index huishoudconsumptie elektriciteit en brandstof

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 16 Dec 2010 18:46:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p.htm/, Retrieved Thu, 16 Dec 2010 19:44:58 +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/2010/Dec/16/t1292525097bt7078a20hymx0p.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

132,1 125 127,1 101,5 85,7 79,3 70,9 77,1 83,9 96,2 111,7 127,2 143,6 134,9 135,6 105,3 86,4 74,6 67,6 73,4 78,5 98,2 118,6 136,9 137,9 115,6 119,3 98,5 84,3 73,5 60,7 69,5 77,9 113,9 126,3 135,1 130,5 113,1 110 90,8 85,4 72,5 64,7 67,2 77,9 105,2 107,2 120,7 121,3 107,9 105,6 81,3 71,7 64,8 57,3 61,9 70,1 88,8 106,8 110,7 114,1 108 111,5 86,8 78,4 68 57,3 65,3 73,3 88,6 101,3 122,9 126,6 114,1 124,7 93,3 77,2 66,5 57,9 63,7 65,8 85 101 105,3 121 117,9 106 86,6 79,9 65,2 61,2 67,6 78,9 95,5 113,1 124,4 122 110,3 114 93,3 75,5 65,4 59,2 63,8 74,2 91,7 107 120,7 127,4 119,7 112,7 84,4 75,6 66,5 59,9 64,8 74,3 100,4 105,9 131,1

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.264786991916332 beta 0 gamma 0.560459608377657 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 143.6 142.173980044541 1.42601995545917 14 134.9 134.365028304488 0.534971695512496 15 135.6 135.774958166406 -0.174958166405872 16 105.3 105.601841065423 -0.301841065422948 17 86.4 86.3180700268043 0.0819299731956988 18 74.6 74.0924554423624 0.507544557637559 19 67.6 72.0429399868427 -4.44293998684273 20 73.4 76.4372287961622 -3.03722879616215 21 78.5 81.7397668170721 -3.23976681707212 22 98.2 92.3344957596896 5.86550424031039 23 118.6 108.878760864691 9.72123913530852 24 136.9 127.189707921916 9.71029207808361 25 137.9 147.644612757203 -9.74461275720321 26 115.6 136.394400516438 -20.7944005164376 27 119.3 131.838319286585 -12.5383192865845 28 98.5 99.9301808323502 -1.43018083235017 29 84.3 81.5647557048365 2.73524429516351 30 73.5 70.7894846140615 2.71051538593845 31 60.7 67.4218853677964 -6.72188536779643 32 69.5 71.479012348698 -1.97901234869806 33 77.9 76.6893604148253 1.21063958517473 34 113.9 91.6924469850936 22.2075530149064 35 126.3 114.276444622482 12.0235553775177 36 135.1 133.383369224023 1.71663077597671 37 130.5 143.639214465184 -13.1392144651844 38 113.1 126.662594057663 -13.5625940576634 39 110 127.315401397604 -17.3154013976038 40 90.8 98.8385397337297 -8.03853973372972 41 85.4 80.8013539679064 4.59864603209361 42 72.5 70.6917247241964 1.80827527580355 43 64.7 63.2852170468452 1.41478295315484 44 67.2 71.5421602325398 -4.34216023253977 45 77.9 77.4642649645822 0.435735035417849 46 105.2 100.383397353405 4.8166026465951 47 107.2 113.447698272686 -6.24769827268567 48 120.7 122.46044767874 -1.7604476787396 49 121.3 125.215775187045 -3.91577518704493 50 107.9 111.433937939176 -3.53393793917628 51 105.6 112.788691259977 -7.18869125997661 52 81.3 91.5659419822415 -10.2659419822415 53 71.7 78.6431468994277 -6.94314689942767 54 64.8 65.3835692010754 -0.583569201075392 55 57.3 57.9301120758796 -0.630112075879637 56 61.9 62.6953672047879 -0.795367204787887 57 70.1 70.722838696787 -0.622838696787028 58 88.8 92.8706743370042 -4.07067433700423 59 106.8 98.1694126780139 8.63058732198614 60 110.7 111.969466595427 -1.26946659542683 61 114.1 113.774555576511 0.325444423489216 62 108 102.160153421408 5.83984657859156 63 111.5 104.407400404395 7.09259959560545 64 86.8 85.8838742119237 0.916125788076286 65 78.4 77.0630361235264 1.33696387647359 66 68 68.200525200477 -0.200525200477031 67 57.3 60.4710569561418 -3.17105695614182 68 65.3 64.672786003542 0.627213996457925 69 73.3 73.5039877680701 -0.203987768070078 70 88.6 95.2545830564975 -6.65458305649746 71 101.3 105.451498128919 -4.15149812891936 72 122.9 111.810219912972 11.0897800870277 73 126.6 117.634212576751 8.96578742324911 74 114.1 110.04132122644 4.0586787735599 75 124.7 112.333334253362 12.3666657466375 76 93.3 91.3123297740655 1.98767022593447 77 77.2 82.394821327376 -5.19482132737605 78 66.5 70.782085782487 -4.282085782487 79 57.9 60.5211339888723 -2.62113398887232 80 63.7 66.6020547613356 -2.90205476133561 81 65.8 74.249820023212 -8.44982002321204 82 85 90.7560925869753 -5.75609258697534 83 101 101.988318606604 -0.988318606603556 84 105.3 115.227173674076 -9.92717367407599 85 121 114.432826619369 6.56717338063099 86 117.9 104.901540256754 12.998459743246 87 106 112.665242402336 -6.66524240233562 88 86.6 84.6486404125142 1.95135958748584 89 79.9 73.7351517341059 6.16484826589411 90 65.2 65.9196959853728 -0.719695985372752 91 61.2 57.5433755080228 3.65662449197723 92 67.6 65.1303761272483 2.46962387275165 93 78.9 71.9123773089754 6.98762269102458 94 95.5 95.0842121279258 0.415787872074205 95 113.1 111.320461914416 1.77953808558435 96 124.4 122.510997187222 1.8890028127783 97 122 132.739630759354 -10.7396307593545 98 110.3 120.284440230791 -9.98444023079098 99 114 113.68138832278 0.318611677219891 100 93.3 89.8787498770735 3.42125012292649 101 75.5 80.4869532874741 -4.9869532874741 102 65.4 66.6818333484786 -1.2818333484786 103 59.2 59.8454344490295 -0.645434449029501 104 63.8 65.7592486826884 -1.95924868268835 105 74.2 72.973954566782 1.22604543321805 106 91.7 91.1024516068109 0.597548393189143 107 107 107.230251561379 -0.230251561378807 108 120.7 117.421726190031 3.27827380996926 109 127.4 122.524134959165 4.87586504083508 110 119.7 114.547258798018 5.15274120198201 111 112.7 116.202276472486 -3.50227647248602 112 84.4 92.3779805670601 -7.97798056706013 113 75.6 76.7584937295897 -1.15849372958974 114 66.5 65.5852433361242 0.91475666387582 115 59.9 59.5906836162079 0.309316383792051 116 64.8 65.2339501219855 -0.433950121985546 117 74.3 74.2586214117738 0.041378588226209 118 100.4 91.9244085036175 8.4755914963825 119 105.9 110.249785506968 -4.34978550696826 120 131.1 121.005813457758 10.0941865422421 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 128.712263377168 120.049377636982 137.375149117355 122 119.321170256173 110.106796928996 128.535543583349 123 115.997286361633 106.24053656276 125.754036160505 124 90.7060434262522 80.9917962838517 100.420290568653 125 79.5466091430092 69.6112754443992 89.4819428416193 126 69.060332706455 58.9851601022579 79.135505310652 127 62.2925527072407 52.0024794229805 72.582625991501 128 67.7647371947554 56.5809821915007 78.9484921980102 129 77.5042770359619 65.0373954501326 89.9711586217911 130 99.4604167751058 84.4219638472468 114.498869702965 131 110.435261069344 93.8438942830944 127.026627855593 132 128.72102132047 -75.5544682539183 332.996510894858

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/1k3ug1292525197.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/1k3ug1292525197.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/2dcu11292525197.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/2dcu11292525197.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/3dcu11292525197.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292525097bt7078a20hymx0p/3dcu11292525197.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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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