Opdracht 10 - eigen cijferreeks evolutie geboorten is België - Sophie Van Landeghem

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 16:09:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq.htm/, Retrieved Thu, 19 May 2011 18:07:30 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

126.304 125.511 125.495 130.133 126.257 110.323 98.417 105.749 120.665 124.075 127.245 146.731 144.979 148.210 144.670 142.970 142.524 146.142 146.522 148.128 148.798 150.181 152.388 155.694 160.662 155.520 158.262 154.338 158.196 160.371 154.856 150.636 145.899 141.242 140.834 141.119 139.104 134.437 129.425 123.155 119.273 120.472 121.523 121.983 123.658 124.794 124.827 120.382 117.395 115.790 114.283 117.271 117.448 118.764 120.550 123.554 125.412 124.182 119.828 115.361 114.226 115.214 115.864 114.276 113.469 114.883 114.172 111.225 112.149 115.618 118.002 121.382 120.663

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.773753532020297 beta 0.0346047116561005 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 144.979 133.515676549145 11.4633234508547 14 148.21 144.516351465839 3.69364853416059 15 144.67 143.665278992085 1.00472100791521 16 142.97 143.278582939518 -0.308582939518118 17 142.524 143.246034184331 -0.722034184331079 18 146.142 147.652534895614 -1.51053489561431 19 146.522 125.69340170912 20.8285982908801 20 148.128 150.70319823366 -2.57519823365959 21 148.798 165.098438934999 -16.3004389349988 22 150.181 157.342190138547 -7.16119013854706 23 152.388 156.346889470515 -3.95888947051478 24 155.694 173.081795605873 -17.3877956058731 25 160.662 158.989424064622 1.67257593537772 26 155.52 160.048135129227 -4.52813512922685 27 158.262 151.398448761946 6.86355123805433 28 154.338 154.576166738474 -0.238166738473836 29 158.196 153.834700138493 4.36129986150718 30 160.371 161.462301177588 -1.09130117758806 31 154.856 144.359174898572 10.496825101428 32 150.636 155.280533903342 -4.64453390334177 33 145.899 164.114758834874 -18.2157588348742 34 141.242 156.038390823322 -14.7963908233218 35 140.834 148.74954298314 -7.91554298313994 36 141.119 158.168497569169 -17.049497569169 37 139.104 147.44305083641 -8.33905083640977 38 134.437 137.877098624352 -3.44009862435249 39 129.425 131.2005031681 -1.77550316809965 40 123.155 124.40955853764 -1.25455853763961 41 119.273 122.21762871106 -2.94462871106042 42 120.472 121.058350410092 -0.586350410091796 43 121.523 105.080964954396 16.4420350456037 44 121.983 115.449218974268 6.53378102573177 45 123.658 128.434014845848 -4.77601484584768 46 124.794 130.461924244474 -5.66792424447364 47 124.827 130.969054696029 -6.14205469602922 48 120.382 138.917240725629 -18.5352407256293 49 117.395 128.196634824461 -10.8016348244609 50 115.79 116.951415265722 -1.16141526572194 51 114.283 111.593375953333 2.68962404666661 52 117.271 107.673565256573 9.5974347434271 53 117.448 113.08496299101 4.36303700898954 54 118.764 117.89816735963 0.865832640369504 55 120.55 106.720507058102 13.8294929418976 56 123.554 112.579119079043 10.9748809209567 57 125.412 126.313872217897 -0.901872217896951 58 124.182 131.113795889218 -6.93179588921801 59 119.828 130.478064115764 -10.6500641157638 60 115.361 131.955876345639 -16.5948763456394 61 114.226 124.359918495297 -10.1339184952969 62 115.214 115.703874119368 -0.489874119368395 63 115.864 111.646168734329 4.21783126567104 64 114.276 110.422042633228 3.85395736677208 65 113.469 110.001716971538 3.46728302846178 66 114.883 113.103190630545 1.77980936945548 67 114.172 105.362769839726 8.80923016027417 68 111.225 106.353734211797 4.87126578820303 69 112.149 112.17793697608 -0.0289369760799048 70 115.618 115.811638575546 -0.193638575546018 71 118.002 119.251342555537 -1.24934255553717 72 121.382 126.612720500418 -5.23072050041813 73 120.663 129.530585399097 -8.8675853990966 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 124.329206562552 107.542214573171 141.116198551932 75 122.0216662129 100.518278024119 143.525054401682 76 117.644739961312 92.046478264596 143.243001658028 77 114.244812640395 84.904855922515 143.584769358274 78 114.278735724641 81.423204321162 147.13426712812 79 106.70096432636 70.484480262408 142.917448390313 80 99.698335070376 60.2308744487108 139.165795692041 81 100.227824346717 57.5894590054352 142.866189687999 82 103.430526869895 57.6802587134843 149.180795026305 83 106.370268849498 57.5516758196873 155.188861879309 84 113.42006787018 61.5650948075685 165.275040932792 85 119.324959201919 64.4565646619633 174.193353741875

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/1t1e71305821378.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/1t1e71305821378.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/2htw21305821378.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/2htw21305821378.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/37rpt1305821378.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058212504y3jlm3i53crmhq/37rpt1305821378.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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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