Tom Knaepen - Goudwaarde te Brussel EUR/kg - Exponential Smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 10:00:33 -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/25/t12117313075a1xx7vflq3pqlx.htm/, Retrieved Sun, 25 May 2008 18:01:47 +0200

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Dataseries X:

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10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.847259609453347 beta 0.0285189422376599 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10812 10914.545 -102.545000000002 14 10738 10758.5325100920 -20.5325100919545 15 10171 10152.2180977162 18.7819022838121 16 9721 9702.50035847478 18.4996415252208 17 9897 9875.82381030026 21.1761896997414 18 9828 9802.51000578773 25.4899942122684 19 9924 9927.92536033625 -3.92536033624674 20 10371 10403.9900914676 -32.9900914675727 21 10846 10853.2156453249 -7.21564532493721 22 10413 10349.7711617599 63.2288382401257 23 10709 10639.2475722834 69.7524277165885 24 10662 10617.7699142865 44.2300857134705 25 10570 11023.6991726782 -453.699172678183 26 10297 10576.4797557018 -279.479755701808 27 10635 9744.30297144189 890.697028558112 28 10872 10041.876900282 830.123099717992 29 10296 10931.4724699731 -635.4724699731 30 10383 10314.8066300171 68.193369982906 31 10431 10485.2827160569 -54.2827160568722 32 10574 10926.3983518576 -352.398351857648 33 10653 11113.3771581826 -460.37715818264 34 10805 10230.2353995896 574.764600410377 35 10872 10959.9604811899 -87.9604811899335 36 10625 10802.9986097014 -177.998609701406 37 10407 10941.2567172338 -534.256717233828 38 10463 10447.1161367781 15.8838632218649 39 10556 10045.7807801648 510.219219835191 40 10646 10004.4041825719 641.59581742813 41 10702 10498.5222248473 203.477775152729 42 11353 10708.5244120152 644.475587984793 43 11346 11370.859951866 -24.8599518660067 44 11451 11814.3868015072 -363.386801507182 45 11964 11998.3140926721 -34.3140926720862 46 12574 11667.3125361300 906.687463870016 47 13031 12618.1040195344 412.89598046557 48 13812 12924.9137617263 887.086238273743 49 14544 13990.0644512583 553.935548741722 50 14931 14607.1320573339 323.867942666113 51 14886 14654.8840954089 231.115904591148 52 16005 14502.9970343061 1502.00296569392 53 17064 15785.8709427092 1278.12905729083 54 15168 17126.3926391424 -1958.39263914245 55 16050 15570.9482258911 479.051774108901 56 15839 16491.6481334537 -652.64813345372 57 15137 16575.7049980647 -1438.70499806466 58 14954 15259.5607950411 -305.560795041072 59 15648 15139.5619948300 508.438005170025 60 15305 15633.7778245057 -328.777824505683 61 15579 15622.5407604476 -43.5407604476204 62 16348 15688.4637410486 659.536258951406 63 15928 16004.7712741020 -76.771274102035 64 16171 15777.0244373676 393.975562632419 65 15937 16051.0284935064 -114.028493506383 66 15713 15648.1567096316 64.843290368377 67 15594 16158.5749061471 -564.57490614714 68 15683 15976.3390119373 -293.339011937251 69 16438 16207.5865352134 230.413464786594 70 17032 16481.8518848546 550.148115145385 71 17696 17235.0236337073 460.976366292685 72 17745 17583.8361052263 161.16389477365 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 18065.79817194 16958.4010881617 19173.1952557182 74 18311.5758923627 16842.7075719243 19780.444212801 75 17976.2609054394 16203.9236211618 19748.5981897170 76 17906.9561577666 15862.7995592416 19951.1127562915 77 17781.5431173197 15485.6345016038 20077.4517330356 78 17517.3345036683 14983.4694825416 20051.1995247950 79 17889.8397003351 15127.9861743893 20651.6932262808 80 18254.1794732254 15271.7782240705 21236.5807223803 81 18847.8528624879 15650.580452979 22045.1252719969 82 19004.0605282223 15596.3093890557 22411.8116673890 83 19292.5266148412 15677.7237035627 22907.3295261197 84 19208.8731510840 15389.7005152808 23028.0457868871

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/1pb601211731224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/1pb601211731224.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/20m5p1211731224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/20m5p1211731224.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/3nl6h1211731224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117313075a1xx7vflq3pqlx/3nl6h1211731224.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')

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Software written by Ed van Stee & Patrick Wessa

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