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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 16:15:27 +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/Jun/06/t127584095689amr8h3lymcl7r.htm/, Retrieved Sun, 06 Jun 2010 18:15:57 +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/Jun/06/t127584095689amr8h3lymcl7r.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

5,074 4,643 5,451 5,397 5,635 5,708 5,578 5,574 5,352 5,302 4,923 4,982 5,101 4,763 5,505 5,385 5,794 5,695 5,798 5,705 5,422 5,311 4,968 5,053 5,236 4,782 5,531 5,566 5,961 5,868 5,872 5,908 5,594 5,526 5,111 5,177 5,835 5,348 6,038 6,039 6,408 6,214 6,138 6,529 6,058 6,026 5,678 5,733 6,488 5,936 6,84 6,694 7,193 6,991 7,209 7,104 6,83 6,848 6,396 6,414 7,151 6,882 7,698 7,626 7,936 8,054 8,128 8,062 7,708 7,574 7,039 7,146 7,07 6,607 7,699 7,663 7,988 7,723 8,087 8,028 7,362

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.553998137465133 beta 1 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 5.451 4.212 1.239 4 5.397 5.1538073846386 0.243192615361401 5 5.635 5.67866758886888 -0.0436675888688809 6 5.708 6.02041601134176 -0.312416011341765 7 5.578 6.04020041992036 -0.462200419920356 8 5.574 5.72094637335361 -0.146946373353612 9 5.352 5.49493446426803 -0.142934464268032 10 5.302 5.19195971835948 0.110040281640522 11 4.923 5.09009462158497 -0.167094621584965 12 4.982 4.74212719545844 0.239872804541559 13 5.101 4.75250805235955 0.348491947640448 14 4.763 5.01612760214491 -0.253127602144911 15 5.505 4.80621882175727 0.698781178242728 16 5.385 5.51078920398326 -0.125789203983255 17 5.794 5.68886214552718 0.105137854472815 18 5.695 6.0531144229011 -0.358114422901099 19 5.798 5.96233107814677 -0.164331078146774 20 5.705 5.88786423423716 -0.182864234237159 21 5.422 5.70182361119575 -0.279823611195746 22 5.311 5.30704591448828 0.00395408551171528 23 4.968 5.07167108921977 -0.103671089219771 24 5.053 4.71923852726892 0.333761472731081 25 5.236 4.79404602415608 0.44195397584392 26 4.782 5.17363364571829 -0.391633645718287 27 5.531 4.87445096722443 0.65654903277557 28 5.566 5.51968648165158 0.0463135183484154 29 5.961 5.8525102605755 0.108489739424503 30 5.868 6.27988266374544 -0.411882663745436 31 5.872 6.19078749620182 -0.318787496201823 32 5.908 5.97665919894139 -0.0686591989413925 33 5.594 5.86306444415719 -0.269064444157188 34 5.526 5.48938435586401 0.0366156441359848 35 5.111 5.30533546579886 -0.194335465798859 36 5.177 4.88567860488831 0.291321395111693 37 5.835 4.89646625066499 0.938533749335014 38 5.348 5.78575428430557 -0.437754284305575 39 6.038 5.67006625252106 0.367933747478943 40 6.039 6.20456250053701 -0.165562500537012 41 6.408 6.35178150387592 0.0562184961240844 42 6.214 6.65301170843406 -0.439011708434061 43 6.138 6.43667363325266 -0.298673633252663 44 6.529 6.13261795380528 0.39638204619472 45 6.058 6.4332167415228 -0.375216741522804 46 6.026 6.0984818620251 -0.0724818620250947 47 5.678 5.89130672535294 -0.213306725352941 48 5.733 5.48794334813406 0.245056651865938 49 6.488 5.47427335688384 1.01372664311616 50 5.936 6.44804778129672 -0.512047781296717 51 6.84 6.29287249926139 0.547127500738611 52 6.694 7.02758596708788 -0.333585967087883 53 7.193 7.08957980964685 0.103420190353151 54 6.991 7.45096884232088 -0.459968842320878 55 7.209 7.24541951828745 -0.0364195182874516 56 7.104 7.25433938559453 -0.150339385594534 57 6.83 7.1168601189862 -0.286860118986194 58 6.848 6.74482864872212 0.103171351277878 59 6.396 6.64603062298484 -0.250030622984839 60 6.414 6.21304286191415 0.200957138085845 61 7.151 6.14123136070608 1.00976863929392 62 6.882 7.0769098701672 -0.194909870167192 63 7.698 7.23721902409638 0.460780975903622 64 7.626 8.0160514879317 -0.390051487931706 65 7.936 8.10743655367772 -0.171436553677724 66 8.054 8.22495835439161 -0.170958354391608 67 8.128 8.24803446670228 -0.120034466702284 68 8.062 8.23282344696064 -0.170823446960643 69 7.708 8.09483955530055 -0.386839555300545 70 7.574 7.62287474882334 -0.0488747488233354 71 7.039 7.31106529584606 -0.272065295846058 72 7.146 6.72488502835075 0.421114971649247 73 7.07 6.7560222479278 0.313977752072207 74 6.607 6.90174873725945 -0.294748737259454 75 7.699 6.54695163381375 1.15204836618625 76 7.663 7.63191008010385 0.0310899198961545 77 7.988 8.11308339268983 -0.12508339268983 78 7.723 8.43844101440343 -0.715441014403434 79 8.087 8.04038862380369 0.0466113761963136 80 8.028 8.0903344538445 -0.0623344538444961 81 7.362 8.04539132562835 -0.683391325628348 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 82 7.27778632562609 6.4802156409 8.07535701035218 83 6.88877884718177 5.6983780161021 8.07917967826143 84 6.49977136873744 4.71815462908445 8.28138810839043 85 6.11076389029312 3.60120242003291 8.62032536055333 86 5.72175641184879 2.37829362494746 9.06521919875012 87 5.33274893340447 1.0657640868295 9.59973377997944 88 4.94374145496014 -0.326326397001926 10.2138093069222 89 4.55473397651582 -1.79101873126404 10.9004866842957 90 4.16572649807149 -3.3230994475414 11.6545524436844 91 3.77671901962717 -4.91844587709575 12.4718839163501 92 3.38771154118285 -6.57367293144941 13.3490960138151 93 2.99870406273852 -8.2859246730961 14.2833327985731

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/1d71r1275840924.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/1d71r1275840924.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/26gic1275840924.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/26gic1275840924.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/36gic1275840924.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t127584095689amr8h3lymcl7r/36gic1275840924.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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