jasper ledeganck opg 10 oef 2 personenwagens '02-'08

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 15:49:06 -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/26/t1211838859n08x3a5gr4i9vib.htm/, Retrieved Mon, 26 May 2008 23:54:20 +0200

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36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 42553

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.448709214642811 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 35022 35338 -316 4 34777 35196.2078881729 -419.207888172874 5 26887 35008.1054458987 -8121.10544589875 6 23970 31364.0905992381 -7394.09059923806 7 22780 28046.2940134562 -5266.29401345616 8 17351 25683.2593626001 -8332.25936260011 9 21382 21944.4978078076 -562.497807807606 10 24561 21692.0998582280 2868.90014177205 11 17409 22979.4017877311 -5570.40178773114 12 11514 20479.9111763134 -8965.91117631339 13 31514 16456.8242138326 15057.1757861674 14 27071 23213.1177355825 3857.88226441747 15 29462 24944.1850566337 4517.81494336628 16 26105 26971.3702517732 -866.370251773158 17 22397 26582.6219365101 -4185.62193651013 18 23843 24704.4948045869 -861.49480458695 19 21705 24317.9341474019 -2612.93414740188 20 18089 23145.4865182078 -5056.4865182078 21 20764 20876.5944237708 -112.594423770817 22 25316 20826.0722683075 4489.92773169255 23 17704 22840.7442145982 -5136.7442145982 24 15548 20535.8397522448 -4987.83975224484 25 28029 18297.7500942509 9731.24990574914 26 29383 22664.2515969525 6718.74840304751 27 36438 25679.0159162666 10758.9840837334 28 32034 30506.6712148331 1527.32878516690 29 22679 31191.9977145267 -8512.9977145267 30 24319 27372.1371957854 -3053.13719578538 31 18004 26002.1664024678 -7998.16640246777 32 17537 22413.3154374339 -4876.31543743394 33 20366 20225.2677671523 140.732232847658 34 22782 20288.4156168283 2493.58438317166 35 19169 21407.3099070469 -2238.30990704687 36 13807 20402.9596265286 -6595.95962652865 37 29743 17443.2917626933 12299.7082373067 38 25591 22962.2841861909 2628.71581380910 39 29096 24141.8131945243 4954.18680547568 40 26482 26364.8024652031 117.197534796913 41 22405 26417.3900789999 -4012.39007899988 42 27044 24616.9936778112 2427.00632218876 43 17970 25706.0137785737 -7736.0137785737 44 18730 22234.7931115239 -3504.79311152393 45 19684 20662.1601469665 -978.160146966493 46 19785 20223.2506756263 -438.250675626263 47 18479 20026.6035591493 -1547.60355914932 48 10698 19332.179581545 -8634.17958154501 49 31956 15457.9436424250 16498.0563575750 50 29506 22860.7735537653 6645.22644623471 51 34506 25842.5478935789 8663.4521064211 52 27165 29729.9186843467 -2564.91868434672 53 26736 28579.0160358708 -1843.01603587083 54 23691 27752.0377578411 -4061.03775784112 55 18157 25929.8126948854 -7772.81269488543 56 17328 22442.0800149977 -5114.08001499772 57 18205 20147.3451878476 -1942.34518784760 58 20995 19275.7970040433 1719.20299595674 59 17382 20047.2192301706 -2665.21923017058 60 9367 18851.3108025498 -9484.31080254982 61 31124 14595.6131509094 16528.3868490906 62 26551 22012.0526332774 4538.94736672261 63 30651 24048.7201415045 6602.27985849545 64 25859 27011.2239516621 -1152.22395166209 65 25100 26494.2104472192 -1394.21044721916 66 25778 25868.6153724006 -90.6153724006472 67 20418 25827.9554198162 -5409.95541981619 68 18688 23400.4585721378 -4712.45857213785 69 20424 21285.9349871971 -861.934987197092 70 24776 20899.1768160187 3876.82318398128 71 19814 22638.743102212 -2824.74310221200 72 12738 21371.2548432508 -8633.25484325076 73 42553 17497.4338427245 25055.5661572755 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 28740.0972555866 15316.6520375960 42163.5424735771 75 28740.0972555866 14027.2422099814 43452.9523011918 76 28740.0972555866 12842.0682687723 44638.1262424008 77 28740.0972555866 11739.3164576884 45740.8780534847 78 28740.0972555866 10703.8623433113 46776.3321678619 79 28740.0972555866 9724.70896390621 47755.4855472669 80 28740.0972555866 8793.5633723283 48686.6311388448 81 28740.0972555866 7903.98830913099 49576.2062020421 82 28740.0972555866 7050.86817520747 50429.3263359657 83 28740.0972555866 6230.0577137786 51250.1367973945 84 28740.0972555866 5438.14235376869 52042.0521574044 85 28740.0972555866 4672.26967769848 52807.9248334746

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/1zk7f1211838538.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/1zk7f1211838538.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/2txsp1211838538.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/2txsp1211838538.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/3usu61211838538.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211838859n08x3a5gr4i9vib/3usu61211838538.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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