opgave 10 oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 02:10:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v.htm/, Retrieved Sat, 16 Jan 2010 10:11:07 +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/Jan/16/t126363306356qv88hyz32h22v.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

102,5 77,7 82,8 77,3 103,1 99,7 99,5 107,2 96,7 97,1 105,2 151,2 102,7 75,4 87,2 83,7 105,8 111,5 99,7 111,2 101,5 110,9 116,3 164,9 118,1 83,7 84 107,2 113,7 120,7 111,2 112,4 112,5 130,4 130,7 174,3 132,2 91,8 104,2 104,8 131,4 141,2 132,7 135,7 136,9 151,2 144 201,5 149,6 108,7 122,8 126,7 139,9 162,5 142,7 151,6 148,1 159 157,8 226,7 153,7 122,3 117,6 166 154,5 183,9 164,4 173,3 160,2 166,4 170,3 238,4 166,8 122,5 141,8 140,5 173,8 188,8 168 187,4 177,7 183,8 196,1 264,6 193,7 141,3 170,1 163,7 190,1 230,7 195,9 210,3 204,7 210,3 221,2 288,2 203,2 162,4 149,2 195,3 213,7 227,9 212,1 226,8 212,6 220,9 228,1 311,6

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.779753800673534 beta 0.0793509153332443 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 82.8 52.9 29.9 4 77.3 53.2646765568975 24.0353234431025 5 103.1 50.5435151554654 52.5564848445346 6 99.7 73.3137270451841 26.3862729548159 7 99.5 77.3102456942241 22.1897543057759 8 107.2 79.4074857807315 27.7925142192685 9 96.7 87.593138170859 9.10686182914098 10 97.1 81.7720616799005 15.3279383200995 11 105.2 81.7502968082492 23.4497031917508 12 151.2 89.512440068511 61.687559931489 13 102.7 130.907564503555 -28.2075645035545 14 75.4 100.461304136446 -25.0613041364463 15 87.2 70.9177046600093 16.2822953399907 16 83.7 74.6193876460005 9.08061235399953 17 105.8 73.267386375907 32.532613624093 18 111.5 92.2151009498316 19.2848990501684 19 99.7 102.026097007533 -2.32609700753298 20 111.2 94.841911413035 16.3580885869651 21 101.5 103.238933830329 -1.73893383032922 22 110.9 97.4171391358326 13.4828608641674 23 116.3 104.298837638047 12.0011623619529 24 164.9 110.767738155714 54.1322618442861 25 118.1 153.43791281633 -35.3379128163299 26 83.7 124.156874437090 -40.4568744370903 27 84 88.381070435679 -4.38107043567891 28 107.2 80.464436585551 26.7355634144489 29 113.7 98.4653572489978 15.2346427510022 30 120.7 108.441022308447 12.2589776915533 31 111.2 116.854915393813 -5.65491539381316 32 112.4 110.950489020383 1.44951097961687 33 112.5 110.675453413342 1.82454658665755 34 130.4 110.805745566220 19.5942544337803 35 130.7 126.004413332797 4.69558666720341 36 174.3 129.876323847819 44.4236761521807 37 132.2 167.475041569822 -35.2750415698216 38 91.8 140.745767044656 -48.9457670446562 39 104.2 100.328213278964 3.8717867210365 40 104.8 101.334911424399 3.4650885756007 41 131.4 102.238884651887 29.1611153481135 42 141.2 124.983752453871 16.2162475461295 43 132.7 138.638177372251 -5.93817737225129 44 135.7 134.650185416143 1.04981458385743 45 136.9 136.176063161123 0.723936838876767 46 151.2 137.492629492598 13.7073705074020 47 144 149.781209853091 -5.78120985309053 48 201.5 146.515788001304 54.984211998696 49 149.6 194.034537698370 -44.4345376983697 50 108.7 161.281788974127 -52.5817889741272 51 122.8 118.922735141596 3.87726485840433 52 126.7 120.827745692709 5.87225430729127 53 139.9 124.651697756097 15.2483022439030 54 162.5 136.730134997818 25.7698650021823 55 142.7 158.607289998823 -15.9072899988232 56 151.6 147.002274496545 4.59772550345537 57 148.1 151.670603250397 -3.57060325039677 58 159 149.748718472849 9.25128152715087 59 157.8 158.397162520648 -0.597162520647913 60 226.7 159.329295951466 67.3707040485338 61 153.7 217.428138585300 -63.7281385852997 62 122.3 169.359034232662 -47.0590342326617 63 117.6 131.375988300761 -13.7759883007609 64 166 118.493145982511 47.5068540174887 65 154.5 156.335280411047 -1.83528041104654 66 183.9 155.589141519088 28.310858480912 67 164.4 180.101280095595 -15.7012800955952 68 173.3 169.323282544695 3.97671745530485 69 160.2 174.135334496716 -13.9353344967155 70 166.4 164.118158496683 2.28184150331720 71 170.3 166.887574185796 3.41242581420397 72 238.4 170.749708329924 67.6502916700761 73 166.8 228.88736869856 -62.08736869856 74 122.5 182.019990413152 -59.5199904131522 75 141.8 133.471784633008 8.3282153669924 76 140.5 138.343776657335 2.15622334266513 77 173.8 138.536548989486 35.2634510105144 78 188.8 166.726704963707 22.0732950362925 79 168 185.997553667658 -17.9975536676583 80 187.4 172.909421962567 14.4905780374328 81 177.7 186.050627033477 -8.35062703347731 82 183.8 180.864627456420 2.93537254357975 83 196.1 184.660552706697 11.439447293303 84 264.6 195.795368960248 68.804631039752 85 193.7 255.918135242085 -62.2181352420852 86 141.3 210.025705577425 -68.7257055774252 87 170.1 154.806626683067 15.2933733169331 88 163.7 166.048008785723 -2.34800878572329 89 190.1 163.388175031573 26.7118249684268 90 230.7 185.040629302103 45.659370697897 91 195.9 224.292640390243 -28.3926403902434 92 210.3 204.045543104659 6.25445689534143 93 204.7 211.201640987912 -6.50164098791174 94 210.3 208.008839374340 2.29116062566044 95 221.2 211.814021917480 9.3859780825195 96 288.2 221.732165014566 66.467834985434 97 203.2 280.272745622270 -77.0727456222696 98 162.4 222.118200182675 -59.7182001826750 99 149.2 173.800912971491 -24.6009129714909 100 195.3 151.344302668888 43.955697331112 101 213.7 185.064692443814 28.6353075561856 102 227.9 208.610736175547 19.2892638244528 103 212.1 226.062674126053 -13.9626741260532 104 226.8 216.722358098201 10.0776419017989 105 212.6 226.751115669478 -14.1511156694778 106 220.9 217.011818791697 3.88818120830285 107 228.1 221.579310231315 6.5206897686846 108 311.6 228.602972544441 82.9970274555593 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 300.394722665652 237.78616821994 363.003277111363 110 307.469225183785 225.637721172808 389.300729194761 111 314.543727701917 215.063998818754 414.023456585081 112 321.618230220050 205.216731985719 438.019728454382 113 328.692732738183 195.705193781353 461.680271695013 114 335.767235256316 186.317042516501 485.217427996131 115 342.841737774449 176.925053745310 508.758421803588 116 349.916240292582 167.448005311602 532.384475273562 117 356.990742810715 157.831746541346 556.149739080084 118 364.065245328848 148.039074311124 580.091416346571 119 371.139747846981 138.043903702881 604.23559199108 120 378.214250365114 127.827714695670 628.600786034557

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/1de361263633012.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/1de361263633012.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/2sim81263633012.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/2sim81263633012.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/3o7tj1263633012.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t126363306356qv88hyz32h22v/3o7tj1263633012.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=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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