dennis volkaerts - opg 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 19 Aug 2009 07:05:28 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv.htm/, Retrieved Wed, 19 Aug 2009 15:06:14 +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/2009/Aug/19/t1250687174o5mb7o0zbun0udv.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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17.23 17.36 17.39 17.29 17.28 17.4 17.51 17.54 17.64 17.65 17.5 17.37 17.56 17.49 17.61 17.79 17.83 17.56 17.95 18.09 18.38 18.38 18.44 18.84 19.01 19.06 19.06 18.97 18.98 19.41 19.55 19.64 19.71 19.48 19.48 19.41 19.25 19.14 19.21 19.3 19.53 19.14 19.16 19.24 19.38 19.27 19.27 19.07 19.15 19.24 19.36 19.57 19.59 19.36 19.46 19.65 19.46 19.51 19.64 19.64 19.69 19.28 19.67 19.65 19.6 19.53 19.64 19.67 19.81 19.73 19.87 19.97 20.12 19.94 20.31 20.13 20.22 20.38 20.44 20.34 20.14 19.97 19.82 19.98 20.12

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.930756132630198 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 17.39 17.36 0.0300000000000011 4 17.29 17.3879226839789 -0.0979226839789078 5 17.28 17.2967805453419 -0.0167805453419270 6 17.4 17.2811619498560 0.118838050143950 7 17.51 17.3917711938173 0.118228806182657 8 17.54 17.5018133802254 0.0381866197745993 9 17.64 17.5373558107650 0.102644189234976 10 17.65 17.6328925193743 0.0171074806256648 11 17.5 17.6488154118805 -0.148815411880523 12 17.37 17.5103045546428 -0.140304554642835 13 17.56 17.3797152299731 0.180284770026930 14 17.49 17.5475163852955 -0.057516385295461 15 17.61 17.493982656955 0.116017343045012 16 17.79 17.6019665104856 0.188033489514407 17 17.83 17.7769798339910 0.0530201660090164 18 17.56 17.8263286786569 -0.266328678656947 19 17.95 17.5784416277017 0.371558372298303 20 18.09 17.9242718613484 0.165728138651563 21 18.38 18.0785243427478 0.301475657252233 22 18.38 18.359124659574 0.0208753404259987 23 18.44 18.3785545106962 0.061445489303761 24 18.84 18.4357452766882 0.404254723311819 25 19.01 18.8120078395554 0.197992160444620 26 19.06 18.9962902571019 0.0637097428980837 27 19.06 19.0555884910126 0.00441150898739906 28 18.97 19.0596945300568 -0.089694530056775 29 18.98 18.9762107961430 0.00378920385695380 30 19.41 18.9797376208707 0.430262379129307 31 19.55 19.3802069688854 0.169793031114647 32 19.64 19.5382428738732 0.101757126126820 33 19.71 19.6329539430545 0.0770460569454592 34 19.48 19.7046650330515 -0.224665033051505 35 19.48 19.4955566757512 -0.0155566757512489 36 19.41 19.4810772043924 -0.0710772043924344 37 19.25 19.4149216605140 -0.164921660513965 38 19.14 19.2614198135870 -0.121419813587035 39 19.21 19.1484075774681 0.0615924225319127 40 19.3 19.2057351024632 0.0942648975367852 41 19.53 19.2934727339373 0.236527266062666 42 19.14 19.5136219373594 -0.373621937359417 43 19.16 19.1658710278770 -0.00587102787696381 44 19.24 19.1604065326756 0.0795934673243615 45 19.38 19.2344886405051 0.145511359494911 46 19.27 19.3699242307223 -0.0999242307223334 47 19.27 19.2769191401792 -0.00691914017916773 48 19.07 19.2704791080249 -0.200479108024879 49 19.15 19.0838819487665 0.0661180512335058 50 19.24 19.1454217304296 0.0945782695703627 51 19.36 19.2334510348458 0.126548965154196 52 19.57 19.3512372602411 0.218762739758922 53 19.59 19.5548520218627 0.0351479781373207 54 19.36 19.5875662180635 -0.227566218063544 55 19.46 19.3757575650214 0.0842424349785631 56 19.65 19.4541667280054 0.195833271994562 57 19.46 19.6364397468874 -0.176439746887411 58 19.51 19.4722173704322 0.0377826295677686 59 19.64 19.5073837846093 0.132616215390673 60 19.64 19.6308171403704 0.00918285962959686 61 19.69 19.6393641432857 0.0506358567142691 62 19.28 19.6864937774535 -0.406493777453520 63 19.67 19.3081472012126 0.361852798787361 64 19.65 19.6449439127934 0.0050560872066221 65 19.6 19.6496498969681 -0.0496498969680523 66 19.53 19.6034379508806 -0.0734379508805816 67 19.64 19.5350851277307 0.104914872269315 68 19.67 19.6327352884995 0.0372647115005371 69 19.81 19.6674196472593 0.142580352740715 70 19.73 19.8001271849653 -0.0701271849652798 71 19.87 19.7348558774948 0.135144122505245 72 19.97 19.8606420983054 0.109357901694558 73 20.12 19.9624276359592 0.157572364040782 74 19.94 20.1090890801232 -0.169089080123214 75 20.31 19.9517083818377 0.358291618162262 76 20.13 20.2851905027123 -0.155190502712259 77 20.22 20.1407459905869 0.0792540094131375 78 20.38 20.2145121458837 0.165487854116328 79 20.44 20.3685409809783 0.071459019021745 80 20.34 20.4350519011645 -0.095051901164485 81 20.14 20.3465817612375 -0.20658176123748 82 19.97 20.1543045200761 -0.18430452007615 83 19.82 19.9827619577438 -0.162761957743808 84 19.98 19.8312702674149 0.148729732585139 85 20.12 19.9697013781229 0.150298621877074 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 20.1095927421609 19.7858371364046 20.4333483479172 87 20.1095927421609 19.6673009939617 20.5518844903601 88 20.1095927421609 19.5744046548574 20.6447808294643 89 20.1095927421609 19.495401740063 20.7237837442588 90 20.1095927421609 19.4254619905319 20.7937234937899 91 20.1095927421609 19.3620372702453 20.8571482140764 92 20.1095927421609 19.3035881008235 20.9155973834982 93 20.1095927421609 19.2490999879068 20.9700854964150 94 20.1095927421609 19.1978624759142 21.0213230084076 95 20.1095927421609 19.1493550754050 21.0698304089167 96 20.1095927421609 19.1031829474335 21.1160025368882 97 20.1095927421609 19.0590381394916 21.1601473448302

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/1gs8g1250687124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/1gs8g1250687124.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/2l7le1250687124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/2l7le1250687124.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/3x6ww1250687124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250687174o5mb7o0zbun0udv/3x6ww1250687124.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=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')

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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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