Jurgen Leemans - opgave 10 - oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 07:00:06 -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/Jun/06/t1244293479yf24fmv1kk9i4iy.htm/, Retrieved Sat, 06 Jun 2009 15:04:42 +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/Jun/06/t1244293479yf24fmv1kk9i4iy.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 «

163.40 162.89 162.29 161.26 161.43 161.44 161.44 161.44 161.92 162.23 161.89 161.40 161.40 159.55 158.93 158.59 158.29 158.03 158.03 163.94 164.36 164.39 163.22 163.22 163.56 162.82 162.80 162.44 161.98 161.53 161.53 161.52 162.07 161.84 161.54 161.47 161.47 161.54 161.57 160.75 160.31 160.57 160.57 159.65 158.76 158.95 159.25 158.72 158.72 158.72 158.53 157.92 157.89 157.81 157.81 157.88 157.52 156.11 155.61 155.31 155.31 155.31 153.09 151.94 151.73 151.65 151.65 151.09 149.94 149.47 149.15 149.22

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 0.887063362952135 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 161.4 162.988408119658 -1.58840811965817 14 159.55 159.670954156608 -0.120954156608377 15 158.93 158.641474840999 0.288525159000983 16 158.59 158.26939629082 0.320603709179949 17 158.29 158.012023447242 0.277976552758474 18 158.03 157.771004281601 0.258995718398666 19 158.03 160.398564579869 -2.36856457986894 20 163.94 158.423645736929 5.51635426307092 21 164.36 163.979816186079 0.380183813921235 22 164.39 164.781961337244 -0.391961337243742 23 163.22 164.239998147262 -1.01999814726244 24 163.22 163.021759845862 0.198240154138404 25 163.56 163.206036637685 0.353963362315312 26 162.82 161.777318569146 1.04268143085397 27 162.8 161.826302967847 0.973697032152614 28 162.44 162.065638127245 0.374361872754861 29 161.98 161.851138013340 0.128861986659700 30 161.53 161.475701147630 0.0542988523695271 31 161.53 163.624934531806 -2.09493453180568 32 161.52 162.783239097023 -1.26323909702256 33 162.07 161.745418842888 0.324581157111794 34 161.84 162.411037437629 -0.571037437629315 35 161.54 161.63929403455 -0.0992940345498994 36 161.47 161.375362356539 0.094637643461141 37 161.47 161.485324012272 -0.0153240122720888 38 161.54 159.806806145871 1.73319385412901 39 161.57 160.460527950925 1.10947204907515 40 160.75 160.752617256072 -0.00261725607185781 41 160.31 160.175986836856 0.134013163144033 42 160.57 159.796698481447 0.773301518552955 43 160.57 162.341005598019 -1.77100559801872 44 159.65 161.880584538051 -2.23058453805066 45 158.76 160.1639906636 -1.40399066359993 46 158.95 159.195108373789 -0.245108373788639 47 159.25 158.765761815657 0.484238184343127 48 158.72 159.041362181660 -0.321362181659623 49 158.72 158.769886933931 -0.0498869339310204 50 158.72 157.258181293659 1.46181870634086 51 158.53 157.600735104378 0.929264895621799 52 157.92 157.607373619735 0.312626380265328 53 157.89 157.325814860782 0.564185139218011 54 157.81 157.400315382081 0.409684617919282 55 157.81 159.334725778587 -1.52472577858745 56 157.88 159.040867223526 -1.16086722352611 57 157.52 158.366533119890 -0.846533119890438 58 156.11 158.023031262051 -1.91303126205071 59 155.61 156.196501365030 -0.586501365030216 60 155.31 155.431306109379 -0.121306109379105 61 155.31 155.367952775427 -0.0579527754268554 62 155.31 154.019819173891 1.29018082610878 63 153.09 154.149974472932 -1.05997447293200 64 151.94 152.322390544104 -0.382390544103799 65 151.73 151.452717935168 0.277282064832377 66 151.65 151.255268481163 0.394731518837091 67 151.65 152.957948726459 -1.30794872645936 68 151.09 152.897478113839 -1.80747811383932 69 149.94 151.685059015895 -1.74505901589504 70 149.47 150.424061041452 -0.95406104145249 71 149.15 149.598012318800 -0.448012318799755 72 149.22 149.008203209974 0.211796790026256 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 149.247488166659 146.861643746193 151.633332587126 74 148.103016024235 144.913755587103 151.292276461367 75 146.823280544838 142.995681993129 150.650879096546 76 146.012485186851 141.638740885886 150.386229487817 77 145.556518425935 140.697632983016 150.415403868854 78 145.126366557372 139.826565024805 150.426168089939 79 146.286599953234 140.579847389667 151.993352516801 80 147.329947567359 141.243392436666 153.416502698052 81 147.727925486548 141.283914166249 154.171936806848 82 148.104238082441 141.321582965650 154.886893199232 83 148.181653396599 141.076476483213 155.286830309986 84 148.063776223776 140.650095120053 155.477457327499

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/18k491244293204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/18k491244293204.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/2e6eq1244293204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/2e6eq1244293204.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/3tzu61244293204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244293479yf24fmv1kk9i4iy/3tzu61244293204.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')

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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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