WS 9.10

*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 08:03:34 -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/t12599390808btzk0w3sp0tv99.htm/, Retrieved Fri, 04 Dec 2009 16:04:45 +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/t12599390808btzk0w3sp0tv99.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:

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95.1 97.0 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99.0 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102.0 106.0 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100.0 110.7 112.8 109.8 117.3 109.1 115.9 96.0 99.8 116.8 115.7 99.4 94.3

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 0.149518688899873 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 94.6 94.919856849353 -0.319856849352945 14 95.9 96.3617041743281 -0.461704174328105 15 104.7 105.090201458249 -0.390201458249422 16 102.8 103.228104975216 -0.428104975216129 17 98.1 98.3098622055097 -0.209862205509722 18 113.9 113.70869326672 0.191306733280030 19 80.9 86.186058175999 -5.28605817599895 20 95.7 94.5274095204302 1.17259047956985 21 113.2 111.907354275041 1.29264572495933 22 105.9 108.595572393490 -2.69557239349042 23 108.8 101.766311366548 7.0336886334517 24 102.3 100.289801916555 2.01019808344506 25 99 93.432230297996 5.56776970200396 26 100.7 95.628212993495 5.07178700650498 27 115.5 105.290271001686 10.2097289983143 28 100.7 104.945952689777 -4.2459526897772 29 109.9 99.575518963534 10.3244810364659 30 114.6 117.380159869492 -2.78015986949163 31 85.4 83.8481389443058 1.55186105569418 32 100.5 99.2823614416082 1.21763855839184 33 114.8 117.455317038801 -2.6553170388012 34 116.5 109.921803365637 6.57819663436301 35 112.9 112.783156856469 0.116843143531099 36 102 105.749217937900 -3.74921793790038 37 106 100.899790878517 5.10020912148258 38 105.3 102.597715371357 2.70228462864254 39 118.8 116.454759617793 2.34524038220671 40 106.1 102.459278055813 3.64072194418722 41 109.3 110.700874128831 -1.40087412883109 42 117.2 115.626901807880 1.5730981921198 43 92.5 86.1033472724347 6.39665272756531 44 104.2 102.267974863519 1.93202513648102 45 112.5 117.549583435051 -5.04958343505081 46 122.4 117.475324743749 4.92467525625108 47 113.3 114.542942131052 -1.24294213105208 48 100 103.868557811495 -3.86855781149458 49 110.7 106.537112415201 4.16288758479921 50 112.8 106.035639434607 6.76436056539315 51 109.8 120.410727400431 -10.6107274004306 52 117.3 105.560826389854 11.7391736101455 53 109.1 110.763744612496 -1.66374461249593 54 115.9 118.263731328191 -2.36373132819064 55 96 92.0389067413026 3.96109325869742 56 99.8 104.054004442563 -4.25400444256285 57 116.8 112.376476851670 4.42352314833039 58 115.7 122.219811614452 -6.51981161445212 59 99.4 112.412014768593 -13.0120147685929 60 94.3 98.0422085770475 -3.74220857704752 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 107.283324107706 97.392467790993 117.17418042442 62 108.281693399631 98.2785808314555 118.284805967807 63 106.804081909883 96.6976633658894 116.910500453877 64 112.229636447467 101.981675390702 122.477597504231 65 104.613675132305 94.3181698332825 114.909180431328 66 111.461710351872 100.992108041063 121.931312662682 67 91.7292885705867 81.3700653732765 102.088511767897 68 95.9416467171662 85.4236820238656 106.459611410467 69 111.622270349227 100.752042590325 122.492498108128 70 111.454141710823 100.484419359337 122.423864062309 71 97.434419716843 86.6295328862718 108.239306547414 72 92.9636262894019 17.9729655925062 167.954286986298

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/1kb0s1259939012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/1kb0s1259939012.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/2xud31259939012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/2xud31259939012.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/3c7qt1259939012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599390808btzk0w3sp0tv99/3c7qt1259939012.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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