*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 06:30:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln.htm/, Retrieved Wed, 20 Jan 2010 14:31:45 +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/Jan/20/t1263994301g65qspdvh9qeiln.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394 20.148 20.108 18.584 18.441 18.391 19.178 18.079 18.483 19.644 19.195 19.650 20.830 23.595 22.937 21.814 21.928 21.777 21.383 21.467

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 0.824846748999328 beta 0.0184321753657881 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10.653 10.6188469551282 0.0341530448717915 14 10.805 10.8272771840405 -0.0222771840404850 15 10.872 10.8836140926889 -0.011614092688923 16 10.625 10.5847365068272 0.0402634931728088 17 10.407 10.3370538005496 0.0699461994503903 18 10.463 10.3927932204730 0.0702067795269752 19 10.556 10.8778983165717 -0.321898316571737 20 10.646 10.8539744137037 -0.207974413703745 21 10.702 10.0930249536784 0.608975046321627 22 11.353 10.6960672858988 0.656932714101233 23 11.346 11.3232384988065 0.0227615011935320 24 11.451 11.5142033745942 -0.0632033745942362 25 11.964 11.5717814924954 0.392218507504602 26 12.574 12.0844434280512 0.489556571948823 27 13.031 12.5913807104575 0.439619289542481 28 13.812 12.7071967557385 1.10480324426148 29 14.544 13.3923889040086 1.15161109599137 30 14.931 14.4064207481191 0.524579251880875 31 14.886 15.2705821796915 -0.384582179691529 32 16.005 15.2869019713030 0.718098028696959 33 17.064 15.5189855878378 1.54501441216219 34 15.168 17.0028220489699 -1.83482204896988 35 16.05 15.526021514718 0.523978485282003 36 15.839 16.1853981436523 -0.3463981436523 37 15.137 16.1548885669791 -1.01788856697908 38 14.954 15.5657744386017 -0.611774438601712 39 15.648 15.183088505554 0.464911494445989 40 15.305 15.4642131771372 -0.159213177137227 41 15.579 15.1237035864131 0.455296413586936 42 16.348 15.4516888385476 0.89631116145242 43 15.928 16.467014230709 -0.539014230708997 44 16.171 16.5505260126632 -0.379526012663245 45 15.937 16.0068238736702 -0.0698238736701615 46 15.713 15.5268741052719 0.186125894728088 47 15.594 16.1211206455525 -0.527120645552506 48 15.683 15.7359948118279 -0.0529948118278867 49 16.438 15.8092876454157 0.628712354584263 50 17.032 16.6539369597172 0.378063040282843 51 17.696 17.2957873222131 0.400212677786904 52 17.745 17.4327312848333 0.312268715166656 53 19.394 17.6144269962959 1.77957300370412 54 20.148 19.1577882292963 0.990211770703663 55 20.108 20.0463985375149 0.0616014624851289 56 18.584 20.7096259065367 -2.12562590653671 57 18.441 18.8097218746401 -0.368721874640141 58 18.391 18.1533307258932 0.237669274106786 59 19.178 18.6912220859018 0.486777914098187 60 18.079 19.2669237749264 -1.18792377492640 61 18.483 18.5476941381383 -0.064694138138254 62 19.644 18.7901617295637 0.853838270436285 63 19.195 19.8492412889133 -0.654241288913337 64 19.65 19.1058949953764 0.544105004623589 65 20.83 19.7442243480598 1.08577565194016 66 23.595 20.5749027194146 3.02009728058540 67 22.937 23.0039230022748 -0.0669230022748337 68 21.814 23.2047979754168 -1.3907979754168 69 21.928 22.2566745199270 -0.328674519926960 70 21.777 21.7780692448329 -0.00106924483286619 71 21.383 22.1975819504328 -0.814581950432768 72 21.467 21.4216580783794 0.0453419216206044 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 21.9502975285382 20.3486204597613 23.5519745973151 74 22.4418719625488 20.350051792726 24.5336921323717 75 22.5543994003943 20.0539642284387 25.0548345723500 76 22.5924216951621 19.7295649579739 25.4552784323502 77 22.9003762973609 19.7053464767487 26.0954061179732 78 23.1813041637366 19.6755713436033 26.6870369838699 79 22.5396339613168 18.7392424237868 26.3400254988468 80 22.525975205158 18.4433484480440 26.608601962272 81 22.8943726725964 18.5393818815070 27.2493634636857 82 22.7325430692666 18.1131846200411 27.3519015184921 83 22.9987530329196 18.121601169386 27.8759048964532 84 23.0460422621547 17.9165642936593 28.1755202306501

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/1ynmt1263994209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/1ynmt1263994209.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/2buqe1263994209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/2buqe1263994209.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/3ctp31263994209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1263994301g65qspdvh9qeiln/3ctp31263994209.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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