Roze Zalm exp smoothie

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 14:00:41 -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/t1212264079ne0yv2rau316k71.htm/, Retrieved Sat, 31 May 2008 20:01:23 +0000

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Dataseries X:

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11.98 11.79 11.66 11.96 11.83 12.36 12.53 12.55 12.53 12.24 12.34 12.05 12.22 12.23 11.92 12.13 12.1 12.15 12.23 12.08 12.02 11.93 12.16 11.87 11.93 11.79 11.43 11.63 11.93 11.89 11.83 11.59 12.04 11.81 11.9 11.72 11.91 11.94 11.91 11.84 12.01 11.89 11.8 11.7 11.5 11.76 11.61 11.27 11.64 11.39 11.54 11.62 11.59 11.44 11.31 11.56 11.4 11.51 11.5 11.24 11.8 11.87 11.86 12.11 11.92 12.61 13.34 13.31 13.47 13.24 13.18 13.3

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.743882684016797 beta 0.0836577071765574 gamma 0.526978787215965 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 12.22 12.2677376624260 -0.0477376624260479 14 12.23 12.2499093149203 -0.0199093149202998 15 11.92 11.9398216041343 -0.0198216041342967 16 12.13 12.142393883475 -0.0123938834750064 17 12.1 12.0958690349825 0.00413096501746146 18 12.15 12.1364110717607 0.0135889282392707 19 12.23 12.2193578323690 0.0106421676309836 20 12.08 12.0817588439362 -0.00175884393621395 21 12.02 12.0331339044428 -0.0131339044428191 22 11.93 11.9476616418300 -0.0176616418300206 23 12.16 12.1645367785168 -0.00453677851675138 24 11.87 11.8608177131991 0.00918228680085775 25 11.93 11.8658233456410 0.0641766543590307 26 11.79 11.9345837473385 -0.144583747338494 27 11.43 11.5338660984570 -0.103866098456965 28 11.63 11.6530126988605 -0.0230126988604606 29 11.93 11.5881417470623 0.341858252937712 30 11.89 11.8878619346215 0.00213806537845151 31 11.83 11.9672040385983 -0.137204038598309 32 11.59 11.7198001332662 -0.129800133266173 33 12.04 11.5655487180540 0.474451281945957 34 11.81 11.8631490856060 -0.0531490856060142 35 11.9 12.0717766206156 -0.171776620615592 36 11.72 11.6584698796601 0.0615301203398655 37 11.91 11.7207867329659 0.189213267034051 38 11.94 11.8733713649015 0.0666286350985033 39 11.91 11.6643480763925 0.245651923607531 40 11.84 12.1176907060079 -0.277690706007881 41 12.01 11.9514725822162 0.0585274177837558 42 11.89 12.0159250033739 -0.125925003373920 43 11.8 11.9945464787100 -0.194546478709986 44 11.7 11.7149264244336 -0.0149264244335914 45 11.5 11.7431141063731 -0.243114106373088 46 11.76 11.4122213731165 0.347778626883493 47 11.61 11.897054413292 -0.287054413292001 48 11.27 11.4243086974453 -0.154308697445261 49 11.64 11.3179509559454 0.322049044054621 50 11.39 11.5376824568551 -0.147682456855064 51 11.54 11.1749268099682 0.365073190031801 52 11.62 11.6182977873987 0.00170221260128223 53 11.59 11.6998938164922 -0.109893816492249 54 11.44 11.6002448918256 -0.160244891825604 55 11.31 11.525086158189 -0.215086158189001 56 11.56 11.2406355598678 0.319364440132162 57 11.4 11.4890983758269 -0.0890983758269428 58 11.51 11.3647618750569 0.145238124943145 59 11.5 11.6095962693882 -0.109596269388241 60 11.24 11.2997082882507 -0.0597082882507465 61 11.8 11.3438432306556 0.456156769344426 62 11.87 11.6244816542671 0.245518345732901 63 11.86 11.6657410777048 0.19425892229523 64 12.11 11.9751732421149 0.134826757885129 65 11.92 12.1906327684804 -0.270632768480386 66 12.61 12.0011507991294 0.608849200870562 67 13.34 12.5808391197117 0.759160880288263 68 13.31 13.2353779167185 0.074622083281497 69 13.47 13.3723775185137 0.0976224814863382 70 13.24 13.5591580053409 -0.319158005340867 71 13.18 13.5562223667439 -0.376222366743885 72 13.3 13.1192563069182 0.180743693081755 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 13.5544211382564 13.162764040443 13.9460782360697 74 13.5355655833541 13.0060303363113 14.0651008303969 75 13.4295668501650 12.77996686193 14.0791668384001 76 13.6582723339976 12.8826319466134 14.4339127213818 77 13.7674382112790 12.8735677802941 14.6613086422640 78 13.9748727075576 12.9575485019567 14.9921969131586 79 14.1529562868116 13.0131402421995 15.2927723314236 80 14.1215423777173 12.8744226365863 15.3686621188483 81 14.1785350662145 12.8165516492286 15.5405184832005 82 14.2006986646847 12.7262679070989 15.6751294222704 83 14.4231279007419 12.8145011190895 16.0317546823943 84 14.3378045349901 9.6422633067386 19.0333457632416

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/1x1f61212264035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/1x1f61212264035.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/2rxuk1212264035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/2rxuk1212264035.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/318xl1212264035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212264079ne0yv2rau316k71/318xl1212264035.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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