*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: Wed, 29 Dec 2010 21:12:18 +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/29/t1293657040uhd9ndmhmzcd0s3.htm/, Retrieved Wed, 29 Dec 2010 22:10:40 +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/29/t1293657040uhd9ndmhmzcd0s3.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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16 17 23 24 27 31 40 47 43 60 64 65 65 55 57 57 57 65 69 70 71 71 73 68 65 57 41 21 21 17 9 11 6 -2 0 5 3 7 4 8 9 14 12 12 7 15 14 19 39 12 11 17 16 25 24 28 25 31 24 24

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 0.783753045322762 beta 0.247471046464428 gamma 0.506225351406623 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 65 48.3731303418804 16.6268696581196 14 55 54.7597647424314 0.240235257568642 15 57 60.3915863099983 -3.39158630999825 16 57 61.0191375177357 -4.0191375177357 17 57 61.1669736368416 -4.16697363684162 18 65 68.7240657657264 -3.72406576572635 19 69 67.9893160272938 1.01068397270625 20 70 74.9531358907618 -4.95313589076181 21 71 65.9071024269039 5.09289757309614 22 71 86.9308106075647 -15.9308106075647 23 73 75.5539108742798 -2.55391087427975 24 68 71.124183563953 -3.12418356395304 25 65 66.5033535112334 -1.50335351123339 26 57 49.7056244922696 7.29437550773038 27 41 54.6558637201675 -13.6558637201675 28 21 39.3665264520581 -18.3665264520581 29 21 17.6670724252066 3.33292757479344 30 17 22.0190753905276 -5.01907539052761 31 9 11.4048498105037 -2.40484981050372 32 11 4.99359355437258 6.00640644562742 33 6 -2.28274161784227 8.28274161784227 34 -2 11.6386351374104 -13.6386351374104 35 0 -3.3337409822462 3.3337409822462 36 5 -8.92582526160538 13.9258252616054 37 3 -2.41366698845414 5.41366698845414 38 7 -13.8929163140589 20.8929163140589 39 4 0.993484728275858 3.00651527172414 40 8 3.0511146816474 4.9488853183526 41 9 11.3262382368491 -2.32623823684908 42 14 18.5565514492309 -4.5565514492309 43 12 16.9087081285295 -4.90870812852954 44 12 17.2878833466367 -5.28788334663668 45 7 7.05026692295144 -0.0502669229514412 46 15 16.0661210302264 -1.06612103022642 47 14 19.2691932847356 -5.26919328473561 48 19 12.8891943350024 6.11080566499762 49 39 15.6238615415626 23.3761384584374 50 12 26.6805727037757 -14.6805727037757 51 11 11.5917364810072 -0.591736481007233 52 17 10.2075649999516 6.79243500004837 53 16 18.6544472596051 -2.65444725960507 54 25 24.8429923352324 0.157007664767566 55 24 27.2247071730162 -3.22470717301617 56 28 29.5826798088786 -1.58267980887857 57 25 24.2415000729458 0.758499927054153 58 31 35.3559996428536 -4.3559996428536 59 24 36.458395403355 -12.4583954033550 60 24 25.2330970453280 -1.23309704532803 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 22.2210880965884 5.52524183830494 38.9169343548718 62 4.37577581046027 -18.9740402380732 27.7255918589937 63 -1.23227575848113 -31.6934580800873 29.228906563125 64 -4.79701750421008 -42.8461059200132 33.252070911593 65 -7.47799742880296 -53.5836923290514 38.6276974714455 66 -3.15652895134019 -57.7721149824151 51.4590570797347 67 -5.55379405619668 -69.115474535291 58.0078864228977 68 -4.1489726506402 -77.0762155428888 68.7782702416084 69 -11.3467410303296 -94.0433039536907 71.3498218930315 70 -4.88702351200861 -97.742159104757 87.9681120807398 71 -3.91311618323876 -107.302765113390 99.4765327469122 72 -4.38444606590153 -118.672346166472 109.903454034669

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/1vrn81293657134.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/1vrn81293657134.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/2vrn81293657134.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/2vrn81293657134.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/360nt1293657134.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3/360nt1293657134.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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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