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 13:15:45 -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/t1212347820cglus0onknj8e1j.htm/, Retrieved Sun, 01 Jun 2008 19:17:00 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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12.23 12.25 12.33 12.37 12.38 12.41 12.41 12.41 12.43 12.44 12.46 12.46 12.46 12.47 12.55 12.58 12.6 12.62 12.62 12.66 12.7 12.76 12.79 12.81 12.86 13.03 13.09 13.15 13.17 13.18 13.18 13.19 13.19 13.19 13.25 13.24 13.3 13.35 13.35 13.35 13.36 13.37 13.38 13.39 13.4 13.4 13.44 13.44 13.44 13.47 13.52 13.58 13.65 13.66 13.68 13.68 13.77 13.78 13.79 13.79 13.82 13.86 13.94 14 14.02 14.03 14.07 14.1 14.1 14.16 14.17 14.17

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 0.851663547967142 beta 0.000749903072261239 gamma 0.086671636330431 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 12.46 12.3015652777778 0.158434722222218 14 12.47 12.4604006291127 0.0095993708872566 15 12.55 12.5599844678501 -0.00998446785011176 16 12.58 12.5899664216077 -0.00996642160766292 17 12.6 12.6074573794863 -0.00745737948631842 18 12.62 12.6258304343119 -0.00583043431194064 19 12.62 12.6226687086755 -0.00266870867547553 20 12.66 12.6534480051011 0.00655199489886016 21 12.7 12.6862510898449 0.0137489101551065 22 12.76 12.7447756392528 0.0152243607472329 23 12.79 12.7733164994148 0.0166835005851702 24 12.81 12.7935273776247 0.0164726223753302 25 12.86 12.8714394383643 -0.0114394383642846 26 13.03 12.8837054047201 0.146294595279945 27 13.09 13.0995628612762 -0.00956286127619954 28 13.15 13.1300114421417 0.0199885578582677 29 13.17 13.1731726811148 -0.00317268111482605 30 13.18 13.1953449701131 -0.0153449701130537 31 13.18 13.1842438293142 -0.00424382931419842 32 13.19 13.2139223127206 -0.0239223127205879 33 13.19 13.2209667184886 -0.0309667184885694 34 13.19 13.2415016582464 -0.0515016582464494 35 13.25 13.2132646363403 0.0367353636596892 36 13.24 13.2505945271423 -0.0105945271423096 37 13.3 13.30512262619 -0.00512262619001014 38 13.35 13.3248273391540 0.0251726608460299 39 13.35 13.4354795421219 -0.0854795421218633 40 13.35 13.4015577716172 -0.051557771617194 41 13.36 13.3833473304182 -0.0233473304182468 42 13.37 13.3880277219281 -0.0180277219280764 43 13.38 13.3746293980535 0.0053706019465185 44 13.39 13.4120941811757 -0.0220941811757420 45 13.4 13.4204571773973 -0.0204571773973008 46 13.4 13.4495376178412 -0.0495376178411657 47 13.44 13.4239678931322 0.0160321068677813 48 13.44 13.4429040233725 -0.00290402337246576 49 13.44 13.5039040539385 -0.0639040539385398 50 13.47 13.4737505791643 -0.00375057916429888 51 13.52 13.5581431519462 -0.0381431519462136 52 13.58 13.5647982549691 0.0152017450309465 53 13.65 13.6036758650107 0.0463241349892645 54 13.66 13.6676745076739 -0.00767450767387956 55 13.68 13.6633142850966 0.0166857149033515 56 13.68 13.7099896854053 -0.0299896854052601 57 13.77 13.7115714227959 0.0584285772040527 58 13.78 13.8074345000235 -0.0274345000235154 59 13.79 13.8015187024960 -0.0115187024959535 60 13.79 13.7967162695329 -0.00671626953291415 61 13.82 13.8536517739228 -0.0336517739228146 62 13.86 13.8500222269483 0.00997777305167347 63 13.94 13.9456591311541 -0.00565913115410943 64 14 13.9806808335652 0.0193191664347605 65 14.02 14.0234831689078 -0.00348316890775102 66 14.03 14.0443546398909 -0.0143546398909251 67 14.07 14.0346002450026 0.0353997549973695 68 14.1 14.0966074419301 0.00339255806985683 69 14.1 14.1277715103394 -0.0277715103394236 70 14.16 14.1490772942579 0.0109227057421055 71 14.17 14.1760181336931 -0.00601813369305049 72 14.17 14.1759501710322 -0.0059501710322305 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 14.2331804184375 14.1578654245148 14.3084954123602 74 14.2587818617299 14.1598230306418 14.3577406928181 75 14.3457237261097 14.2277426690368 14.4637047831826 76 14.3858935562012 14.2515343671961 14.5202527452063 77 14.4119442804811 14.2629763631165 14.5609121978458 78 14.4356396727095 14.2733538734015 14.5979254720176 79 14.4387566426888 14.2641481748048 14.6133651105727 80 14.4701874183597 14.2840537184809 14.6563211182385 81 14.4980431014345 14.3010415867047 14.6950446161644 82 14.5434976752212 14.3361823371248 14.7508130133177 83 14.5609105996221 14.3437564684835 14.7780647307608 84 14.5659651356540 14.3393853412882 14.7925449300199

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/1ldsg1212347739.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/1ldsg1212347739.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/22t8q1212347739.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/22t8q1212347739.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/3svaa1212347739.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347820cglus0onknj8e1j/3svaa1212347739.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

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')

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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