opgave 10 oef 2

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 12:25:10 -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/Jun/01/t12123452251niyqcr49lnq4ce.htm/, Retrieved Sun, 01 Jun 2008 18:33:49 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

78 69 78 74 81 80 76 71 72 69 70 68 62 57 49 57 57 58 53 55 62 54 62 68 73 74 79 77 76 83 77 84 78 74 75 79 79 82 88 81 69 62 62 68 57 67 72 75 81 80 79 81 83 84 90 84 90 92 93 85 93 94 94 102 96 96 92 90 84 86 70 67

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.690039354681511 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 62 65.8847045912947 -3.88470459129474 14 57 59.6486145488604 -2.64861454886037 15 49 50.600721688916 -1.60072168891604 16 57 58.5915634346292 -1.59156343462922 17 57 58.4405615755904 -1.44056157559039 18 58 58.7912637201857 -0.791263720185704 19 53 52.8056290424035 0.194370957596519 20 55 53.8595188196722 1.14048118032778 21 62 59.637277193768 2.362722806232 22 54 51.6114192593807 2.38858074061930 23 62 59.6241356220141 2.37586437798591 24 68 65.3525690340732 2.64743096592683 25 73 63.9870278787659 9.01297212123413 26 74 66.5847040370439 7.41529596295612 27 79 63.0136979098609 15.9863020901391 28 77 87.7791692072488 -10.7791692072488 29 76 81.731326468887 -5.73132646888706 30 83 79.882869347289 3.11713065271103 31 77 74.772014700037 2.22798529996304 32 84 78.0485933061938 5.95140669380625 33 78 90.1469770895449 -12.1469770895449 34 74 69.0108833666548 4.98911663334525 35 75 80.9613005725973 -5.96130057259728 36 79 81.9926691848068 -2.99266918480676 37 79 78.2035411489692 0.796458851030806 38 82 74.134883152519 7.86511684748096 39 88 72.2839198700277 15.7160801299723 40 81 88.5253943469738 -7.52539434697377 41 69 86.4326655125165 -17.4326655125165 42 62 79.1258300697769 -17.1258300697769 43 62 61.1846449041123 0.81535509588769 44 68 63.9934965273492 4.00650347265081 45 57 68.3443836448818 -11.3443836448818 46 67 54.6848934027793 12.3151065972207 47 72 67.4643961606507 4.53560383934929 48 75 76.280351811562 -1.280351811562 49 81 74.8706928491182 6.12930715088179 50 80 76.5033307681197 3.49666923188026 51 79 73.642050704093 5.35794929590706 52 81 75.623251473068 5.37674852693206 53 83 78.5064132170846 4.49358678291539 54 84 86.2025933492362 -2.20259334923624 55 90 83.9111075890135 6.08889241098647 56 84 92.637590478116 -8.63759047811602 57 90 82.0543780167202 7.94562198327978 58 92 89.0555395635605 2.94446043643946 59 93 93.5452324173059 -0.545232417305854 60 85 98.1882770617686 -13.1882770617686 61 93 91.070292263917 1.92970773608306 62 94 88.4708205885685 5.52917941143147 63 94 86.7760091581974 7.22399084180259 64 102 89.6839057858829 12.3160942141171 65 96 96.784093133400 -0.78409313339992 66 96 99.15076370676 -3.15076370675992 67 92 98.9489664716977 -6.94896647169774 68 90 93.919750225103 -3.9197502251029 69 84 91.6090946664054 -7.60909466640538 70 86 86.3084784684595 -0.308478468459498 71 70 87.3828854337043 -17.3828854337043 72 67 75.9415462386613 -8.94154623866126 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 75.2381727533417 60.3856416556873 90.0907038509962 74 72.903196092184 55.1680918824504 90.6383003019175 75 68.9427856122443 48.5447897992377 89.3407814252508 76 68.334747276201 46.2032556717812 90.4662388806207 77 64.6766199760073 39.9418235674869 89.4114163845278 78 66.1266266435401 39.2201276741974 93.0331256128829 79 66.5987200829767 37.6526428715279 95.5447972944255 80 67.0828310058941 36.6090079872785 97.5566540245098 81 66.4173524758906 33.5982774203083 99.236427531473 82 68.1668376322062 35.3571637951204 100.976511469292 83 64.3127136970675 28.7670521407279 99.8583752534072 84 67 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/1gndd1212344700.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/1gndd1212344700.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/2xlrl1212344700.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/2xlrl1212344700.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/3v04y1212344700.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123452251niyqcr49lnq4ce/3v04y1212344700.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=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')

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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