Exponential smoothing prijsindexcijfer ruwe aardolie_Jan De Cleermaecker

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 29 May 2008 12:40:59 -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/29/t1212086506my2986rq52cl5u5.htm/, Retrieved Thu, 29 May 2008 18:41:49 +0000

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Dataseries X:

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68.4 70.6 83.9 90.1 90.6 87.1 90.8 94.1 99.8 96.8 87 96.3 107.1 115.2 106.1 89.5 91.3 97.6 100.7 104.6 94.7 101.8 102.5 105.3 110.3 109.8 117.3 118.8 131.3 125.9 133.1 147 145.8 164.4 149.8 137.7 151.7 156.8 180 180.4 170.4 191.6 199.5 218.2 217.5 205 194 199.3 219.3 211.1 215.2 240.2 242.2 240.7 255.4 253 218.2 203.7 205.6 215.6 188.5 202.9 214 230.3 230 241 259.6 247.8 270.3 289.7 322.7 315 320.2

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 70.6 68.4 2.19999999999999 3 83.9 70.6 13.3 4 90.1 83.9 6.19999999999999 5 90.6 90.1 0.5 6 87.1 90.6 -3.5 7 90.8 87.1 3.7 8 94.1 90.8 3.3 9 99.8 94.1 5.7 10 96.8 99.8 -3 11 87 96.8 -9.8 12 96.3 87 9.3 13 107.1 96.3 10.8 14 115.2 107.1 8.10000000000001 15 106.1 115.2 -9.1 16 89.5 106.1 -16.6 17 91.3 89.5 1.80000000000000 18 97.6 91.3 6.3 19 100.7 97.6 3.10000000000001 20 104.6 100.7 3.89999999999999 21 94.7 104.6 -9.9 22 101.8 94.7 7.1 23 102.5 101.8 0.700000000000003 24 105.3 102.5 2.800 25 110.3 105.3 5 26 109.8 110.3 -0.5 27 117.3 109.8 7.5 28 118.8 117.3 1.5 29 131.3 118.8 12.5000000000000 30 125.9 131.3 -5.40000000000001 31 133.1 125.9 7.19999999999999 32 147 133.1 13.9 33 145.8 147 -1.19999999999999 34 164.4 145.8 18.6 35 149.8 164.4 -14.6 36 137.7 149.8 -12.1000000000000 37 151.7 137.7 14 38 156.8 151.7 5.10000000000002 39 180 156.8 23.2 40 180.4 180 0.400000000000006 41 170.4 180.4 -10 42 191.6 170.4 21.2 43 199.5 191.6 7.9 44 218.2 199.5 18.7 45 217.5 218.2 -0.699999999999989 46 205 217.5 -12.5 47 194 205 -11 48 199.3 194 5.30000000000001 49 219.3 199.3 20 50 211.1 219.3 -8.20000000000002 51 215.2 211.1 4.09999999999999 52 240.2 215.2 25 53 242.2 240.2 2 54 240.7 242.2 -1.5 55 255.4 240.7 14.7000000000000 56 253 255.4 -2.40000000000001 57 218.2 253 -34.8 58 203.7 218.2 -14.5 59 205.6 203.7 1.90000000000001 60 215.6 205.6 10 61 188.5 215.6 -27.1 62 202.9 188.5 14.4 63 214 202.9 11.1 64 230.3 214 16.3 65 230 230.3 -0.300000000000011 66 241 230 11 67 259.6 241 18.6000000000000 68 247.8 259.6 -11.8 69 270.3 247.8 22.5 70 289.7 270.3 19.4000000000000 71 322.7 289.7 33 72 315 322.7 -7.69999999999999 73 320.2 315 5.19999999999999 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 320.2 296.397229952147 344.002770047853 75 320.2 286.537799776278 353.862200223722 76 320.2 278.97239291624 361.42760708376 77 320.2 272.594459904294 367.805540095706 78 320.2 266.975388120205 373.424611879795 79 320.2 261.895358917957 378.504641082043 80 320.2 257.223789938924 383.176210061076 81 320.2 252.875599552556 387.524400447444 82 320.2 248.791689856441 391.608310143559 83 320.2 244.929032027549 395.470967972451 84 320.2 241.255142780162 399.144857219838 85 320.2 237.744785832480 402.65521416752

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/1zg1k1212086453.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/1zg1k1212086453.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/2wcuu1212086453.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/2wcuu1212086453.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/3gvys1212086453.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086506my2986rq52cl5u5/3gvys1212086453.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')

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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