opgave 10.1

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 12:42:28 -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/18/t1250620980dsqo8xcbndcvv0z.htm/, Retrieved Tue, 18 Aug 2009 20:43:04 +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/18/t1250620980dsqo8xcbndcvv0z.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:

» Textbox « » Textfile « » CSV «

108,87 106,38 104,77 105,38 106,74 110 110,73 115,7 115,44 113,66 118,4 116,71 119,7 114,17 110,52 111,27 111,41 111,62 113,91 118,54 122,26 120,44 121,37 121,49 125 117,24 117,18 115,15 115,27 114,6 117,48 120,8 118,62 116,79 115,46 112,83 115,56 106,66 103,39 102,65 103,22 104,1 104,32

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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.681306178212979 beta 0.19014940357291 gamma 0.686106027377372 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 119.7 117.356955128205 2.34304487179487 14 114.17 113.867608338444 0.302391661555873 15 110.52 110.755460070989 -0.235460070988893 16 111.27 111.482199584934 -0.212199584934027 17 111.41 111.747712829934 -0.337712829933551 18 111.62 112.037295774230 -0.417295774230311 19 113.91 116.117764381270 -2.20776438126973 20 118.54 119.100276536231 -0.560276536230816 21 122.26 118.114315200431 4.14568479956931 22 120.44 119.430794378018 1.00920562198219 23 121.37 125.306113465507 -3.93611346550738 24 121.49 121.050149416579 0.439850583420792 25 125 125.086947594697 -0.086947594696511 26 117.24 119.224207960210 -1.98420796020952 27 117.18 113.868731574494 3.31126842550589 28 115.15 116.908595540085 -1.75859554008545 29 115.27 115.784390012376 -0.514390012375515 30 114.6 115.604606540000 -1.00460653999951 31 117.48 118.485757031860 -1.00575703185983 32 120.8 122.39548039581 -1.5954803958101 33 118.62 121.347152766279 -2.72715276627878 34 116.79 116.018863471564 0.771136528436188 35 115.46 119.343364127123 -3.88336412712276 36 112.83 114.779722532049 -1.94972253204939 37 115.56 115.463277710046 0.0967222899537603 38 106.66 107.724593675186 -1.06459367518632 39 103.39 102.686460001761 0.703539998238583 40 102.65 101.036173154580 1.61382684542036 41 103.22 101.113647947701 2.10635205229873 42 104.1 101.583692560525 2.51630743947483 43 104.32 106.291036181868 -1.97103618186829 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 44 108.716733679828 104.936846395675 112.496620963982 45 108.017234559261 103.150877130440 112.883591988083 46 105.174468702014 99.148124660124 111.200812743903 47 106.718515253124 99.4608783865305 113.976152119718 48 105.489197661900 96.9317198149326 114.046675508868 49 108.466926661335 98.5438320582813 118.390021264389 50 100.914228815461 89.5623561754648 112.266101455457 51 97.6317580172387 84.7903552025186 110.473160831959 52 96.2537752099995 81.864291922032 110.643258497967 53 95.6829519601663 79.6888467048854 111.677057215447 54 94.8782057011409 77.2247718010534 112.531639601228 55 96.6346333836248 77.2688442882669 116.000422478983

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/1v85l1250620935.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/1v85l1250620935.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/2v05o1250620935.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/2v05o1250620935.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/32o1j1250620935.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250620980dsqo8xcbndcvv0z/32o1j1250620935.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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