Triple exponential smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 Jul 2010 09:49:04 +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/Jul/24/t1279964958afz9h6cwly5yqfd.htm/, Retrieved Sat, 24 Jul 2010 11:49:22 +0200

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/Jul/24/t1279964958afz9h6cwly5yqfd.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:

Febiri Lordina

Dataseries X:

» Textbox « » Textfile « » CSV «

297 296 295 293 291 290 291 293 294 294 295 297 302 297 301 298 295 287 290 288 288 287 274 282 296 292 298 296 292 296 293 295 294 291 279 284 299 296 299 299 291 298 288 284 277 270 251 257 269 271 268 268 258 261 255 251 239 229 210 218 226 227 222 215 203 205 194 190 182 179 158 163 165 169 163 154 142 146 133 131 128 120 88 95

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.509341826247958 beta 0.078544945072969 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 302 300.999732905983 1.00026709401698 14 297 296.626296450144 0.373703549856259 15 301 301.157008776380 -0.157008776379655 16 298 298.494459121936 -0.494459121936472 17 295 296.265250448955 -1.2652504489551 18 287 288.926160952036 -1.92616095203596 19 290 289.006716995916 0.99328300408439 20 288 291.030672126812 -3.03067212681174 21 288 289.842146182603 -1.84214618260268 22 287 288.018622230618 -1.01862223061840 23 274 287.657135574702 -13.6571355747016 24 282 281.645288335265 0.35471166473485 25 296 286.48357419176 9.51642580824029 26 292 285.654136124440 6.34586387555964 27 298 292.719035831855 5.28096416814458 28 296 292.630967926127 3.36903207387326 29 292 292.116232999024 -0.116232999024191 30 296 285.208904008870 10.7910959911295 31 293 293.878908422203 -0.878908422202755 32 295 293.57956081756 1.42043918244013 33 294 296.024073310026 -2.0240733100257 34 291 295.28741810765 -4.28741810764978 35 279 287.704498014518 -8.7044980145182 36 284 291.933090849267 -7.93309084926716 37 299 297.556585706452 1.4434142935483 38 296 291.247855900657 4.7521440993433 39 299 297.103039825277 1.89696017472301 40 299 294.342404912262 4.65759508773829 41 291 292.814618647480 -1.81461864747968 42 298 290.366758351913 7.63324164808733 43 288 291.548775999850 -3.54877599984974 44 284 290.757359124645 -6.75735912464529 45 277 286.758948099093 -9.7589480990934 46 270 280.075075289218 -10.0750752892178 47 251 266.248446905583 -15.2484469055829 48 257 266.132095343942 -9.1320953439423 49 269 274.307243558909 -5.30724355890897 50 271 264.475205943233 6.524794056767 51 268 268.194901603801 -0.194901603800758 52 268 264.002180882003 3.99781911799749 53 258 257.215162206955 0.784837793044858 54 261 259.083441780305 1.91655821969528 55 255 249.994920264635 5.00507973536531 56 251 250.455985010327 0.544014989673258 57 239 247.465778122548 -8.46577812254827 58 229 240.099258407255 -11.0992584072547 59 210 221.985437880254 -11.9854378802537 60 218 225.435476083455 -7.43547608345511 61 226 235.322718477454 -9.3227184774538 62 227 228.061513740369 -1.06151374036861 63 222 223.1272086282 -1.12720862820001 64 215 218.986616247199 -3.98661624719853 65 203 204.706686619467 -1.70668661946675 66 205 203.91191147498 1.08808852501997 67 194 193.934375071696 0.065624928304402 68 190 187.510653113197 2.48934688680305 69 182 178.988323988319 3.01167601168112 70 179 174.532550212722 4.46744978727796 71 158 162.892396424216 -4.8923964242164 72 163 171.451161439866 -8.4511614398663 73 165 179.117916333114 -14.1179163331138 74 169 172.498741064334 -3.49874106433359 75 163 165.224312807779 -2.22431280777860 76 154 158.011529067990 -4.01152906799032 77 142 143.726181146087 -1.72618114608693 78 146 143.180580729859 2.81941927014068 79 133 132.540292215315 0.459707784685293 80 131 126.479366742414 4.52063325758616 81 128 118.302060496914 9.69793950308576 82 120 117.287778562844 2.71222143715582 83 88 99.4125193325367 -11.4125193325367 84 95 101.894721206481 -6.89472120648109 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 106.626609214165 95.0943192121202 118.158899216209 86 112.026281536148 98.868432478417 125.184130593879 87 106.916805667433 92.107253891232 121.726357443633 88 99.8066201529557 83.3141697280492 116.299070577862 89 88.6928974918854 70.4833122189284 106.902482764842 90 91.3329684060636 71.3701840169507 111.295752795176 91 78.0621447538117 56.3090316973706 99.8152578102527 92 73.704530731515 50.1233897620381 97.285671700992 93 65.5290446163823 40.0819363668526 90.976152865912 94 55.5236989413782 28.1726666658299 82.8747312169264 95 28.6041687821459 -0.688609621680868 57.8969471859727 96 38.8401068997453 7.56799902603302 70.1122147734576

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/1nkyo1279964940.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/1nkyo1279964940.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/2gty91279964940.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/2gty91279964940.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/3gty91279964940.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/24/t1279964958afz9h6cwly5yqfd/3gty91279964940.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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