WS 9 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: Fri, 04 Dec 2009 03:24:57 -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/04/t1259922348gc6apgi5uewb3bu.htm/, Retrieved Fri, 04 Dec 2009 11:25:53 +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/04/t1259922348gc6apgi5uewb3bu.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:

SHW WS 9 Exponential Smoothing

Dataseries X:

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14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5 22.2 20.9 22.2 23.5 21.5 24.3 22.8 20.3 23.7 23.3 19.6 18 17.3 16.8 18.2 16.5 16 18.4

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 0.317087774037496 beta 1 gamma 0.738379041593874 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 17.5 16.413176736086 1.08682326391400 14 14.5 14.1771676505587 0.322832349441292 15 14.4 14.5732869780867 -0.173286978086702 16 16.6 17.1319032562038 -0.531903256203826 17 16.7 17.3034566455206 -0.603456645520573 18 16.6 17.0118877403367 -0.411887740336734 19 16.9 16.8921326725477 0.00786732745228846 20 15.7 15.9393910683414 -0.239391068341405 21 16.4 16.1077395575255 0.292260442474461 22 18.4 18.9064054728083 -0.506405472808321 23 16.9 16.5501983596690 0.349801640331023 24 16.5 15.3381030069777 1.16189699302232 25 18.3 20.0935234065092 -1.79352340650924 26 15.1 15.6275565387011 -0.527556538701084 27 15.7 14.7292652713238 0.970734728676204 28 18.1 17.1184215169862 0.981578483013802 29 16.8 17.7762601846023 -0.976260184602303 30 18.9 17.3821207869692 1.51787921303081 31 19 18.6431069553436 0.356893044656434 32 18.1 18.1646179990937 -0.0646179990937306 33 17.8 19.4299709565994 -1.62997095659941 34 21.5 21.6566019190386 -0.1566019190386 35 17.1 19.7409316726321 -2.64093167263206 36 18.7 17.1347700592616 1.56522994073841 37 19 19.997718610579 -0.997718610578982 38 16.4 15.8433752534974 0.5566247465026 39 16.9 15.9937643896181 0.906235610381929 40 18.6 18.3600792603501 0.239920739649932 41 19.3 17.4372456978755 1.86275430212455 42 19.4 19.8534457152028 -0.4534457152028 43 17.6 19.8426632968719 -2.24266329687188 44 18.6 17.5152844587379 1.08471554126212 45 18.1 17.9060016341834 0.193998365816643 46 20.4 21.5809089377904 -1.18090893779042 47 18.1 17.9289191276284 0.171080872371633 48 19.6 19.0639956822859 0.536004317714077 49 19.9 20.7616097208104 -0.861609720810378 50 19.2 17.6342614314299 1.56573856857007 51 17.8 19.0380416453745 -1.23804164537448 52 19.2 20.6175198079932 -1.41751980799319 53 22 19.4441285258105 2.55587147418955 54 21.1 20.6096315175494 0.490368482450613 55 19.5 19.8658549968483 -0.36585499684827 56 22.2 20.3800344005380 1.81996559946203 57 20.9 21.2286391355478 -0.328639135547832 58 22.2 25.1539248642576 -2.95392486425764 59 23.5 21.2692412952022 2.23075870479783 60 21.5 24.3108188211452 -2.81081882114518 61 24.3 24.0910107714239 0.208989228576133 62 22.8 22.2395505681161 0.56044943188391 63 20.3 21.4533952185358 -1.15339521853578 64 23.7 22.9797368967395 0.720263103260521 65 23.3 25.1663445591757 -1.86634455917566 66 19.6 22.7398461236589 -3.13984612365891 67 18 18.3892614822285 -0.389261482228502 68 17.3 17.7901178246006 -0.490117824600606 69 16.8 14.5347867187220 2.26521328127796 70 18.2 15.4712205220359 2.72877947796406 71 16.5 15.8703521824509 0.629647817549079 72 16 15.3928287204286 0.607171279571432 73 18.4 17.4502533991752 0.949746600824781 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 17.0026542751035 14.8473261992480 19.1579823509590 75 15.9841952727693 13.3466291585509 18.6217613869878 76 18.9199727429859 15.0203913639017 22.8195541220702 77 19.9893956231536 14.5802897396054 25.3985015067018 78 18.7904260799382 12.2738716218386 25.3069805380379 79 18.7711089803540 10.7737927304279 26.7684252302802 80 20.4492140930143 10.0718314714030 30.8265967146256 81 21.0169478089856 8.54907926298566 33.4848163549855 82 23.5189046868944 7.52903592983942 39.5087734439493 83 22.2496725746468 5.12573473685641 39.3736104124371 84 21.7781244322791 3.05341302363635 40.5028358409219 85 24.7810518400923 0.906736925614762 48.6553667545698

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/1tbxa1259922296.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/1tbxa1259922296.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/2ca0h1259922296.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/2ca0h1259922296.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/33aj21259922296.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922348gc6apgi5uewb3bu/33aj21259922296.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

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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