*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: Sun, 19 Dec 2010 14:05:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls.htm/, Retrieved Sun, 19 Dec 2010 15:04:22 +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/2010/Dec/19/t1292767458lekmrtby0ovqnls.htm/}, year = {2010}, } @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 = {2010}, 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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41,85 41,75 41,75 41,75 41,58 41,61 41,42 41,37 41,37 41,33 41,37 41,34 41,33 41,29 41,29 41,27 41,04 40,90 40,89 40,72 40,72 40,58 40,24 40,07 40,12 40,10 40,10 40,08 40,06 39,99 40,05 39,66 39,66 39,67 39,56 39,64 39,73 39,70 39,70 39,68 39,76 40,00 39,96 40,01 40,01 40,01 40,00 39,91 39,86 39,79 39,79 39,80 39,64 39,55 39,36 39,28

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0.194972412796345 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 41.33 41.6101522435898 -0.280152243589754 14 41.29 41.2866768648019 0.0033231351981442 15 41.29 41.2916768648019 -0.00167686480186546 16 41.27 41.2758435314685 -0.00584353146854255 17 41.04 41.0658435314685 -0.0258435314685244 18 40.9 40.9475101981352 -0.0475101981352068 19 40.89 40.7629268648019 0.127073135198138 20 40.72 40.8283435314685 -0.108343531468527 21 40.72 40.7058435314685 0.0141564685314677 22 40.58 40.6666768648019 -0.0866768648018663 23 40.24 40.6100101981352 -0.370010198135191 24 40.07 40.2095935314685 -0.139593531468542 25 40.12 40.0591768648019 0.0608231351981345 26 40.1 40.0766768648019 0.0233231351981473 27 40.1 40.1016768648019 -0.00167686480186546 28 40.08 40.0858435314685 -0.00584353146854966 29 40.06 39.8758435314685 0.184156468531484 30 39.99 39.9675101981352 0.0224898018647934 31 40.05 39.8529268648019 0.197073135198131 32 39.66 39.9883435314685 -0.328343531468526 33 39.66 39.6458435314685 0.0141564685314677 34 39.67 39.6066768648019 0.0633231351981394 35 39.56 39.7000101981352 -0.140010198135194 36 39.64 39.5295935314685 0.110406468531458 37 39.73 39.6291768648019 0.100823135198134 38 39.7 39.6866768648019 0.0133231351981493 39 39.7 39.7016768648019 -0.00167686480186546 40 39.68 39.6858435314685 -0.00584353146854966 41 39.76 39.4758435314685 0.284156468531478 42 40 39.6675101981352 0.332489801864796 43 39.96 39.8629268648019 0.097073135198137 44 40.01 39.8983435314685 0.111656468531471 45 40.01 39.9958435314685 0.0141564685314677 46 40.01 39.9566768648019 0.0533231351981343 47 40 40.0400101981352 -0.0400101981351924 48 39.91 39.9695935314685 -0.0595935314685434 49 39.86 39.8991768648019 -0.0391768648018598 50 39.79 39.8166768648019 -0.0266768648018569 51 39.79 39.7916768648019 -0.00167686480186546 52 39.8 39.7758435314685 0.0241564685314515 53 39.64 39.5958435314685 0.044156468531483 54 39.55 39.5475101981352 0.00248980186479031 55 39.36 39.4129268648019 -0.0529268648018615 56 39.28 39.2983435314685 -0.0183435314685241 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 57 39.2658435314685 39.0097350318951 39.521952031042 58 39.2125203962704 38.8503282827346 39.5747125098062 59 39.2425305944056 38.7989376608941 39.6861235279171 60 39.2121241258741 38.6999071267272 39.7243411250211 61 39.201300990676 38.6286249760142 39.7739770053378 62 39.1579778554778 38.530642712733 39.7853129982227 63 39.1596547202797 38.4820553217584 39.837254118801 64 39.1454982517483 38.4211140246766 39.8698824788199 65 38.9413417832168 38.1730162844963 39.7096672819372 66 38.848851981352 38.0389657945715 39.6587381681324 67 38.7117788461538 37.8623630474477 39.56119464486 68 38.6501223776224 37.7629365105994 39.5373082446454

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/123wr1292767542.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/123wr1292767542.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/2p9661292767542.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/2p9661292767542.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/3p9661292767542.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767458lekmrtby0ovqnls/3p9661292767542.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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