oef 10.2 eigen waarden

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 13:19:16 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle.htm/, Retrieved Sun, 16 Jan 2011 14:17:05 +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/2011/Jan/16/t1295183822c0a9jvw2amd5wle.htm/}, year = {2011}, } @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 = {2011}, 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 «

89,3 88,1 93,6 79,7 83,8 62,3 62,3 77,6 80,3 97 94 75,1 74 77,6 75,1 85 75,4 63,2 64,7 77 82,6 97,6 99 75,3 71,6 76,8 83,9 79,7 77,5 73,1 65,6 85,2 98,3 98 100,6 84,1 76,7 82,4 95,5 79,9 82,4 83,6 73,1 91,1 118,6 102,9 111,8 93,9 91,6 92 91,1 97,5 94,7 96,7 78,7 103,5 113,8 106,1 120,3 114,2 106,3 98,8 113,1 97,7 116,3 107,2 94,5 123,5 126,6 126,5 141,4 124,3 124,9 108,9 126,7 107,7 121,8 118,3 122,8 149,5 147 139,3 162,1 142,2 141,4 124,7 114 126,6 121,9 125,1 122,1 135,9 148,4 137,5 145,3 139,9 128,2 115,4 124,7 111,5 121,1 122,5 127,4 143,7 157,8 148,8 162,9 153,9

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' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.731350595836053 beta 0.015292862227736 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 93.6 86.9 6.7 4 79.7 90.6749847662469 -10.9749847662469 5 83.8 81.4006097908594 2.39939020914062 6 62.3 81.9344277678502 -19.6344277678502 7 62.3 66.1341996829024 -3.83419968290244 8 77.6 61.8465944309632 15.7534055690368 9 80.3 72.060589031888 8.23941096811195 10 97 76.8713724340784 20.1286275659216 11 94 90.602468984942 3.39753101505802 12 75.1 92.1352675993852 -17.0352675993852 13 74 78.5339967777313 -4.53399677773135 14 77.6 74.0248275875882 3.5751724124118 15 75.1 75.4862904316792 -0.386290431679242 16 85 74.0462146206988 10.9537853793012 17 75.4 81.0222220089975 -5.62222200899748 18 63.2 75.8124750906152 -12.6124750906152 19 64.7 65.349338895827 -0.649338895826986 20 77 63.628186990711 13.371813009289 21 82.6 72.3109691781838 10.2890308218162 22 97.6 78.8542338640511 18.7457661359489 23 99 91.7919979304902 7.20800206950977 24 75.3 96.3722288671173 -21.0722288671173 25 71.6 80.0340148962004 -8.43401489620045 26 76.8 72.8444364767395 3.95556352326049 27 83.9 74.7602243948367 9.1397756051633 28 79.7 80.5697122155095 -0.869712215509466 29 77.5 79.049027907034 -1.54902790703399 30 73.1 77.014200647072 -3.91420064707197 31 65.6 73.2058247368685 -7.60582473686847 32 85.2 66.6125104288894 18.5874895711106 33 98.3 79.3835828813644 18.9164171186356 34 98 92.6067862978045 5.39321370219554 35 100.6 96.0001069341242 4.59989306587578 36 84.1 98.8646792963343 -14.7646792963343 37 76.7 87.4018253960065 -10.7018253960065 38 82.4 78.7906481506845 3.60935184931554 39 95.5 80.6863275041264 14.8136724958736 40 79.9 90.9419761273838 -11.0419761273838 41 82.4 82.1645823617271 0.235417638272921 42 83.6 81.63755026143 1.96244973856993 43 73.1 82.3955330257254 -9.29553302572538 44 91.1 74.8160180197732 16.2839819802268 45 118.6 86.1262238375851 32.4737761624149 46 102.9 109.640046404788 -6.74004640478756 47 111.8 104.399432801544 7.40056719845596 48 93.9 109.583336611196 -15.6833366111963 49 91.6 97.7094042169086 -6.1094042169086 50 92 92.7690426949368 -0.769042694936829 51 91.1 91.725756439159 -0.625756439159062 52 97.5 90.7802639341292 6.71973606587082 53 94.7 95.2820582604291 -0.582058260429122 54 96.7 94.4371709575557 2.26282904244434 55 78.7 95.6982021632108 -16.9982021632108 56 103.5 82.682551281659 20.817448718341 57 113.8 97.5562307916374 16.2437692083626 58 106.1 109.266624592303 -3.16662459230274 59 120.3 106.745798386327 13.5542016136732 60 114.2 116.605354596551 -2.40535459655094 61 106.3 114.765977309598 -8.46597730959843 62 98.8 108.399472742024 -9.59947274202383 63 113.1 101.096620850193 12.0033791498073 64 97.7 109.727278681949 -12.0272786819493 65 116.3 100.648582166403 15.6514178335972 66 107.2 111.987769244218 -4.78776924421778 67 94.5 108.325196137739 -13.8251961377391 68 123.5 97.8984683572181 25.6015316427819 69 126.6 116.592840325319 10.0071596746815 70 126.5 123.994183578862 2.50581642113758 71 141.4 125.937441137548 15.4625588624521 72 124.3 137.529560122966 -13.229560122966 73 124.9 127.989715519552 -3.08971551955231 74 108.9 125.831095558628 -16.9310955586278 75 126.7 113.360209170452 13.3397908295477 76 107.7 123.177151720956 -15.4771517209558 77 121.8 111.745702831785 10.054297168215 78 118.3 119.099146022922 -0.799146022921832 79 122.8 118.505979065485 4.29402093451512 80 149.5 121.685729033319 27.8142709666807 81 147 142.378115029701 4.62188497029899 82 139.3 146.160428921942 -6.86042892194237 83 162.1 141.468415625093 20.6315843749067 84 142.2 157.113455431684 -14.9134554316841 85 141.4 146.595810491043 -5.1958104910434 86 124.7 143.1270587169 -18.4270587168995 87 114 129.775529264618 -15.7755292646176 88 126.6 118.18675693505 8.41324306495022 89 121.9 124.38255510635 -2.48255510635032 90 125.1 122.58193879464 2.51806120536048 91 122.1 124.46668931634 -2.3666893163398 92 135.9 122.752504529591 13.1474954704087 93 148.4 132.531675456086 15.8683245439136 94 137.5 144.478204732342 -6.9782047323422 95 145.3 139.637863870255 5.66213612974516 96 139.9 144.105371673136 -4.2053716731362 97 128.2 141.309237021397 -13.1092370213969 98 115.4 131.854635615895 -16.4546356158954 99 124.7 119.76933900602 4.93066099398028 100 111.5 123.379338515196 -11.8793385151957 101 121.1 114.562471072113 6.53752892788745 102 122.5 119.287909232515 3.21209076748457 103 127.4 121.61721166189 5.78278833811028 104 143.7 125.891272563022 17.8087274369781 105 157.8 139.159691902589 18.6403080974108 106 148.8 153.244769733887 -4.44476973388669 107 162.9 150.396849860596 12.5031501394042 108 153.9 160.083642066154 -6.18364206615405 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 156.034677060112 132.773109212627 179.296244907597 110 156.508122363589 127.535017526592 185.481227200585 111 156.981567667065 123.116596609688 190.846538724442 112 157.455012970542 119.200310048516 195.709715892567 113 157.928458274018 115.627934977412 200.228981570625 114 158.401903577495 112.307353295223 204.496453859767 115 158.875348880971 109.179498412428 208.571199349515 116 159.348794184448 106.203901580995 212.493686787901 117 159.822239487924 103.351458474094 216.293020501755 118 160.295684791401 100.600446926937 219.990922655865 119 160.769130094878 97.9341722254992 223.604087964256 120 161.242575398354 95.3394950224593 227.145655774249

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/16jyh1295183954.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/16jyh1295183954.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/2eemj1295183954.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/2eemj1295183954.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/347c01295183954.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295183822c0a9jvw2amd5wle/347c01295183954.ps (open in new window)

Parameters (Session):

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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