*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 07 Jun 2010 07:44:25 +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/Jun/07/t1275896681ju8macmgszgv0zz.htm/, Retrieved Mon, 07 Jun 2010 09:44:41 +0200

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/Jun/07/t1275896681ju8macmgszgv0zz.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 «

10.383 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 22.052 22.680 24.320 24.977 25.204 25.739 26.434 27.525 30.695

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 0.933411388023692 beta 0.000993563346089219 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 11.353 10.5391442307692 0.813855769230768 14 11.346 11.2257547197317 0.120245280268254 15 11.451 11.3236777953187 0.127322204681256 16 11.964 11.8282829651165 0.135717034883516 17 12.574 12.4007248294572 0.17327517054275 18 13.031 12.7707179146409 0.260282085359146 19 13.812 13.5290406314267 0.282959368573293 20 14.544 13.7367513334115 0.807248666588531 21 14.931 14.7124632818938 0.218536718106209 22 14.886 15.1593674650798 -0.273367465079810 23 16.005 15.1067024932961 0.898297506703855 24 17.064 16.0791826999003 0.984817300099735 25 15.168 17.7234449824935 -2.55544498249354 26 16.05 15.2200194533057 0.829980546694332 27 15.839 15.9826411953866 -0.143641195386605 28 15.137 16.2363861933076 -1.09938619330764 29 14.954 15.6588252957237 -0.704825295723738 30 15.648 15.2145244347801 0.43347556521992 31 15.305 16.1357199462489 -0.830719946248909 32 15.579 15.3374905393195 0.241509460680513 33 16.348 15.7440780399407 0.603921960059346 34 15.928 16.5164518686078 -0.588451868607802 35 16.171 16.2459127488755 -0.0749127488754695 36 15.937 16.3130557728083 -0.376055772808327 37 15.713 16.4473675217059 -0.734367521705879 38 15.594 15.8669211347928 -0.27292113479278 39 15.683 15.5319608473673 0.151039152632706 40 16.438 15.9941064729403 0.443893527059702 41 17.032 16.8817493143326 0.150250685667402 42 17.696 17.3105925972785 0.385407402721523 43 17.745 18.1019037464118 -0.356903746411842 44 19.394 17.8169414952126 1.57705850478743 45 20.148 19.4951202718552 0.652879728144846 46 20.108 20.2346807678668 -0.126680767866812 47 18.584 20.430675604756 -1.84667560475602 48 18.441 18.82365486272 -0.382654862719999 49 18.391 18.9276139004689 -0.536613900468915 50 19.178 18.5623299039560 0.615670096044028 51 18.079 19.0856956341500 -1.00669563415003 52 18.483 18.4862994210085 -0.00329942100850289 53 19.644 18.9361595038458 0.707840496154201 54 19.195 19.9008248368261 -0.705824836826093 55 19.65 19.6228285167805 0.0271714832195045 56 20.83 19.8241931126191 1.0058068873809 57 23.595 20.9061363534540 2.68886364654597 58 22.937 23.4946027629047 -0.557602762904672 59 21.814 23.1738435845337 -1.35984358453371 60 21.928 22.1191815440399 -0.191181544039939 61 21.777 22.3922466530137 -0.615246653013706 62 21.383 22.0308566311477 -0.647856631147729 63 21.467 21.2661909335213 0.200809066478708 64 22.052 21.8612178545331 0.190782145466908 65 22.68 22.5402794280211 0.13972057197887 66 24.32 22.8806839916668 1.43931600833318 67 24.977 24.655948033708 0.321051966291993 68 25.204 25.1992147988653 0.00478520113473024 69 25.739 25.4603618672192 0.278638132780795 70 26.434 25.5821798468365 0.851820153163484 71 27.525 26.5241402740581 1.00085972594191 72 30.695 27.7535628025689 2.94143719743115 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 30.9280748453794 29.1659295776893 32.6902201130696 74 31.1450250177069 28.7334025646757 33.5566474707382 75 31.0484217876497 28.1274504203144 33.969393154985 76 31.4619915688523 28.1073509168193 34.8166322208854 77 31.9660458722398 28.2269886750641 35.7051030694155 78 32.2689134181852 28.1807740457354 36.3570527906350 79 32.6312465293129 28.2209604093329 37.041532649293 80 32.8584888960254 28.1474619952702 37.5695157967806 81 33.1381093798842 28.1438785813955 38.132340178373 82 33.0424568285719 27.7797266028966 38.3051870542472 83 33.2028990619052 27.6842267324426 38.7215713913677 84 33.6300559833535 27.8663253195269 39.3937866471802

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/1bq5c1275896660.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/1bq5c1275896660.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/2bq5c1275896660.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/2bq5c1275896660.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/33z5x1275896660.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275896681ju8macmgszgv0zz/33z5x1275896660.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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