Joeri Van de Velde opgave 10 oef 2

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 13:26:26 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8.htm/, Retrieved Tue, 27 May 2008 21:27:30 +0200

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Dataseries X:

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105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 97,82 97,83 97,82 97,83 97,82 97,82 97,8 97,8 97,44 97,44 97,44 97,44 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 89,38 89,38 89,38 89,38 87,69 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94

Text written by user:

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.981229383786507 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 105.18 105.18 0 3 105.18 105.18 0 4 105.18 105.18 0 5 105.18 105.18 0 6 105.18 105.18 0 7 105.18 105.18 0 8 105.18 105.18 0 9 105.18 105.18 0 10 105.18 105.18 0 11 97.82 105.18 -7.36000000000001 12 97.83 97.9581517353313 -0.128151735331301 13 97.82 97.832405487041 -0.0124054870409935 14 97.83 97.8202328586362 0.00976714136382384 15 97.82 97.829816664738 -0.00981666473795428 16 97.82 97.8201842648463 -0.000184264846296855 17 97.8 97.8200034587647 -0.0200034587647053 18 97.8 97.8003754772474 -0.000375477247416711 19 97.44 97.8000070479393 -0.360007047939305 20 97.44 97.446757554131 -0.00675755413101342 21 97.44 97.4401268434551 -0.000126843455134917 22 97.44 97.4400023809298 -2.38092981419413e-06 23 97.7 97.4400000446915 0.259999955308487 24 97.7 97.6951196406234 0.00488035937662801 25 97.7 97.6999083926472 9.16073528429706e-05 26 97.7 97.6999982804735 1.71952646610407e-06 27 97.7 97.6999999677234 3.22765743021591e-08 28 97.7 97.6999999993942 6.05851369073207e-10 29 97.7 97.6999999999886 1.13686837721616e-11 30 97.7 97.6999999999998 2.1316282072803e-13 31 97.7 97.7 1.4210854715202e-14 32 97.7 97.7 0 33 97.7 97.7 0 34 89.38 97.7 -8.32 35 89.38 89.5361715268963 -0.156171526896273 36 89.38 89.3829314357948 -0.00293143579484934 37 89.38 89.3800550248563 -5.50248562660727e-05 38 87.69 89.3800010328505 -1.69000103285046 39 89.21 87.721722360788 1.48827763921196 40 89.21 89.1820641116152 0.0279358883847749 41 89.21 89.2094756261605 0.000524373839454029 42 89.21 89.2099901571799 9.84282009142134e-06 43 89.21 89.2099998152442 1.84755805321402e-07 44 89.21 89.209999996532 3.46797435213375e-09 45 89.21 89.209999999935 6.50999254503404e-11 46 89.21 89.2099999999988 1.22213350550737e-12 47 89.21 89.21 2.8421709430404e-14 48 89.21 89.21 0 49 89.21 89.21 0 50 89.21 89.21 0 51 89.21 89.21 0 52 89.21 89.21 0 53 89.21 89.21 0 54 89.21 89.21 0 55 89.21 89.21 0 56 89.21 89.21 0 57 89.21 89.21 0 58 89.21 89.21 0 59 89.21 89.21 0 60 89.21 89.21 0 61 89.21 89.21 0 62 89.21 89.21 0 63 89.21 89.21 0 64 89.21 89.21 0 65 89.21 89.21 0 66 89.21 89.21 0 67 89.21 89.21 0 68 89.21 89.21 0 69 89.21 89.21 0 70 89.21 89.21 0 71 92.07 89.21 2.86 72 92.07 92.0163160376294 0.0536839623705845 73 92.07 92.0689923189455 0.00100768105447457 74 92.07 92.0699810852057 1.89147943387979e-05 75 92.07 92.0699996449576 3.5504234574546e-07 76 92.07 92.0699999933356 6.66435084895056e-09 77 92.07 92.0699999998749 1.25083943203208e-10 78 92.07 92.0699999999976 2.34479102800833e-12 79 92.07 92.07 4.2632564145606e-14 80 92.07 92.07 0 81 94 92.07 1.93000000000001 82 94 93.963772710708 0.036227289292043 83 94 93.9993199914562 0.000680008543753274 84 94 93.9999872358206 1.27641793881139e-05 85 94 93.9999997604085 2.39591500417191e-07 86 94 93.9999999955027 4.49728077001055e-09 87 94 93.9999999999156 8.44124770082999e-11 88 94 93.9999999999984 1.57740487338742e-12 89 94 94 2.8421709430404e-14 90 94 94 0 91 94 94 0 92 94 94 0 93 94 94 0 94 94 94 0 95 94 94 0 96 94 94 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 94 91.6145311220365 96.3854688779635 98 94 90.657949500329 97.342050499671 99 94 89.919786608893 98.080213391107 100 94 89.2960674864973 98.7039325135027 101 94 88.7458758231075 99.2541241768925 102 94 88.2480733105485 99.7519266894515 103 94 87.7900482759169 100.209951724083 104 94 87.3635596747909 100.636440325209 105 94 86.962871326693 101.037128673307 106 94 86.5838001820812 101.416199817919 107 94 86.2231844875993 101.776815512401 108 94 85.878565441467 102.121434558533

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/1jlyj1211916380.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/1jlyj1211916380.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/2j3v41211916380.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/2j3v41211916380.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/3e8m01211916380.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211916446e5e54l289jtzwm8/3e8m01211916380.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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Software written by Ed van Stee & Patrick Wessa

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