Exponential Smoothing - huurprijzen - Charlotte Van Opstal

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 31 May 2008 05:38:49 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/31/t121223418374q61ajefouybs5.htm/, Retrieved Sat, 31 May 2008 11:43:03 +0000

User-defined keywords:

Dataseries X:

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103,6 103,7 103,8 104 104 104,1 104,2 104,3 104,4 104,5 104,7 104,7 104,9 105 105,2 105,3 105,4 105,5 105,7 105,8 105,9 106 106,1 106,2 106,6 106,8 107 107,1 107,3 107,4 107,6 107,7 107,9 108,2 108,3 108,5 108,92 109,23 109,41 109,65 109,91 110,01 110,2 110,49 110,57 110,72 110,94 111,09 111,28 111,41 111,62 111,76 111,89 112,04 112,12 112,3 112,47 112,59 112,78 112,73 112,99 113,1 113,33 113,38 113,68 113,65 113,81 113,88 114,02 114,25 114,28 114,38 114,73 114,97 115,05 115,29 115,37 115,54 115,76 115,92 116,02 116,21 116,26 116,51

Text written by user:

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 0.887355825989984 beta 0.0349852410870049 gamma 0.000576885537757277 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 104.9 104.127194444444 0.772805555555522 14 105 104.950214570789 0.0497854292106865 15 105.2 105.233204132377 -0.0332041323768379 16 105.3 105.341521622037 -0.0415216220372798 17 105.4 105.445336193378 -0.0453361933779775 18 105.5 105.544358449621 -0.0443584496208302 19 105.7 105.730371232915 -0.0303712329146464 20 105.8 105.815352799030 -0.0153527990297135 21 105.9 105.909017775501 -0.00901777550140537 22 106 106.008024220962 -0.00802422096217015 23 106.1 106.103496529381 -0.00349652938086820 24 106.2 106.198711297128 0.00128870287225880 25 106.6 106.564929161277 0.0350708387225751 26 106.8 106.728782015877 0.0712179841233507 27 107 107.026962758075 -0.0269627580747454 28 107.1 107.137190057582 -0.0371900575823929 29 107.3 107.241354521124 0.058645478876457 30 107.4 107.432380128908 -0.0323801289084713 31 107.6 107.629129258405 -0.0291292584052911 32 107.7 107.715358834682 -0.0153588346823170 33 107.9 107.809163640583 0.0908363594173522 34 108.2 108.000020979972 0.199979020028181 35 108.3 108.289768478300 0.0102315216998079 36 108.5 108.407293409606 0.0927065903936608 37 108.92 108.867599860183 0.0524001398166831 38 109.23 109.060336493108 0.169663506892405 39 109.41 109.462427414518 -0.0524274145180925 40 109.65 109.565827655377 0.084172344623255 41 109.91 109.797227416235 0.112772583764993 42 110.01 110.057494886986 -0.0474948869858167 43 110.2 110.261580607339 -0.0615806073390814 44 110.49 110.338756301886 0.151243698114456 45 110.57 110.605316922304 -0.0353169223036645 46 110.72 110.705235342563 0.0147646574374249 47 110.94 110.845866443957 0.0941335560430474 48 111.09 111.055699355551 0.0343006444495018 49 111.28 111.480214817270 -0.20021481726954 50 111.41 111.456995934128 -0.0469959341281623 51 111.62 111.668288570797 -0.0482885707969274 52 111.76 111.776968967715 -0.0169689677150870 53 111.89 111.917081039623 -0.0270810396231838 54 112.04 112.047355287642 -0.00735528764214166 55 112.12 112.282421427464 -0.162421427464082 56 112.3 112.26236195169 0.0376380483099013 57 112.47 112.416807688248 0.0531923117517152 58 112.59 112.586722134336 0.00327786566450072 59 112.78 112.708262508565 0.0717374914349165 60 112.73 112.888619969027 -0.158619969027185 61 112.99 113.126343579847 -0.136343579847320 62 113.1 113.146206628359 -0.0462066283589593 63 113.33 113.344619540014 -0.0146195400138112 64 113.38 113.470643580129 -0.0906435801289831 65 113.68 113.530557414708 0.149442585292434 66 113.65 113.808130290408 -0.158130290408451 67 113.81 113.895372642246 -0.0853726422463126 68 113.88 113.932065151143 -0.0520651511434664 69 114.02 113.992497759422 0.0275022405778316 70 114.25 114.124399713455 0.125600286544966 71 114.28 114.343072456016 -0.0630724560163856 72 114.38 114.388189873547 -0.00818987354749368 73 114.73 114.748469277854 -0.0184692778538533 74 114.97 114.865663288572 0.104336711427564 75 115.05 115.195065939976 -0.145065939975581 76 115.29 115.198685219683 0.0913147803172336 77 115.37 115.419077800185 -0.049077800185259 78 115.54 115.513310863716 0.0266891362842614 79 115.76 115.763134534343 -0.00313453434252153 80 115.92 115.873932696804 0.0460673031958976 81 116.02 116.02562436465 -0.00562436464988991 82 116.21 116.131284697027 0.078715302972796 83 116.26 116.310033091394 -0.0500330913940132 84 116.51 116.368821005822 0.141178994177665 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 116.868376511980 116.629965754023 117.106787269937 86 117.009274125983 116.685574216604 117.332974035362 87 117.250144517287 116.855151502630 117.645137531945 88 117.391075479099 116.932095306168 117.850055652029 89 117.536166639935 117.017686994605 118.054646285264 90 117.681214093457 117.106232293045 118.256195893869 91 117.913784512921 117.284402957392 118.543166068450 92 118.033896077006 117.351633725510 118.716158428502 93 118.149804923115 117.415777709017 118.883832137212 94 118.265734780856 117.480768026473 119.050701535239 95 118.377455892096 117.542158317358 119.212753466833 96 118.485036198328 117.599850789270 119.370221607386

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/184g81212233923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/184g81212233923.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/2pg9r1212233923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/2pg9r1212233923.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/37wfc1212233923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t121223418374q61ajefouybs5/37wfc1212233923.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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')

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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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