opgave 10(2) dennis gys

*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 05:35:11 -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/t1244288191ymfflby88z6zqc3.htm/, Retrieved Sat, 06 Jun 2009 13:36:34 +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/t1244288191ymfflby88z6zqc3.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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10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394 20.148 20.108 18.584 18.441 18.391 19.178 18.079 18.483 19.644 19.195 19.650 20.830

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 0.734065025144526 beta 0.0248623119871675 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10.297 10.0234262820513 0.273573717948715 14 10.635 10.5944580007374 0.0405419992626399 15 10.872 10.8862941989203 -0.0142941989202647 16 10.296 10.3097828515273 -0.0137828515272513 17 10.383 10.4142703216996 -0.0312703216995658 18 10.431 10.4799334842889 -0.0489334842888773 19 10.574 10.6905710071398 -0.116571007139800 20 10.653 11.1083057046558 -0.455305704655805 21 10.805 10.2947441933882 0.510255806611832 22 10.872 10.9309884014872 -0.0589884014871682 23 10.625 10.8301271080005 -0.205127108000454 24 10.407 10.5687468179479 -0.161746817947913 25 10.463 10.2426779990915 0.220322000908512 26 10.556 10.7065360984725 -0.150536098472536 27 10.646 10.8339262919257 -0.187926291925704 28 10.702 10.1173254080117 0.584674591988321 29 11.353 10.6546229313009 0.698377068699068 30 11.346 11.2626678447677 0.0833321552323198 31 11.451 11.5662940594310 -0.115294059431035 32 11.964 11.9087923160853 0.0552076839147215 33 12.574 11.7499821562080 0.82401784379205 34 13.031 12.4941172405043 0.536882759495665 35 13.812 12.8316267938044 0.980373206195605 36 14.544 13.5134792564192 1.03052074358080 37 14.931 14.2474394583303 0.683560541669712 38 14.886 15.0443966308006 -0.158396630800594 39 16.005 15.2476058645211 0.757394135478927 40 17.064 15.5391784040401 1.52482159595990 41 15.168 16.9227857935655 -1.75478579356547 42 16.05 15.6476594816149 0.402340518385138 43 15.839 16.2196307866016 -0.380630786601587 44 15.137 16.4948483322086 -1.35784833220859 45 14.954 15.5595789516196 -0.605578951619558 46 15.648 15.2082091026351 0.439790897364880 47 15.305 15.6208858919815 -0.315885891981493 48 15.579 15.3693777804169 0.209622219583117 49 16.348 15.3983362907485 0.949663709251526 50 15.928 16.1614412189243 -0.233441218924302 51 16.171 16.5464506210905 -0.375450621090536 52 15.937 16.1831991857762 -0.246199185776197 53 15.713 15.3349496795971 0.378050320402904 54 15.594 16.1783943624217 -0.584394362421724 55 15.683 15.7790854577268 -0.0960854577268098 56 16.438 15.9697613734201 0.468238626579939 57 17.032 16.5748003185268 0.45719968147316 58 17.696 17.300762814123 0.395237185877001 59 17.745 17.4981435803011 0.246856419698858 60 19.394 17.8281164492584 1.5658835507416 61 20.148 19.1028549478297 1.04514505217028 62 20.108 19.6765560635774 0.431443936422632 63 18.584 20.5791393119491 -1.99513931194912 64 18.441 19.0990134935879 -0.658013493587891 65 18.391 18.1446694041251 0.246330595874880 66 19.178 18.6632657038286 0.514734296171401 67 18.079 19.2484969907143 -1.16949699071426 68 18.483 18.8295520677096 -0.346552067709617 69 19.644 18.8469351525211 0.797064847478904 70 19.195 19.8254946452781 -0.63049464527807 71 19.65 19.2313336001050 0.418666399895027 72 20.83 20.0422089270876 0.787791072912384 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 20.5971010669677 19.2620987933537 21.9321033405818 74 20.2111253821925 18.5405159279301 21.8817348364550 75 20.1145454999296 18.152614015613 22.0764769842462 76 20.4538407172898 18.2271535069463 22.6805279276334 77 20.2342976784622 17.7606353005207 22.7079600564037 78 20.650233200866 17.9422872464816 23.3581791552504 79 20.4071098193265 17.4743260924067 23.3398935462464 80 21.0842353197897 17.9338480242642 24.2346226153153 81 21.6851964077620 18.3228582746555 25.0475345408684 82 21.7095321158996 18.1397225301943 25.2793417016049 83 21.8792222713963 18.1055243975502 25.6529201452425 84 22.4953100209104 18.5206061983996 26.4700138434211

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/1mjex1244288109.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/1mjex1244288109.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/25bsy1244288109.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/25bsy1244288109.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/3smqu1244288109.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288191ymfflby88z6zqc3/3smqu1244288109.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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