Exponential smoothing porto

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 25 Jan 2010 10:48:59 -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/25/t1264441784arxa7rbghz2ljjr.htm/, Retrieved Mon, 25 Jan 2010 18:49:49 +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/25/t1264441784arxa7rbghz2ljjr.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 «

8,2 8,21 8,22 8,2 8,18 8,2 8,19 8,24 8,31 8,27 8,36 8,32 8,29 8,27 8,27 8,43 8,46 8,48 8,46 8,46 8,43 8,4 8,38 8,3 8,39 8,53 8,52 8,54 8,62 8,52 8,49 8,44 8,31 8,26 8,21 8,03 7,89 7,83 7,85 7,84 7,88 8,01 8,08 8,11 8,11 8,07 8,06 7,95 7,95 8,07 8,17 8,21 8,2 8,19 8,18 8,16 8,17 8,17 8,19 8,01 8,04 8,13 8,14 8,17 8,25 8,27 8,27 8,26 8,24 8,21 8,25 8,06 8,16 8,32 8,43 8,39 8,41

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.731983554074229 beta 0.0105744478801132 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.29 8.18600694444445 0.103993055555552 14 8.27 8.23780051482116 0.0321994851788414 15 8.27 8.26354160677549 0.00645839322451103 16 8.43 8.43424063279812 -0.00424063279812081 17 8.46 8.47124199053114 -0.0112419905311434 18 8.48 8.49928145292143 -0.0192814529214296 19 8.46 8.35253691640531 0.107463083594688 20 8.46 8.49189909505162 -0.0318990950516191 21 8.43 8.5506702082702 -0.120670208270198 22 8.4 8.4264449669418 -0.0264449669417992 23 8.38 8.49140302675327 -0.111403026753266 24 8.3 8.361227555371 -0.0612275553710102 25 8.39 8.30559429868584 0.0844057013141626 26 8.53 8.32260181139872 0.20739818860128 27 8.52 8.46983595242318 0.0501640475768159 28 8.54 8.67014709500729 -0.13014709500729 29 8.62 8.61262376876823 0.007376231231774 30 8.52 8.65179412092145 -0.131794120921455 31 8.49 8.45544826351241 0.0345517364875914 32 8.44 8.5023113035444 -0.0623113035444032 33 8.31 8.51301578594351 -0.203015785943512 34 8.26 8.35111819292922 -0.0911181929292244 35 8.21 8.34281510871978 -0.132815108719781 36 8.03 8.20709721161844 -0.17709721161844 37 7.89 8.10146752619301 -0.211467526193014 38 7.83 7.92836070374696 -0.0983607037469643 39 7.85 7.80077234829062 0.0492276517093826 40 7.84 7.9431937847836 -0.103193784783596 41 7.88 7.93358905066529 -0.0535890506652912 42 8.01 7.88169268420754 0.128307315792455 43 8.08 7.91319230348858 0.166807696511417 44 8.11 8.02479942429184 0.0852005757081642 45 8.11 8.10080663130807 0.00919336869192833 46 8.07 8.1209131821462 -0.0509131821461999 47 8.06 8.12785538262013 -0.0678553826201291 48 7.95 8.0253127512322 -0.075312751232203 49 7.95 7.98325779817257 -0.033257798172567 50 8.07 7.97057344590386 0.0994265540961425 51 8.17 8.0285105454636 0.141489454536407 52 8.21 8.1995211172403 0.0104788827597098 53 8.2 8.28920411853051 -0.089204118530514 54 8.19 8.26249998137135 -0.0724999813713545 55 8.18 8.15828703925754 0.0217129607424589 56 8.16 8.14164841170842 0.0183515882915781 57 8.17 8.14766790764906 0.0223320923509380 58 8.17 8.16069977175474 0.00930022824526056 59 8.19 8.20706000895451 -0.0170600089545108 60 8.01 8.13997682976858 -0.129976829768578 61 8.04 8.06903374319487 -0.0290337431948728 62 8.13 8.09488926769235 0.0351107323076523 63 8.14 8.11641031681687 0.0235896831831326 64 8.17 8.16448314921984 0.00551685078015929 65 8.25 8.22225487536849 0.0277451246315117 66 8.27 8.2849754035192 -0.0149754035191947 67 8.27 8.24790814218609 0.0220918578139084 68 8.26 8.23043690868187 0.0295630913181295 69 8.24 8.24560761236589 -0.00560761236588725 70 8.21 8.23435678726281 -0.024356787262807 71 8.25 8.24841661845882 0.00158338154117921 72 8.06 8.16426178826803 -0.104261788268026 73 8.16 8.13894039792921 0.0210596020707889 74 8.32 8.21878724175905 0.101212758240948 75 8.43 8.28624974715914 0.143750252840855 76 8.39 8.41900809662625 -0.0290080966262494 77 8.41 8.45877221035183 -0.0487722103518315 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 78 8.45474777309023 8.28380953700138 8.62568600917908 79 8.43940708045606 8.2267835909739 8.65203056993821 80 8.40842656967638 8.16036614309418 8.65648699625858 81 8.39296160773423 8.11332065453893 8.67260256092952 82 8.38126413819412 8.07270699282208 8.68982128356615 83 8.42076742107446 8.08526358461096 8.75627125753795 84 8.30773537165044 7.9468080923464 8.66866265095448 85 8.39377714533211 8.00864334620577 8.77891094445845 86 8.48098511879009 8.0726409595202 8.88932927805997 87 8.48627292643602 8.05554943071757 8.91699642215447 88 8.4669043314847 8.01450530786855 8.91930335510085 89 8.52222727474816 8.0487561625336 8.99569838696272

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/1iukj1264441736.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/1iukj1264441736.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/250ne1264441736.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/250ne1264441736.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/3gu5v1264441736.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t1264441784arxa7rbghz2ljjr/3gu5v1264441736.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 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=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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