Exponential smoothing

*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: Sat, 11 Dec 2010 13:48:03 +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/11/t1292075190bor4n9stk7gg76z.htm/, Retrieved Sat, 11 Dec 2010 14:46:33 +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/11/t1292075190bor4n9stk7gg76z.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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16198,9 16554,2 19554,2 15903,8 18003,8 18329,6 16260,7 14851,9 18174,1 18406,6 18466,5 16016,5 17428,5 17167,2 19630 17183,6 18344,7 19301,4 18147,5 16192,9 18374,4 20515,2 18957,2 16471,5 18746,8 19009,5 19211,2 20547,7 19325,8 20605,5 20056,9 16141,4 20359,8 19711,6 15638,6 14384,5 13855,6 14308,3 15290,6 14423,8 13779,7 15686,3 14733,8 12522,5 16189,4 16059,1 16007,1 15806,8 15160 15692,1 18908,9 16969,9 16997,5 19858,9 17681,2

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.630243947316295 beta 0 gamma 0.749185747177312 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 17428.5 17045.0413728632 383.458627136752 14 17167.2 16972.2721121519 194.927887848087 15 19630 19575.0533274542 54.9466725458369 16 17183.6 17148.4288957409 35.1711042591451 17 18344.7 18304.7410318101 39.958968189876 18 19301.4 19328.5706901423 -27.1706901423095 19 18147.5 17198.0131209586 949.48687904144 20 16192.9 16392.1964066868 -199.296406686839 21 18374.4 19641.4409798067 -1267.04097980675 22 20515.2 19100.2626651047 1414.93733489531 23 18957.2 20065.7391167438 -1108.53911674381 24 16471.5 16943.7431418755 -472.243141875519 25 18746.8 18126.5805153514 620.219484648616 26 19009.5 18150.8023274469 858.69767255308 27 19211.2 21133.1434005877 -1921.94340058765 28 20547.7 17455.1178176478 3092.58218235222 29 19325.8 20539.6710948882 -1213.87109488816 30 20605.5 20754.6859579458 -149.185957945836 31 20056.9 18817.7787433632 1239.12125663684 32 16141.4 17876.2710324896 -1734.87103248964 33 20359.8 19861.9466991722 497.853300827766 34 19711.6 21176.0331323852 -1464.43313238521 35 15638.6 19627.7605115353 -3989.16051153528 36 14384.5 14866.5344813411 -482.034481341103 37 13855.6 16345.8305106622 -2490.23051066216 38 14308.3 14475.7723050423 -167.472305042258 39 15290.6 16041.0939917945 -750.493991794543 40 14423.8 14490.4709497192 -66.6709497191696 41 13779.7 14390.9677538183 -611.267753818256 42 15686.3 15280.7045054266 405.595494573441 43 14733.8 14078.0282055907 655.771794409327 44 12522.5 11945.0246842833 577.475315716734 45 16189.4 16006.5429259088 182.857074091233 46 16059.1 16578.5202246694 -519.420224669355 47 16007.1 14926.4464787478 1080.65352125218 48 15806.8 14331.9699569763 1474.83004302370 49 15160 16488.2656483216 -1328.26564832162 50 15692.1 15993.9698690558 -301.869869055789 51 18908.9 17313.0819896142 1595.81801038576 52 16969.9 17430.6377850470 -460.737785046964 53 16997.5 16931.9143423353 65.5856576646911 54 19858.9 18529.9212133739 1328.97878662613 55 17681.2 17978.5044734271 -297.304473427073 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 56 15223.1410284149 12823.7453771385 17622.5366796913 57 18811.3933947315 15975.2230538323 21647.5637356306 58 19073.584105987 15859.4551549603 22287.7130570137 59 18192.1177849397 14640.0215552382 21744.2140146412 60 17025.7591116554 13165.1697348514 20886.3484884594 61 17476.0498382518 13329.8572417213 21622.2424347822 62 18103.2134611267 13689.8614743988 22516.5654478547 63 20138.2670779740 15473.0298417782 24803.5043141698 64 18680.3694439107 13776.1670438033 23584.5718440182 65 18617.8231977009 13485.7705973809 23749.8757980209 66 20524.4751712578 15174.2670815025 25874.6832610131 67 18684.9711689265 13125.1609819763 24244.7813558767

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/1ogkg1292075280.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/1ogkg1292075280.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/2z7211292075280.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/2z7211292075280.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/3z7211292075280.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t1292075190bor4n9stk7gg76z/3z7211292075280.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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