*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, 16 Dec 2009 07:14:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i.htm/, Retrieved Wed, 16 Dec 2009 15:16:39 +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/2009/Dec/16/t12609729950uv9lhl5rvnij1i.htm/}, year = {2009}, } @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 = {2009}, 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:

» Textbox « » Textfile « » CSV «

19915 19843 19761 20858 21968 23061 22661 22269 21857 21568 21274 20987 19683 19381 19071 20772 22485 24181 23479 22782 22067 21489 20903 20330 19736 19483 19242 20334 21423 22523 21986 21462 20908 20575 20237 19904 19610 19251 18941 20450 21946 23409 22741 22069 21539 21189 20960 20704 19697 19598 19456 20316 21083 22158 21469 20892 20578 20233 19947 20049

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' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.598370702820769 beta 0.0107745129481494 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 19683 19555.2445023852 127.755497614751 14 19381 19300.0097996718 80.9902003282441 15 19071 19031.9880642479 39.0119357521253 16 20772 20771.3965615316 0.603438468384411 17 22485 22527.9424913596 -42.942491359634 18 24181 24273.0405170656 -92.040517065554 19 23479 22811.4104974059 667.589502594074 20 22782 22867.2479659161 -85.2479659161218 21 22067 22470.6351640011 -403.635164001094 22 21489 21991.6786582602 -502.678658260164 23 20903 21396.6514386398 -493.651438639772 24 20330 20766.0182017139 -436.01820171385 25 19736 19220.9352701911 515.064729808906 26 19483 19177.3644472700 305.63555273004 27 19242 19024.6391491622 217.360850837838 28 20334 20861.1049392308 -527.104939230769 29 21423 22260.2714793545 -837.271479354516 30 22523 23443.2061833741 -920.206183374095 31 21986 21830.7669769188 155.233023081189 32 21462 21303.4537869478 158.546213052217 33 20908 20936.7489180875 -28.7489180874945 34 20575 20641.1143367415 -66.114336741528 35 20237 20309.8613155447 -72.8613155446583 36 19904 19953.5953116783 -49.5953116782694 37 19610 19031.1261848107 578.873815189312 38 19251 18943.5175002801 307.482499719870 39 18941 18757.8803619225 183.119638077493 40 20450 20238.9907461483 211.009253851709 41 21946 21948.8905239335 -2.89052393353268 42 23409 23633.3330987482 -224.333098748197 43 22741 22850.0509888369 -109.050988836931 44 22069 22149.6809603769 -80.6809603769252 45 21539 21553.4840770882 -14.4840770881929 46 21189 21247.2876431217 -58.2876431216646 47 20960 20913.7079999788 46.2920000212107 48 20704 20633.0468805794 70.9531194205738 49 19697 20012.0874739407 -315.087473940694 50 19598 19273.8826648136 324.117335186431 51 19456 19043.5873658153 412.412634184657 52 20316 20700.0625314756 -384.062531475611 53 21083 21967.7457822828 -884.745782282811 54 22158 22990.6224750623 -832.622475062348 55 21469 21902.2384502922 -433.238450292247 56 20892 21036.8092259392 -144.809225939214 57 20578 20442.6467721509 135.353227849053 58 20233 20211.8165008786 21.1834991214419 59 19947 19968.5491458151 -21.5491458151373 60 20049 19660.3160643856 388.683935614412 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 19096.530449936 18373.6950488505 19819.3658510215 62 18804.4012499258 17963.1275625705 19645.6749372812 63 18420.7485063612 17478.7668398243 19362.730172898 64 19439.3662269767 18366.962386029 20511.7700679244 65 20661.4687602458 19452.3358210436 21870.6016994479 66 22190.8023929648 20831.0182596563 23550.5865262732 67 21758.2311283075 20341.3069433343 23175.1553132807 68 21263.6381222788 19796.5538263068 22730.7224182508 69 20864.8820662616 19345.8131461007 22383.9509864226 70 20504.7652467097 18934.4872908085 22075.0432026110 71 20230.3658527651 18606.1638305337 21854.5678749965 72 20098.5855044901 18566.5558759810 21630.6151329992

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/1iu5u1260972876.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/1iu5u1260972876.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/242tb1260972876.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/242tb1260972876.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/3ojki1260972876.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609729950uv9lhl5rvnij1i/3ojki1260972876.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=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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