Paper Exponential Smoothing Triple

*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: Tue, 28 Dec 2010 23:11:20 +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/t1293577801kr98xey9m3hxr6a.htm/, Retrieved Wed, 29 Dec 2010 00:10:02 +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/t1293577801kr98xey9m3hxr6a.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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1203 1319 1328 1260 1286 1274 1389 1255 1244 1336 1214 1239 1174 1061 1116 1123 1086 1074 965 1035 1016 941 1003 998 891 828 833 887 842 793 778 699 686 727 641 619 627 593 535 536 504 487 477 435 433 393 389 377 339 370 350 341 367 396 408 405 391 396 368 356

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.51204887375077 beta 0 gamma 0.581472577695563 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1174 1274.22783119658 -100.227831196582 14 1061 1116.34086936098 -55.3408693609758 15 1116 1141.27155911272 -25.2715591127196 16 1123 1140.89087197821 -17.8908719782114 17 1086 1099.5811240451 -13.5811240451021 18 1074 1079.06151102062 -5.06151102062427 19 965 1152.73768958346 -187.737689583456 20 1035 914.166403318762 120.833596681238 21 1016 964.22369665773 51.776303342269 22 941 1076.87861405154 -135.878614051538 23 1003 878.945042340052 124.054957659948 24 998 963.735163273447 34.2648367265526 25 891 893.444024734543 -2.44402473454306 26 828 798.362937490622 29.6370625093784 27 833 875.33805293588 -42.33805293588 28 887 868.31261069103 18.6873893089695 29 842 846.955525893215 -4.95552589321539 30 793 833.26991218812 -40.2699121881208 31 778 837.086920059398 -59.0869200593984 32 699 751.942107946567 -52.9421079465669 33 686 693.424107852443 -7.42410785244329 34 727 722.522154281117 4.47784571888337 35 641 670.208953791284 -29.2089537912836 36 619 651.044292583544 -32.044292583544 37 627 536.384226488365 90.615773511635 38 593 498.056677401168 94.9433225988323 39 535 588.050275933568 -53.0502759335682 40 536 592.854412849929 -56.8544128499291 41 504 526.108024296281 -22.1080242962807 42 487 493.619735244879 -6.61973524487928 43 477 509.328324930364 -32.3283249303644 44 435 439.628690081141 -4.62869008114097 45 433 418.764352424566 14.2356475754337 46 393 462.330195883101 -69.330195883101 47 389 362.665708482816 26.3342915171839 48 377 371.137432239499 5.86256776050124 49 339 310.689896274256 28.3101037257437 50 370 241.686655509333 128.313344490667 51 350 306.777082981063 43.2229170189369 52 341 359.798451396197 -18.7984513961973 53 367 322.397174789186 44.6028252108143 54 396 328.4625964322 67.5374035678003 55 408 374.848962255465 33.1510377445351 56 405 346.537184230537 58.4628157694629 57 391 363.331163368507 27.6688366314934 58 396 390.065302745813 5.93469725418726 59 368 356.083023172988 11.9169768270118 60 356 351.363930921229 4.63606907877067 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 296.657411537635 176.420513171112 416.894309904157 62 241.531953464013 106.448912512924 376.614994415102 63 216.776953468123 68.3251290388298 365.228777897416 64 230.068740690291 69.356387710883 390.781093669699 65 220.282046788274 48.1804005905409 392.383692986008 66 210.015874501087 27.2332362452558 392.798512756918 67 212.063338467655 19.1902997308891 404.936377204421 68 173.958324722318 -28.5028451235221 376.419494568158 69 152.079303055195 -59.53601188949 363.69461799988 70 158.479014103048 -61.9105449575624 378.868573163659 71 123.155232859851 -105.672374667568 351.98284038727 72 110.268252639763 -126.69712498008 347.233630259605

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/1568h1293577876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/1568h1293577876.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/2568h1293577876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/2568h1293577876.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/3gxp21293577876.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577801kr98xey9m3hxr6a/3gxp21293577876.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')

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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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