Paper

*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: Mon, 21 Dec 2009 15:02:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76.htm/, Retrieved Mon, 21 Dec 2009 23:03:07 +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/2009/Dec/21/t126143298259mzyyp9z5zyu76.htm/}, year = {2009}, } @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 = {2009}, 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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25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 23.5 23.6301148459851 -0.130114845985076 14 22.9 22.9437996857881 -0.0437996857881267 15 21.9 21.9463706339436 -0.0463706339436101 16 21.5 21.5244856179741 -0.0244856179740971 17 20.5 20.5031491944293 -0.00314919442930162 18 20.2 20.1831232356379 0.0168767643621131 19 19.4 19.7431788967428 -0.343178896742813 20 19.2 19.5608170367688 -0.360817036768811 21 18.8 18.6247076581915 0.175292341808486 22 18.8 18.469045348585 0.330954651414999 23 22.6 22.2204117107894 0.379588289210556 24 23.3 22.9579508253039 0.342049174696136 25 23 23.2985525957402 -0.298552595740205 26 21.4 22.4545640949381 -1.05456409493806 27 19.9 20.5056726303232 -0.605672630323188 28 18.8 19.554435563383 -0.754435563382998 29 18.6 17.9226264555644 0.677373544435621 30 18.4 18.3083350456507 0.0916649543492731 31 18.6 17.9799704794691 0.620029520530938 32 19.9 18.7523543723900 1.14764562760995 33 19.2 19.3053074364747 -0.105307436474696 34 18.4 18.8629082197206 -0.4629082197206 35 21.1 21.7465655569433 -0.646565556943287 36 20.5 21.4307901943330 -0.930790194332968 37 19.1 20.4925522061045 -1.39255220610451 38 18.1 18.6385264863076 -0.538526486307553 39 17 17.3361370223583 -0.336137022358262 40 17.1 16.6978629842259 0.402137015774091 41 17.4 16.2978528792420 1.10214712075797 42 16.8 17.1242582940799 -0.324258294079879 43 15.3 16.4126741085591 -1.11267410855907 44 14.3 15.4174458818276 -1.11744588182761 45 13.4 13.8605092102093 -0.460509210209255 46 15.3 13.1518965882544 2.14810341174558 47 22.1 18.0742578646356 4.0257421353644 48 23.7 22.4488972816469 1.25110271835310 49 22.2 23.6994097942596 -1.49940979425959 50 19.5 21.6717871495780 -2.17178714957796 51 16.6 18.680788492404 -2.08078849240398 52 17.3 16.3038529733077 0.996147026692313 53 19.8 16.4890027117505 3.31099728824946 54 21.2 19.4924117972216 1.70758820277844 55 21.5 20.7227391285616 0.777260871438443 56 20.6 21.6830315307631 -1.08303153076309 57 19.1 19.9859072147579 -0.885907214757875 58 19.6 18.7644425019367 0.835557498063299 59 23.5 23.1681040184818 0.331895981518244 60 24 23.8742472038864 0.125752796113602 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 24.0000526931491 21.6975200010197 26.3025853852786 62 23.4330868353661 20.2116750253280 26.6544986454041 63 22.4583820602558 18.6015920376905 26.315172082821 64 22.0745059221189 17.6321730407109 26.5168388035268 65 21.0522327483702 16.222315541508 25.8821499552324 66 20.7280282013055 15.4351305081929 26.0209258944181 67 20.2604143240205 14.5874172089530 25.9334114390881 68 20.4303331078529 14.2522236080770 26.6084426076288 69 19.820942573076 13.3878770500546 26.2540080960975 70 19.4743237813257 12.7344553930482 26.2141921696032 71 23.0192260363599 14.7096931678474 31.3287589048724 72 23.3847678241084 -30.8218387265673 77.5913743747842

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/1v9lk1261432923.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/1v9lk1261432923.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/24zyi1261432923.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/24zyi1261432923.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/3hbvu1261432923.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t126143298259mzyyp9z5zyu76/3hbvu1261432923.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 1 ;

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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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