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: Tue, 21 Dec 2010 20:45:40 +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/21/t1292964268obmo3wfx642giiy.htm/, Retrieved Tue, 21 Dec 2010 21:44:28 +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/21/t1292964268obmo3wfx642giiy.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 «

102,8 106,3 103,7 106,9 104,3 105,4 96,2 95,7 95,9 93,6 94,7 94,5 96,6 96,7 98,9 102 105,2 106,4 99,3 96,4 93,1 95,6 93,3 96,7 105,6 105,2 107 104,9 104,5 105,2 99,7 100,2 98,5 98,4 97,1 98,4 100,6 111,3 119 117,8 108,8 109,3 103,5 103,7 110 105,5 110,4 106,7 110,2 105,2 108 108,1 107,2 106 99,4 100,2 100,3 100,8 99,5 100,2 103 111 120,5 109,5 106,6 105,5 103,9 104,9 104,8 99,6 97 95,4 99,3 103,9 107,4 107,4 111 113,2 108,5 113,3 113,8 105,3 107,5 109,4 118,9 119 115 124,1 120,5 117,7 117,1 118,1 119,6 118,8 124,9 124 124,9 121,7 121,6 125,1 127,9 129 130,1 130,3 127,9 124,1 125,7 129,2 129,2 132,6 131,5 131 125,8 127,2 127,3 127,5 122 118,4 118,3 115,5

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.77855541108374 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 96.6 97.7089398501379 -1.10893985013787 14 96.7 96.7897038891088 -0.089703889108776 15 98.9 99.008428293043 -0.108428293043062 16 102 102.059395097890 -0.0593950978896061 17 105.2 105.18678664398 0.0132133560200600 18 106.4 106.360946274092 0.0390537259078485 19 99.3 94.7616345639049 4.53836543609511 20 96.4 98.4338157545798 -2.03381575457982 21 93.1 97.6440661311446 -4.54406613114462 22 95.6 92.2277731320427 3.37222686795727 23 93.3 96.1313235211291 -2.83132352112911 24 96.7 93.6528912554094 3.04710874459056 25 105.6 97.7398345609094 7.86016543909055 26 105.2 104.041996214102 1.15800378589783 27 107 107.422705544400 -0.422705544400458 28 104.9 110.500499711075 -5.60049971107517 29 104.5 109.459383802520 -4.95938380251964 30 105.2 106.772248171377 -1.57224817137711 31 99.7 94.9640902507496 4.7359097492504 32 100.2 97.3359827040107 2.86401729598933 33 98.5 99.772324387962 -1.27232438796197 34 98.4 98.6266956788422 -0.226695678842148 35 97.1 98.3365377411824 -1.23653774118236 36 98.4 98.428954656649 -0.0289546566489065 37 100.6 101.131533757941 -0.531533757941119 38 111.3 99.47421059304 11.8257894069599 39 119 110.880500893443 8.1194991065566 40 117.8 119.621984034453 -1.82198403445284 41 108.8 122.058320044582 -13.2583200445820 42 109.3 113.788979031937 -4.48897903193748 43 103.5 100.620929571758 2.87907042824216 44 103.7 101.063126761092 2.63687323890774 45 110 102.383100044595 7.61689995540515 46 105.5 108.397295902632 -2.89729590263192 47 110.4 105.774847473923 4.62515252607683 48 106.7 110.865527500676 -4.16552750067643 49 110.2 110.480711300359 -0.280711300359158 50 105.2 111.655364126819 -6.4553641268194 51 108 107.857268948042 0.142731051957824 52 108.1 108.162258536412 -0.0622585364121022 53 107.2 109.078464936905 -1.87846493690466 54 106 111.536263536928 -5.53626353692796 55 99.4 99.323422121087 0.076577878912957 56 100.2 97.5926329267454 2.60736707325459 57 100.3 99.8891756125352 0.410824387464814 58 100.8 98.1520713214823 2.64792867851769 59 99.5 101.415569659227 -1.91556965922692 60 100.2 99.485483122993 0.714516877007043 61 103 103.528165322715 -0.528165322714656 62 111 103.078108570833 7.92189142916675 63 120.5 112.037989923223 8.4620100767766 64 109.5 118.789206739553 -9.28920673955265 65 106.6 112.131688191518 -5.53168819151797 66 105.5 110.903813653349 -5.40381365334935 67 103.9 99.9932470725936 3.90675292740639 68 104.9 101.747717439540 3.15228256045957 69 104.8 103.973011866593 0.826988133407127 70 99.6 102.975518176800 -3.3755181768005 71 97 100.531705543012 -3.53170554301244 72 95.4 97.9224402468721 -2.52244024687209 73 99.3 99.033411199412 0.266588800588096 74 103.9 100.911035861822 2.98896413817772 75 107.4 105.849557387799 1.55044261220125 76 107.4 103.590697163785 3.80930283621491 77 111 107.877749064313 3.12225093568661 78 113.2 113.475033976598 -0.275033976597953 79 108.5 108.250411405929 0.249588594070985 80 113.3 106.909733238539 6.39026676146052 81 113.8 111.090321123654 2.70967887634609 82 105.3 110.400689552354 -5.10068955235367 83 107.5 106.565908549835 0.934091450164686 84 109.4 107.682976115507 1.71702388449324 85 118.9 113.239230879872 5.66076912012845 86 119 120.321643898434 -1.32164389843385 87 115 121.920810426206 -6.9208104262064 88 124.1 113.289160211407 10.8108397885933 89 120.5 123.013621652757 -2.51362165275742 90 117.7 123.689352238269 -5.98935223826882 91 117.1 113.879980463688 3.22001953631215 92 118.1 116.131534877619 1.96846512238109 93 119.6 115.980845541884 3.61915445811552 94 118.8 114.026806056171 4.77319394382938 95 124.9 119.388223994573 5.51177600542707 96 124 124.322050280934 -0.322050280933666 97 124.9 129.793813980514 -4.8938139805139 98 121.7 127.177267622756 -5.4772676227563 99 121.6 124.273599698928 -2.6735996989277 100 125.1 122.742024549008 2.35797545099160 101 127.9 122.919473485239 4.98052651476061 102 129 128.702815230009 0.297184769990992 103 130.1 125.513848834900 4.58615116510025 104 130.3 128.49109982425 1.80890017574998 105 127.9 128.429155155938 -0.529155155938128 106 124.1 123.147434118408 0.952565881591767 107 125.7 125.731156537994 -0.0311565379938656 108 129.2 125.053293887754 4.14670611224612 109 129.2 133.120574075532 -3.92057407553236 110 132.6 131.132765709815 1.46723429018539 111 131.5 134.417858232361 -2.9178582323612 112 131 133.946299047731 -2.94629904773143 113 125.8 130.482888123026 -4.68288812302639 114 127.2 127.698289009671 -0.498289009671254 115 127.3 124.844406723115 2.45559327688485 116 127.5 125.574717873833 1.92528212616745 117 122 125.134490760238 -3.13449076023811 118 118.4 118.336136079827 0.0638639201727642 119 118.3 119.935325135947 -1.635325135947 120 115.5 118.896673067673 -3.39667306767285 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 118.980330752302 110.84551129802 127.115150206585 122 121.056842234052 110.713119969415 131.400564498688 123 122.116415073612 109.897024073180 134.335806074043 124 123.771709292713 110.116558223922 137.426860361504 125 122.275186176138 107.071037540023 137.479334812253 126 124.012708175293 107.720046410486 140.305369940100 127 122.238295909037 104.89806015235 139.578531665724 128 120.986176406582 102.883255152599 139.089097660565 129 118.069763193211 99.3601554020778 136.779370984345 130 114.537611829211 94.6229844919517 134.452239166471 131 115.668772997793 94.7971668929008 136.540379102686 132 115.5 NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/1w0hx1292964335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/1w0hx1292964335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/27azi1292964335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/27azi1292964335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/37azi1292964335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292964268obmo3wfx642giiy/37azi1292964335.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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