*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Dec 2009 10:42:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr.htm/, Retrieved Fri, 04 Dec 2009 18:42:57 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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92.9 107.7 103.5 91.1 79.8 71.9 82.9 90.1 100.7 90.7 108.8 44.1 93.6 107.4 96.5 93.6 76.5 76.7 84 103.3 88.5 99 105.9 44.7 94 107.1 104.8 102.5 77.7 85.2 91.3 106.5 92.4 97.5 107 51.1 98.6 102.2 114.3 99.4 72.5 92.3 99.4 85.9 109.4 97.6 104.7 56.9 86.7 108.5 103.4 86.2 71 75.9 87.1 102 88.5 87.8 100.8 50.6 85.9

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0891527488222475 beta 0 gamma 0.387141299341678 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 93.6 93.6828978169662 -0.082897816966252 14 107.4 106.85352354983 0.546476450170047 15 96.5 96.0847495543388 0.415250445661215 16 93.6 93.4780972449641 0.121902755035862 17 76.5 76.2774461229164 0.222553877083556 18 76.7 76.6401496533908 0.0598503466091529 19 84 83.284868150639 0.715131849361029 20 103.3 90.6426954627715 12.6573045372285 21 88.5 103.001433309035 -14.5014333090347 22 99 91.8761039562127 7.12389604378734 23 105.9 111.102212407489 -5.20221240748862 24 44.7 44.8489009079516 -0.148900907951578 25 94 94.9425007726662 -0.94250077266625 26 107.1 108.430680469889 -1.33068046988868 27 104.8 97.3238835152013 7.47611648479868 28 102.5 95.1927975968834 7.30720240311659 29 77.7 78.2420728597341 -0.542072859734134 30 85.2 78.4845727511662 6.71542724883379 31 91.3 86.1679965409424 5.1320034590576 32 106.5 98.487389579751 8.01261042024896 33 92.4 100.836755634577 -8.43675563457685 34 97.5 97.777473127026 -0.277473127025885 35 107 112.395987350937 -5.39598735093736 36 51.1 46.0761894680138 5.02381053198618 37 98.6 98.2849316760285 0.315068323971445 38 102.2 112.282634052712 -10.0826340527121 39 114.3 103.221150469854 11.0788495301457 40 99.4 101.229113249806 -1.82911324980645 41 72.5 80.1467947217325 -7.64679472173252 42 92.3 82.3490672940105 9.95093270598949 43 99.4 89.8943486584906 9.50565134150943 44 85.9 103.932416067746 -18.0324160677456 45 109.4 98.1245225985606 11.2754774014394 46 97.6 99.7100950694742 -2.11009506947426 47 104.7 112.595805599851 -7.89580559985058 48 56.9 48.6472934866579 8.25270651334211 49 86.7 100.609831659968 -13.9098316599678 50 108.5 109.742063010662 -1.24206301066177 51 103.4 108.880110355078 -5.48011035507831 52 86.2 100.839641963244 -14.6396419632436 53 71 76.744148221227 -5.74414822122696 54 75.9 85.2212656499404 -9.32126564994044 55 87.1 90.6863277515733 -3.58632775157328 56 102 93.6156540199694 8.38434598003062 57 88.5 100.356814159878 -11.856814159878 58 87.8 95.3141764528612 -7.51417645286118 59 100.8 105.202842870332 -4.4028428703316 60 50.6 49.486674476101 1.11332552389902 61 85.9 90.6958197761224 -4.79581977612244 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 104.451596059448 97.9257210369499 110.977471081946 63 102.298614066857 95.6466961243565 108.950532009358 64 91.8759575992854 85.1438379345507 98.60807726402 65 72.730527994489 65.9938368804723 79.4672191085057 66 80.2741889311909 73.3389747162 87.2094031461818 67 88.5038005105708 81.3358680222301 95.6717329989115 68 95.9011285733948 88.4898251123848 103.312432034405 69 94.7311269793395 87.227866820326 102.234387138353 70 92.2685028300905 84.7042663026629 99.8327393575181 71 103.952851075344 95.995044678344 111.910657472345 72 50.2139759986585 43.2985749836182 57.1293770136988 73 89.4156253643006 -1.62654105975824 180.457791788359

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/1jsx51259948537.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/1jsx51259948537.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/2ex7b1259948537.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/2ex7b1259948537.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/3l6qx1259948537.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948572rl6a084c1tujrhr/3l6qx1259948537.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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