*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 20:44:32 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1.htm/, Retrieved Sun, 16 Jan 2011 21:42:36 +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/2011/Jan/16/t12952105537rpcnfj52vaz4n1.htm/}, year = {2011}, } @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 = {2011}, 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 «

47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 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 1 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.434895061810831 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 107 109.712152105484 -2.71215210548438 14 58 57.9695835402017 0.0304164597983032 15 36 36.1277445966824 -0.12774459668244 16 52 51.8629081648112 0.137091835188784 17 79 79.4599600239307 -0.459960023930705 18 77 79.6279980698353 -2.62799806983531 19 54 52.535304361424 1.46469563857601 20 84 61.2322118725791 22.7677881274209 21 48 85.879172493516 -37.8791724935161 22 96 56.7246384175323 39.2753615824677 23 83 167.882856301175 -84.8828563011751 24 66 67.1347028385988 -1.13470283859881 25 61 95.2099895082458 -34.2099895082458 26 53 43.4680896271021 9.53191037289793 27 30 29.56884010582 0.431159894179963 28 74 42.8901162527502 31.1098837472498 29 69 85.9622315902852 -16.9622315902852 30 59 77.7094009460039 -18.7094009460039 31 42 48.1821119025566 -6.18211190255661 32 65 60.8628655122481 4.13713448775189 33 70 44.2436049808929 25.7563950191071 34 100 85.2853395431992 14.7146604568008 35 63 101.593273536218 -38.593273536218 36 105 67.9454354543462 37.0545645456538 37 82 92.1827854617672 -10.1827854617672 38 81 69.7377596324338 11.2622403675662 39 75 42.0490131882789 32.9509868117211 40 102 105.998614544043 -3.99861454404311 41 121 106.473416112174 14.526583887826 42 98 107.921527005735 -9.9215270057353 43 76 78.2912045478421 -2.2912045478421 44 77 116.488186049249 -39.4881860492494 45 63 85.5098420440093 -22.5098420440093 46 37 100.655582674904 -63.6555826749038 47 35 54.9861524299234 -19.9861524299234 48 23 62.2536123864517 -39.2536123864517 49 40 36.8676893237789 3.1323106762211 50 29 35.1133023270487 -6.11330232704866 51 37 22.2784347698102 14.7215652301898 52 51 39.4648774940411 11.5351225059589 53 20 49.6151912998426 -29.6151912998426 54 28 30.7866838335932 -2.78668383359322 55 13 23.0690447967357 -10.0690447967357 56 22 22.0015794539673 -0.0015794539672811 57 25 20.1445699483997 4.85543005160029 58 13 17.8948314310559 -4.89483143105591 59 16 17.5785870884904 -1.5785870884904 60 13 15.1833106324713 -2.18331063247129 61 16 23.7335877527623 -7.73358775276226 62 17 15.8368187109431 1.16318128905692 63 9 16.0705550843557 -7.07055508435574 64 17 15.661948050682 1.338051949318 65 25 8.47424091600656 16.5257590839934 66 14 22.7636241575371 -8.7636241575371 67 8 10.8087440393825 -2.80874403938249 68 7 16.1523853797942 -9.15238537979418 69 10 12.3907371346961 -2.39073713469611 70 7 6.60548601466493 0.394513985335066 71 10 8.57300630730047 1.42699369269953 72 3 7.8845311083214 -4.88453110832141 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 8.10083159762423 -34.6151573214557 50.8168205167041 74 8.1926835661484 -38.7534484975716 55.1388156298684 75 5.26004867967327 -41.0689879640961 51.5890853234426 76 9.4250564486454 -54.9022930412978 73.7524059385886 77 7.36489625833425 -52.5029464974261 67.2327390140946 78 4.80830968310635 -48.1094567093238 57.7260760755365 79 3.00917633805022 -45.8714878794862 51.8898405555866 80 3.39472623537472 -52.2256628688409 59.0151153395903 81 5.16297917021532 -71.8733123868266 82.1992707272572 82 3.43656612422804 -59.872321292512 66.7454535409681 83 4.45423749090523 -76.4694277326241 85.3779027144346 84 1.77232110726812 -46.0350066486905 49.5796488632268

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/1pg2k1295210670.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/1pg2k1295210670.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/2dinc1295210670.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/2dinc1295210670.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/3us9e1295210670.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12952105537rpcnfj52vaz4n1/3us9e1295210670.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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