opgave 10 - oefening 2 - Seghers Sanne 2MAR03

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 08:09:02 -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/Jun/01/t1212329418h35ur1pdul867e4.htm/, Retrieved Sun, 01 Jun 2008 14:10:18 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

additief triple model PPI

Dataseries X:

» Textbox « » Textfile « » CSV «

121.3 124.0 122.9 120.1 118.3 118.1 118.4 116.6 116.4 116.7 117.7 119.5 123.3 124.6 125.4 127.0 126.8 131.8 128.1 130.1 133.5 142.7 140.0 137.9 132.6 133.7 137.0 141.1 145.3 146.1 141.8 140.0 137.4 139.5 140.3 142.7 143.3 146.0 147.2 146.1 147.1 141.7 138.8 138.3 140.2 143.1 142.0 142.4 141.2 138.0 137.9 136.8 135.9 138.8 139.5 138.0 139.7 137.5 137.8 137.4 141.7 145.3 148.9 151.3 151.4 149.2 143.8 143.6 144.3 142.0 140.8 141.8

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.829991115439346 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 123.3 116.077234299517 7.22276570048308 14 124.6 122.405398993151 2.19460100684874 15 125.4 123.75189833077 1.64810166923002 16 127 124.923974740238 2.07602525976171 17 126.8 124.434557261268 2.36544273873179 18 131.8 129.702020385163 2.09797961483727 19 128.1 126.589158159184 1.5108418408161 20 130.1 129.076476797229 1.0235232027714 21 133.5 132.463491961975 1.03650803802515 22 142.7 141.452951091284 1.24704890871615 23 140 138.429657272703 1.57034272729678 24 137.9 136.266361117888 1.63363888211234 25 132.6 138.575201216059 -5.97520121605925 26 133.7 133.094337956149 0.605662043850998 27 137 133.029122328702 3.9708776712975 28 141.1 136.201832995346 4.89816700465397 29 145.3 138.103971633919 7.19602836608095 30 146.1 147.335306803528 -1.23530680352798 31 141.8 141.356027827047 0.443972172953437 32 140 142.875005621354 -2.87500562135395 33 137.4 143.028484036150 -5.62848403614967 34 139.5 146.521852778001 -7.02185277800052 35 140.3 136.690406846486 3.60959315351411 36 142.7 136.230431336264 6.46956866373617 37 143.3 141.259479770181 2.04052022981884 38 146 143.55039931645 2.4496006835501 39 147.2 145.587752932497 1.61224706750275 40 146.1 146.960468578617 -0.860468578616718 41 147.1 144.473647692953 2.62635230704655 42 141.7 148.478790445586 -6.77879044558568 43 138.8 138.183961643271 0.616038356729206 44 138.3 139.281497128688 -0.981497128687835 45 140.2 140.538454975444 -0.338454975444165 46 143.1 148.185615772513 -5.08561577251277 47 142 141.768669617022 0.231330382978427 48 142.4 138.990987267999 3.409012732001 49 141.2 140.726823886356 0.473176113644399 50 138 141.786409052998 -3.78640905299781 51 137.9 138.50557243767 -0.605572437670077 52 136.8 137.617133970016 -0.817133970015561 53 135.9 135.759070953917 0.140929046083272 54 138.8 136.102376653334 2.69762334666558 55 139.5 134.930073701014 4.56992629898645 56 138 139.037705824025 -1.03770582402504 57 139.7 140.357333832239 -0.657333832239487 58 137.5 146.932768499327 -9.43276849932681 59 137.8 137.811652288286 -0.0116522882861432 60 137.4 135.372530712554 2.02746928744634 61 141.7 135.462580237597 6.23741976240271 62 145.3 140.582269097065 4.71773090293539 63 148.9 144.900563574556 3.99943642544426 64 151.3 147.798274209676 3.50172579032446 65 151.4 149.687705648193 1.71229435180680 66 149.2 151.769891336676 -2.56989133667565 67 143.8 146.543906133219 -2.74390613321893 68 143.6 143.627775035428 -0.0277750354281636 69 144.3 145.850303243428 -1.55030324342820 70 142 150.192679373583 -8.19267937358342 71 140.8 143.702499577618 -2.90249957761804 72 141.8 139.210669220222 2.58933077977798 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 140.482787776311 133.352005410921 147.613570141701 74 140.167113041841 130.900153789418 149.434072294265 75 140.447616341958 129.451934897427 151.443297786489 76 139.941215047284 127.453881982409 152.428548112160 77 138.620025948267 124.801127160135 152.438924736400 78 138.553012925353 123.520034499233 153.585991351473 79 135.430430637524 119.274350760162 151.586510514886 80 135.253483670160 118.047455841308 152.459511499012 81 137.240221588443 119.044731205088 155.435711971797 82 141.74007268016 122.606219253987 160.873926106333 83 142.949121542149 122.920820975756 162.977422108543 84 141.8 120.915524899550 162.684475100451

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/1murr1212329336.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/1murr1212329336.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/2gpd11212329336.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/2gpd11212329336.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/35g2p1212329336.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329418h35ur1pdul867e4/35g2p1212329336.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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