Opgave 10 oef 1 Laura Quaglia

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 19:43:47 +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/May/31/t1275335110wh5ohuxf87n630x.htm/, Retrieved Mon, 31 May 2010 21:45:11 +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/May/31/t1275335110wh5ohuxf87n630x.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.567263099764302 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 39690 41086 -1396 3 43129 40294.100712729 2834.89928727096 4 37863 41902.234469946 -4039.23446994597 5 35953 39610.9258038496 -3657.9258038496 6 29133 37535.9194736501 -8402.91947365005 7 24693 32769.2533259575 -8076.2533259575 8 22205 28187.8928297931 -5982.8928297931 9 21725 24794.018497607 -3069.01849760705 10 27192 23053.0775514205 4138.92244857951 11 21790 25400.9355292858 -3610.93552928576 12 13253 23352.5850478941 -10099.5850478941 13 37702 17623.4631272925 20078.5368727075 14 30364 29013.2761924364 1350.72380756362 15 32609 29779.4919664404 2829.50803355964 16 30212 31384.5674643654 -1172.56746436539 17 29965 30719.4132098467 -754.413209846713 18 28352 30291.4624339259 -1939.46243392593 19 25814 29191.2769617807 -3377.27696178069 20 22414 27275.4723636784 -4861.47236367841 21 20506 24517.7384812397 -4011.73848123971 22 28806 22242.0272749279 6563.97272507206 23 22228 25965.5267897207 -3737.52678972065 24 13971 23845.3657575316 -9874.3657575316 25 36845 18244.0024297077 18600.9975702923 26 35338 28795.66197014 6542.33802986002 27 35022 32506.8889206642 2515.11107933575 28 34777 33933.6186277798 843.38137222021 29 26887 34412.0377592689 -7525.0377592689 30 23970 30143.3615141026 -6173.36151410261 31 22780 26641.4413256471 -3861.44132564712 32 17351 24450.9881497026 -7099.98814970256 33 21382 20423.4268636125 958.573136387527 34 24561 20967.1900323104 3593.80996768955 35 17409 23005.8258145459 -5596.82581454587 36 11514 19830.9530541457 -8316.95305414572 37 31514 15113.0524840568 16400.9475159432 38 27071 24416.7048110224 2654.29518897762 39 29462 25922.3885276113 3539.6114723887 40 26105 27930.2795033998 -1825.2795033998 41 22397 26894.865794365 -4497.86579436498 42 23843 24343.3925015297 -500.392501529677 43 21705 24059.5383000131 -2354.53830001314 44 18089 22723.8956054339 -4634.89560543392 45 20764 20094.6903572115 669.309642788467 46 25316 20474.3650198819 4841.63498011814 47 17704 23220.8458866309 -5516.84588663095 48 15548 20091.3427880587 -4543.34278805874 49 28029 17514.0720748128 10514.9279251872 50 29383 23478.8026834527 5904.19731654731 51 36438 26828.0359548574 9609.9640451426 52 32034 32279.4139477285 -245.413947728477 53 22679 32140.1996710146 -9461.19967101463 54 24319 26773.2102181459 -2454.21021814588 55 18004 25381.0273223272 -7377.02732232722 56 17537 21196.3119364179 -3659.31193641793 57 20366 19120.519304361 1245.48069563901 58 22782 19827.0345444658 2954.96545553423 59 19169 21503.2774084686 -2334.27740846855 60 13807 20179.1279700309 -6372.1279700309 61 29743 16564.4549056564 13178.5450943436 62 25591 24040.1572462574 1550.84275374263 63 29096 24919.8931139924 4176.10688600758 64 26482 27288.8444510961 -806.844451096127 65 22405 26831.1513667397 -4426.15136673971 66 27044 24320.3590224169 2723.64097758306 67 17970 25865.3800460058 -7895.38004600578 68 18730 21386.6222872913 -2656.62228729132 69 19684 19879.6184936995 -195.618493699516 70 19785 19768.6513405923 16.3486594076967 71 18479 19777.9253318049 -1298.9253318049 72 10698 19041.0929217229 -8343.09292172288 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 14308.3641693248 1802.46543534106 26814.2629033084 74 14308.3641693248 -69.5443314622153 28686.2726701117 75 14308.3641693248 -1724.4460200759 30341.1743587254 76 14308.3641693248 -3223.82771536828 31840.5560540178 77 14308.3641693248 -4604.71336961754 33221.441708267 78 14308.3641693248 -5891.41928759356 34508.1476262431 79 14308.3641693248 -7100.93290971868 35717.6612483682 80 14308.3641693248 -8245.67651369 36862.4048523395 81 14308.3641693248 -9335.05988142204 37951.7882200715 82 14308.3641693248 -10376.4135399393 38993.1418785888 83 14308.3641693248 -11375.5802370184 39992.3085756679 84 14308.3641693248 -12337.3062103162 40954.0345489657

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/1gasq1275335022.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/1gasq1275335022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/2gasq1275335022.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/2gasq1275335022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/3gasq1275335022.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275335110wh5ohuxf87n630x/3gasq1275335022.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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