Laurane Potié -Goudkoers 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 13:18:37 -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/t121174319980bdxltyysxn89m.htm/, Retrieved Sun, 25 May 2008 21:20:03 +0200

User-defined keywords:

periode: januari 2000 tot en met januari 2008

Dataseries X:

» Textbox « » Textfile « » CSV «

9026 9787 9536 9490 9736 9694 9647 9753 10070 10137 9984 9732 9103 9155 9308 9394 9948 10177 10002 9728 10002 10063 10018 9960 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 19394

Text written by user:

bron: belgostat

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 9787 9026 761 3 9536 9787 -251 4 9490 9536 -46 5 9736 9490 246 6 9694 9736 -42 7 9647 9694 -47 8 9753 9647 106 9 10070 9753 317 10 10137 10070 67 11 9984 10137 -153 12 9732 9984 -252 13 9103 9732 -629 14 9155 9103 52 15 9308 9155 153 16 9394 9308 86 17 9948 9394 554 18 10177 9948 229 19 10002 10177 -175 20 9728 10002 -274 21 10002 9728 274 22 10063 10002 61 23 10018 10063 -45 24 9960 10018 -58 25 10236 9960 276 26 10893 10236 657 27 10756 10893 -137 28 10940 10756 184 29 10997 10940 57 30 10827 10997 -170 31 10166 10827 -661 32 10186 10166 20 33 10457 10186 271 34 10368 10457 -89 35 10244 10368 -124 36 10511 10244 267 37 10812 10511 301 38 10738 10812 -74 39 10171 10738 -567 40 9721 10171 -450 41 9897 9721 176 42 9828 9897 -69 43 9924 9828 96 44 10371 9924 447 45 10846 10371 475 46 10413 10846 -433 47 10709 10413 296 48 10662 10709 -47 49 10570 10662 -92 50 10297 10570 -273 51 10635 10297 338 52 10872 10635 237 53 10296 10872 -576 54 10383 10296 87 55 10431 10383 48 56 10574 10431 143 57 10653 10574 79 58 10805 10653 152 59 10872 10805 67 60 10625 10872 -247 61 10407 10625 -218 62 10463 10407 56 63 10556 10463 93 64 10646 10556 90 65 10702 10646 56 66 11353 10702 651 67 11346 11353 -7 68 11451 11346 105 69 11964 11451 513 70 12574 11964 610 71 13031 12574 457 72 13812 13031 781 73 14544 13812 732 74 14931 14544 387 75 14886 14931 -45 76 16005 14886 1119 77 17064 16005 1059 78 15168 17064 -1896 79 16050 15168 882 80 15839 16050 -211 81 15137 15839 -702 82 14954 15137 -183 83 15648 14954 694 84 15305 15648 -343 85 15579 15305 274 86 16348 15579 769 87 15928 16348 -420 88 16171 15928 243 89 15937 16171 -234 90 15713 15937 -224 91 15594 15713 -119 92 15683 15594 89 93 16438 15683 755 94 17032 16438 594 95 17696 17032 664 96 17745 17696 49 97 19394 17745 1649 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 98 19394 18500.9239740325 20287.0760259675 99 19394 18130.9997718466 20657.0002281534 100 19394 17847.1469480027 20940.8530519973 101 19394 17607.8479480651 21180.1520519349 102 19394 17397.0212968614 21390.9787031386 103 19394 17206.4194348672 21581.5805651328 104 19394 17031.1429334162 21756.8570665838 105 19394 16867.9995436931 21920.0004563069 106 19394 16714.7719220976 22073.2280779024 107 19394 16569.8456342512 22218.1543657488 108 19394 16432.0019126043 22355.9980873957 109 19394 16300.2938960053 22487.7061039947

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/1cr311211743111.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/1cr311211743111.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/2q8og1211743111.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/2q8og1211743111.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/3x1l91211743111.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t121174319980bdxltyysxn89m/3x1l91211743111.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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