*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 26 Dec 2010 21:05:11 +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/26/t1293397512bmtssyq3lnwh9rr.htm/, Retrieved Sun, 26 Dec 2010 22:05:15 +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/26/t1293397512bmtssyq3lnwh9rr.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

84,9 81,9 95,9 81 89,2 102,5 89,8 88,8 83,2 90,2 100,4 187,1 87,6 85,4 86,1 86,7 89,1 103,7 86,9 85,2 80,8 91,2 102,8 182,5 80,9 83,1 88,3 86,6 93 105,3 93,8 86,4 87 96,7 100,5 196,7 86,8 88,2 93,8 85 90,4 115,9 94,9 87,7 91,7 95,9 106,8 204,5 90,2 90,5 93,2 97,8 99,4 120 108,2 98,5 104,3 102,9 111,1 188,1 93,8 94,5 112,4 102,5 115,8 136,5 122,1 110,6 116,4 112,6 121,5 199,3

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 13 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.644729072186909 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 87.6 87.4724469700408 0.127553029959202 14 85.4 85.5382562478315 -0.138256247831535 15 86.1 86.3157813753947 -0.215781375394712 16 86.7 86.7741529029184 -0.0741529029184278 17 89.1 88.9413142914888 0.158685708511157 18 103.7 103.666075891299 0.0339241087009725 19 86.9 89.278745363225 -2.37874536322504 20 85.2 86.4840624504951 -1.28406245049513 21 80.8 80.4169163609974 0.383083639002592 22 91.2 87.5462356294813 3.65376437051872 23 102.8 99.7668833134924 3.03311668650763 24 182.5 189.358002003619 -6.85800200361865 25 80.9 86.6391802311585 -5.73918023115847 26 83.1 80.9374978762835 2.16250212371654 27 88.3 83.1386204143813 5.1613795856187 28 86.6 87.1170957441602 -0.51709574416023 29 93 89.0836078855098 3.91639211449022 30 105.3 106.599044512895 -1.29904451289522 31 93.8 90.1777204327327 3.6222795672673 32 86.4 91.583542678437 -5.18354267843705 33 87 83.4301281740665 3.56987182593353 34 96.7 94.2344732208526 2.46552677914741 35 100.5 105.939005876964 -5.43900587696407 36 196.7 186.194541374702 10.5054586252984 37 86.8 89.359567826622 -2.55956782662197 38 88.2 88.5734116381013 -0.37341163810126 39 93.8 90.2513582201432 3.54864177985682 40 85 91.1089397508686 -6.10893975086857 41 90.4 91.0326108358374 -0.632610835837426 42 115.9 103.421510198418 12.4784898015819 43 94.9 96.7900562672123 -1.8900562672123 44 87.7 91.3667883309254 -3.66678833092544 45 91.7 87.2163764241893 4.48362357581071 46 95.9 98.4941888530737 -2.59418885307366 47 106.8 104.071360554321 2.72863944567895 48 204.5 199.869019423906 4.63098057609446 49 90.2 91.2018616197427 -1.00186161974266 50 90.5 92.2696540844687 -1.76965408446871 51 93.2 94.5204417166908 -1.32044171669081 52 97.8 88.7165094348287 9.08349056517127 53 99.4 101.040170174393 -1.64017017439268 54 120 118.941042126819 1.05895787318140 55 108.2 99.1997715829135 9.0002284170865 56 98.5 99.6191824008073 -1.11918240080726 57 104.3 100.097826923268 4.20217307673171 58 102.9 109.380095146458 -6.4800951464576 59 111.1 115.218063119950 -4.11806311994972 60 188.1 212.369097414048 -24.2690974140483 61 93.8 87.3862583315429 6.41374166845712 62 94.5 92.9762447806444 1.52375521935565 63 112.4 97.643421997561 14.7565780024390 64 102.5 105.491389777753 -2.99138977775341 65 115.8 106.373629935142 9.4263700648576 66 136.5 134.989985668953 1.51001433104702 67 122.1 115.826677184015 6.27332281598508 68 110.6 109.926902339804 0.673097660196191 69 116.4 113.78632567993 2.61367432007010 70 112.6 118.451713817369 -5.85171381736859 71 121.5 126.745246385535 -5.24524638553484 72 199.3 225.488196993613 -26.1881969936130 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 99.3305840296409 86.2244507253583 112.436717333924 74 99.0287314660762 83.446171141228 114.611291790924 75 107.331671700762 88.9118834927104 125.751459908814 76 99.6983844444636 80.2525330254099 119.144235863517 77 106.545871233623 84.4244622858312 128.667280181415 78 124.686876142073 98.1335032457983 151.240249038348 79 107.764713374511 82.7851607369448 132.744266012077 80 97.2247580979414 72.7618566929547 121.687659502928 81 100.823394425824 74.2155591368782 127.431229714770 82 100.733141895246 72.8233085780659 128.642975212427 83 111.668350183227 79.9412958734655 143.395404492989 84 197.989939633358 -178.160681586067 574.140560852784

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/1xmgy1293397497.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/1xmgy1293397497.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/2xmgy1293397497.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/2xmgy1293397497.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/38wg11293397497.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293397512bmtssyq3lnwh9rr/38wg11293397497.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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