1925536177 95 197922 196713.536485746 1208.46351425373 96 194596 198279.950262193 -3683.95026219264 97 194581 190729.090050541 3851.9099494589 98 185686 191278.927945051 -5592.92794505131 99 178106 179159.00117226 -1053.00117226044 100 172608 172574.581267 33.4187330002605 101 167302 164610.437912258 2691.56208774194 102 168053 164961.754155406 3091.2458445938 103 202300 197414.376094765 4885.62390523477 104 202388 208703.725659621 -6315.72565962127 105 182516 187645.695259936 -5129.69525993612 106 173476 168453.759284008 5022.24071599171 107 166444 160459.741451465 5984.25854853509 108 171297 165203.671089951 6093.32891004876 109 169701 168613.714556009 1087.28544399096 110 164182 166297.126878904 -2115.12687890409 111 161914 159630.579876351 2283.4201236488 112 159612 158060.539554743 1551.46044525696 113 151001 154201.424991103 -3200.42499110274 114 158114 151624.562134489 6489.43786551084 115 186530 189171.601050889 -2641.60105088935 116 187069 193266.148679688 -6197.1486796877 117 174330 173684.922388921 645.077611079469 118 169362 163039.411629568 6322.58837043165 119 166827 158271.00234883 8555.99765117007 120 178037 167373.950770153 10663.049229847 121 186413 176183.815808527 10229.1841914731 122 189226 184368.839357316 4857.16064268383 123 191563 188972.400892033 2590.59910796714 124 188906 192372.294027709 -3466.2940277087 125 186005 187821.724755109 -1816.72475510943 126 195309 192839.215792401 2469.78420759932 127 223532 229223.087110721 -5691.08711072078 128 226899 233733.22180034 -6834.2218003402 129 214126 218605.044575765 -4479.04457576541 130 206903 208006.298620989 -1103.29862098879 131 204442 199829.420257716 4612.57974228362 132 220375 207753.529268728 12621.4707312718 133 214320 219725.686840237 -5405.68684023729 134 212588 214263.16287187 -1675.16287187007 135 205816 212242.323659017 -6426.32365901687 136 202196 205149.962306198 -2953.96230619837 137 195722 199310.402816273 -3588.40281627342 138 198563 201587.356456262 -3024.356456262 139 229139 228974.239624871 164.760375128622 140 229527 235630.86822827 -6103.8682282705 141 211868 219452.446170661 -7584.4461706613 142 203555 204622.969306616 -1067.96930661576 143 195770 195189.669246087 580.330753913237 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 144 198652.315847294 188946.127403196 208358.504291392 145 192306.353232724 179187.823603683 205424.882861766 146 188010.821329436 171506.694169215 204514.948489657 147 182618.374637994 162670.698972004 202566.050303985 148 178433.51109528 154949.581220205 201917.440970355 149 172255.700582968 145126.928102233 199384.473063704 150 175388.800333884 144499.251040267 206278.3496275 151 204118.502515189 169349.186597036 238887.818433341 152 207571.683921272 168802.85614486 246340.511697684 153 194890.525319291 152002.96560706 237778.085031523 154 187357.973538483 140233.710876445 234482.236200521 155 179187.517956563 127710.236010507 230664.799902619

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/1eblz1293661987.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/1eblz1293661987.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/2eblz1293661987.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/2eblz1293661987.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/3eblz1293661987.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293661916zjykw53n265dnvp/3eblz1293661987.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=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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