prijsindex van de grondstoffen

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Dec 2009 02:22:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d.htm/, Retrieved Sat, 05 Dec 2009 10:24:14 +0100

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/Dec/05/t1260005050giqt74wdzck181d.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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226.9 235.9 216.2 226.2 198.3 176.7 166.2 157.6 163.4 159.7 191.0 239.4 321.9 362.7 413.6 407.1 383.2 347.7 333.8 312.3 295.4 283.3 287.6 265.7 250.2 234.7 244.0 231.2 223.8 223.5 210.5 201.6 190.7 207.5 198.8 196.6 204.2 227.4 229.7 217.9 221.4 216.3 197.0 193.8 196.8 180.5 174.8 181.6 190.0 190.6 179.0 174.1 161.1 168.6 169.4 152.2 148.3 137.7 145.0 153.4

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.640813350950387 gamma 0.0132538546896654 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 321.9 232.266313151761 89.6336868482385 14 362.7 424.105164663350 -61.4051646633504 15 413.6 439.765982393856 -26.1659823938562 16 407.1 417.695074950639 -10.5950749506388 17 383.2 388.403694396960 -5.20369439696043 18 347.7 353.597581998779 -5.89758199877889 19 333.8 282.434728471431 51.3652715285689 20 312.3 337.787962975724 -25.4879629757245 21 295.4 322.583749900528 -27.1837499005278 22 283.3 270.549876133684 12.7501238663161 23 287.6 328.688040900699 -41.0880409006987 24 265.7 321.482017935623 -55.7820179356235 25 250.2 269.356770640194 -19.1567706401941 26 234.7 180.528904238534 54.1710957614658 27 244 198.185710326222 45.8142896737777 28 231.2 203.865633998877 27.3343660011232 29 223.8 201.691554415966 22.1084455840337 30 223.5 203.802540546999 19.6974594530012 31 210.5 190.838126701136 19.6618732988645 32 201.6 214.107213908746 -12.5072139087458 33 190.7 211.253968577793 -20.553968577793 34 207.5 175.651909210897 31.8480907891033 35 198.8 257.992220671398 -59.192220671398 36 196.6 219.776947524338 -23.1769475243378 37 204.2 212.190526676053 -7.99052667605304 38 227.4 172.215421338878 55.1845786611218 39 229.7 236.024807127731 -6.32480712773136 40 217.9 202.086221362007 15.8137786379931 41 221.4 193.588061642078 27.811938357922 42 216.3 208.556181594702 7.74381840529841 43 197 184.506302165573 12.4936978344268 44 193.8 197.156854180762 -3.35685418076247 45 196.8 204.777036474587 -7.97703647458681 46 180.5 189.600765525653 -9.10076552565283 47 174.8 207.557007956886 -32.7570079568859 48 181.6 187.635103774232 -6.03510377423228 49 190 202.309840874521 -12.3098408745212 50 190.6 163.949053249528 26.6509467504724 51 179 183.325126363219 -4.32512636321928 52 174.1 143.307455628881 30.7925443711193 53 161.1 152.649455661984 8.45054433801633 54 168.6 142.827673266112 25.7723267338880 55 169.4 146.333263826017 23.0667361739826 56 152.2 178.062411980083 -25.8624119800834 57 148.3 155.979266925498 -7.6792669254975 58 137.7 137.943961846718 -0.243961846718207 59 145 157.519386599767 -12.5193865997667 60 153.4 165.429132664147 -12.0291326641474 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 178.093251040712 117.860407019853 238.326095061572 62 172.332598674871 50.1411476166094 294.524049733132 63 167.810049445170 -36.214610360908 371.834709251248 64 139.588179235370 -128.767673374502 407.944031845242 65 109.355192181661 -211.389234931566 430.099619294888 66 81.2918193655818 -279.551594597375 442.135233328538 67 51.5973899941917 -301.716044738163 404.910824726546 68 34.9426157839616 -352.811245948082 422.696477516005 69 22.5144941487851 -428.189482833777 473.218471131347 70 10.0355827945042 -475.121983083101 495.19314867211 71 -0.541713241566507 -635.840853210128 634.757426726995 72 -14.6453323552816 -878.233768694767 848.943103984204

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/1theb1260004924.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/1theb1260004924.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/2wvya1260004924.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/2wvya1260004924.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/3ud6b1260004924.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/05/t1260005050giqt74wdzck181d/3ud6b1260004924.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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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