Exponential Smoothing - Blue Jeans - Raf Pleysier

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 12:32:25 -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/25/t12117403882x5ko8vix6yn29e.htm/, Retrieved Sun, 25 May 2008 20:33:12 +0200

User-defined keywords:

Dataseries X:

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48,04 48,06 48,04 48,09 48,12 48,16 48,16 48,16 48,08 48,13 48,16 48,15 48,15 48,15 48,27 48,47 48,51 48,53 48,53 48,53 48,68 48,64 48,67 48,66 48,66 48,67 48,71 48,96 49,01 49,04 49,04 49,04 49,06 49,13 49,19 49,26 49,26 49,26 49,29 49,43 49,43 49,45 49,45 49,46 49,57 49,68 49,71 49,7 49,7 49,8 49,84 50,09 50,2 50,16 50,16 50,29 50,36 51,02 51,03 51,04

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.641886638714992 beta 0.220255401384085 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 48.15 47.9412142002061 0.208785799793937 14 48.15 48.1124331691076 0.0375668308924375 15 48.27 48.2894889364246 -0.0194889364246436 16 48.47 48.5014620378868 -0.0314620378868113 17 48.51 48.5450348788863 -0.0350348788863499 18 48.53 48.5613471793674 -0.0313471793674367 19 48.53 48.5555781352128 -0.0255781352128324 20 48.53 48.5494716676626 -0.0194716676625859 21 48.68 48.6974952763094 -0.0174952763093756 22 48.64 48.6555254862202 -0.0155254862201915 23 48.67 48.6801321428864 -0.0101321428863912 24 48.66 48.6659297909034 -0.00592979090337309 25 48.66 48.7202147708866 -0.0602147708866454 26 48.67 48.6234507416995 0.0465492583005158 27 48.71 48.7547096337696 -0.0447096337695783 28 48.96 48.9121905215452 0.0478094784548233 29 49.01 48.9811096377737 0.0288903622263064 30 49.04 49.0243851490509 0.0156148509490635 31 49.04 49.0418771340071 -0.00187713400707423 32 49.04 49.047569435257 -0.00756943525704656 33 49.06 49.2016115087932 -0.14161150879319 34 49.13 49.0589759933539 0.071024006646148 35 49.19 49.1322064908829 0.0577935091170616 36 49.26 49.1634202284943 0.0965797715056667 37 49.26 49.2793112363648 -0.0193112363647714 38 49.26 49.2674177178635 -0.00741771786351819 39 49.29 49.345126988948 -0.055126988948004 40 49.43 49.543328825983 -0.113328825982990 41 49.43 49.491164915695 -0.0611649156950378 42 49.45 49.4481632306667 0.00183676933328769 43 49.45 49.424749568827 0.0252504311729567 44 49.46 49.423913088832 0.0360869111679563 45 49.57 49.5430130925027 0.0269869074972533 46 49.68 49.5931130994787 0.0868869005212929 47 49.71 49.682274204998 0.0277257950020555 48 49.7 49.714040595124 -0.0140405951239799 49 49.7 49.7077549457867 -0.00775494578667946 50 49.8 49.6994710960488 0.100528903951229 51 49.84 49.8371332015398 0.00286679846015403 52 50.09 50.0694050697911 0.020594930208901 53 50.2 50.1568046085136 0.043195391486428 54 50.16 50.2528716384357 -0.0928716384357244 55 50.16 50.2126194865499 -0.0526194865499079 56 50.29 50.1902196983817 0.099780301618317 57 50.36 50.3820976336702 -0.0220976336702066 58 51.02 50.4496544529174 0.570345547082638 59 51.03 50.9226600000086 0.107339999991410 60 51.04 51.0958790705607 -0.0558790705606853 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 51.1644258113314 50.9639500461815 51.3649015764813 62 51.301194027067 51.0465674358751 51.5558206182589 63 51.4260766746197 51.1112224014807 51.7409309477587 64 51.7557354335319 51.3742791720175 52.1371916950463 65 51.923008115056 51.4708901901367 52.3751260399754 66 52.0190567739106 51.4924695169184 52.5456440309028 67 52.1432392194839 51.5379499274995 52.7485285114683 68 52.3085316295887 51.6202706919198 52.9967925672575 69 52.4781877301664 51.7032014703292 53.2531739900036 70 52.8685310623659 51.9998449430347 53.7372171816972 71 52.8095217031225 51.8508461034938 53.7681973027512 72 52.8435611218792 51.1578485702723 54.5292736734862

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/1kbx11211740340.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/1kbx11211740340.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/2dihw1211740340.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/2dihw1211740340.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/34gbd1211740340.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t12117403882x5ko8vix6yn29e/34gbd1211740340.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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