Tijdreeks 2 - stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 05 Aug 2010 14:38:15 +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/Aug/05/t1281019081iga32tinv0upn5w.htm/, Retrieved Thu, 05 Aug 2010 16:38:05 +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/Aug/05/t1281019081iga32tinv0upn5w.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:

Ghielens Nick

Dataseries X:

» Textbox « » Textfile « » CSV «

80 79 78 76 74 73 74 76 77 77 78 80 90 90 89 82 78 76 74 78 81 82 88 99 117 113 106 100 97 96 100 104 104 111 117 118 140 147 134 126 116 114 120 122 117 119 132 134 154 152 132 130 123 129 124 128 128 129 141 138 155 160 142 133 131 140 134 134 134 136 145 137 152 168 160 157 147 161 159 164 163 158 175 163

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0183448029323068 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 78 78 0 4 76 77 -1 5 74 74.9816551970677 -0.981655197067695 6 73 72.96364692593 0.0363530740699929 7 74 71.9643138159098 2.03568618409020 8 76 73.001658077789 2.99834192221104 9 77 75.0566620694756 1.94333793052441 10 77 76.092312220842 0.907687779158053 11 78 76.1089635742747 1.89103642572533 12 80 77.1436542648424 2.85634573515759 13 90 79.1960533644604 10.8039466355396 14 90 89.3942496363805 0.605750363619464 15 89 89.4053620074273 -0.405362007427314 16 82 88.3979257212848 -6.39792572128482 17 78 81.2805570347523 -3.28055703475231 18 76 77.2203758624416 -1.22037586244159 19 74 75.1979883077418 -1.19798830774175 20 78 73.176011448321 4.82398855167898 21 81 77.2645065676493 3.73549343235072 22 82 80.3330334585207 1.66696654147933 23 88 81.3636136312189 6.63638636878113 24 99 87.4853568313368 11.5146431686632 25 117 98.6965906911018 18.3034093088982 26 113 117.032363127863 -4.03236312786285 27 106 112.958390220931 -6.95839022093071 28 100 105.830739923602 -5.83073992360164 29 97 99.7237761487536 -2.72377614875363 30 96 96.673809012073 -0.673809012073036 31 100 95.6614481185325 4.33855188146747 32 104 99.7410379978096 4.25896200219036 33 104 103.819167816436 0.180832183563993 34 111 103.822485147207 7.17751485279268 35 117 110.954155242726 6.04584475727449 36 118 117.065065073357 0.934934926642981 37 140 118.082216270341 21.9177837296592 38 147 140.484293693574 6.51570630642567 39 134 147.603823041730 -13.6038230417305 40 126 134.354263588904 -8.35426358890399 41 116 126.201006269721 -10.201006269721 42 114 116.013870819992 -2.01387081999174 43 120 113.976926756668 6.02307324333214 44 122 120.087418848364 1.91258115163636 45 117 122.122504772682 -5.12250477268245 46 119 117.028533432108 1.97146656789221 47 132 119.064699597783 12.9353004022166 48 134 132.301995134532 1.69800486546774 49 154 134.333144699167 19.6668553008326 50 152 154.693929283959 -2.69392928395933 51 132 152.644509682132 -20.6445096821315 52 130 132.265790220379 -2.26579022037873 53 123 130.2242247453 -7.22422474529992 54 129 123.091697766009 5.90830223399129 55 124 129.200084406156 -5.20008440615578 56 128 124.104689882494 3.8953101175065 57 128 128.176148578959 -0.176148578959385 58 129 128.172917167992 0.827082832008443 59 141 129.188089839553 11.8119101604466 60 138 141.404777003701 -3.40477700370096 61 155 138.342317040540 16.6576829594604 62 160 155.647898951740 4.35210104826024 63 142 160.727737387812 -18.7277373878116 64 133 142.384180736064 -9.38418073606417 65 131 133.21202978978 -2.21202978977993 66 140 131.171450539206 8.82854946079397 67 134 140.333408539242 -6.33340853924241 68 134 134.217223407700 -0.217223407700232 69 134 134.213238487094 -0.213238487093690 70 136 134.209326669070 1.79067333092965 71 145 136.242176218442 8.75782378155759 72 137 145.402836769831 -8.40283676983094 73 152 137.248688385216 14.7513116147839 74 168 152.519298289782 15.4807017102177 75 160 168.80328871191 -8.80328871191008 76 157 160.641794115334 -3.64179411533388 77 147 157.574986119968 -10.5749861199681 78 161 147.380990083585 13.6190099164146 79 159 161.630828136635 -2.63082813663513 80 164 159.582566112920 4.41743388708022 81 163 164.663603067045 -1.66360306704476 82 158 163.633084596622 -5.63308459662224 83 175 158.529746769796 16.4702532302038 84 163 175.831890319549 -12.8318903195495 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 163.596491820388 147.477366090804 179.715617549973 86 164.192983640777 141.187054193133 187.19891308842 87 164.789475461165 136.355084207689 193.223866714641 88 165.385967281553 132.254010767216 198.517923795890 89 165.982459101942 128.604879206357 203.360038997527 90 166.578950922330 125.265995391784 207.891906452876 91 167.175442742719 122.153982643268 212.196902842169 92 167.771934563107 119.215028948480 216.328840177733 93 168.368426383495 116.412109978487 220.324742788504 94 168.964918203884 113.718525167057 224.21131124071 95 169.561410024272 111.114311293551 228.008508754993 96 170.157901844660 108.584109421917 231.731694267404

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/16qbn1281019091.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/16qbn1281019091.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/26qbn1281019091.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/26qbn1281019091.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/3cwlj1281019091.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t1281019081iga32tinv0upn5w/3cwlj1281019091.ps (open in new window)

Parameters (Session):

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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