*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 19:56:30 +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/06/t1275854414ezahivfj1emsdgq.htm/, Retrieved Sun, 06 Jun 2010 22:00:14 +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/06/t1275854414ezahivfj1emsdgq.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 «

2 2.4 1.5 1.2 1.5 0.6 2.7 3.7 4.9 6.6 7.4 7.2 5.3 4.7 6.1 6.6 7 7.5 6.6 7.8 4.7 5.4 4.3 4.5 5.8 4.6 5.2 3.6 4.8 6.7 6.3 4.8 8.7 6.8 7.4 9 7.9 9.1 8.7 9.8 6.4 6.1 4.7 4.8 4.2 2.8 6.1 5.8 4.9 4.6 4.1 3.6 5.9 4.5 4.8 5.7 5 7 4.6 2.6 5 4.1 3.2 0 2.3 3.8 4.5 5.9 5 4.2 4.5 6

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 0.52534352356398 beta 0 gamma 0.582031924980555 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5.3 2.43320707070707 2.86679292929293 14 4.7 3.00592483617679 1.69407516382321 15 6.1 5.1333962519219 0.966603748078098 16 6.6 6.19952860416073 0.400471395839267 17 7 6.98908032500418 0.0109196749958151 18 7.5 7.73648357220933 -0.236483572209326 19 6.6 5.18724845911988 1.41275154088012 20 7.8 6.69609499819295 1.10390500180705 21 4.7 8.18852434152217 -3.48852434152217 22 5.4 7.63918400524153 -2.23918400524153 23 4.3 6.80867652335317 -2.50867652335317 24 4.5 4.77409289242592 -0.274092892425916 25 5.8 3.07209515353663 2.72790484646337 26 4.6 3.24786782956801 1.35213217043199 27 5.2 4.9947266556395 0.205273344360502 28 3.6 5.50449633063275 -1.90449633063275 29 4.8 4.97552859144418 -0.175528591444176 30 6.7 5.55663353621333 1.14336646378667 31 6.3 4.18792000880073 2.11207999119927 32 4.8 5.97883066220063 -1.17883066220063 33 8.7 5.00331109323701 3.69668890676299 34 6.8 8.57382528858044 -1.77382528858044 35 7.4 7.9133395840961 -0.513339584096101 36 9 7.54433103594088 1.45566896405912 37 7.9 7.58040005949676 0.319599940503242 38 9.1 6.1109072057075 2.98909279429250 39 8.7 8.40089548488099 0.299104515119012 40 9.8 8.37710276866554 1.42289723133446 41 6.4 10.0738133450862 -3.67381334508625 42 6.1 9.18148188707782 -3.08148188707782 43 4.7 5.86089349886677 -1.16089349886677 44 4.8 5.02320456196742 -0.223204561967418 45 4.2 5.8966534751326 -1.69665347513261 46 2.8 5.12249735740854 -2.32249735740854 47 6.1 4.52199869884496 1.57800130115504 48 5.8 5.79563112534486 0.00436887465514246 49 4.9 4.75541268440685 0.144587315593146 50 4.6 3.93146611928604 0.668533880713963 51 4.1 4.2592135911977 -0.159213591197697 52 3.6 4.30511127109319 -0.70511127109319 53 5.9 3.47584248032091 2.42415751967909 54 4.5 5.95068110514855 -1.45068110514855 55 4.8 4.01741512470159 0.782584875298406 56 5.7 4.4597708078179 1.24022919218210 57 5 5.69496247378058 -0.69496247378058 58 7 5.2741393367264 1.7258606632736 59 4.6 7.8779914758853 -3.27799147588531 60 2.6 6.16581963376298 -3.56581963376298 61 5 3.28876326083519 1.71123673916481 62 4.1 3.43259403857089 0.667405961429107 63 3.2 3.53107112573691 -0.331071125736907 64 0 3.33587201878725 -3.33587201878725 65 2.3 1.98905824649006 0.310941753509940 66 3.8 2.28324949911276 1.51675050088724 67 4.5 2.52587821791776 1.97412178208224 68 5.9 3.7206313072146 2.17936869278540 69 5 4.91456767100788 0.0854323289921188 70 4.2 5.5725091324515 -1.3725091324515 71 4.5 5.16626244031471 -0.666262440314706 72 6 4.74662862220244 1.25337137779756 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 5.85917019000151 2.32222230242531 9.3961180775777 74 4.8156396872761 0.820319545073796 8.8109598294784 75 4.28765488018601 -0.118609492039648 8.69391925241167 76 3.43625985714 -1.34576360549618 8.21828331977618 77 4.84941266424374 -0.280921737767561 9.97974706625504 78 5.31337570256353 -0.143080450996068 10.7698318561231 79 4.88554514771385 -0.878611029470816 10.6497013248985 80 5.09990872755792 -0.956334259165267 11.1561517142811 81 4.57044606730768 -1.76443055291876 10.9053226875341 82 4.78072768550555 -1.82103302454365 11.3824883955548 83 5.29063117680796 -1.56763588944186 12.1488982430578 84 5.75134208094253 -1.3541775926116 12.8568617544967

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/1m13f1275854186.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/1m13f1275854186.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/2fa201275854186.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/2fa201275854186.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/3fa201275854186.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275854414ezahivfj1emsdgq/3fa201275854186.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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