ws 8

*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: Sun, 12 Dec 2010 19:21:34 +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/12/t12921815647x0vcvs9ampg23l.htm/, Retrieved Sun, 12 Dec 2010 20:19:27 +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/12/t12921815647x0vcvs9ampg23l.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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1.3031 1.3241 1.2961 1.2865 1.2305 1.2101 1.2125 1.2350 1.2014 1.1992 1.1791 1.1832 1.2159 1.1922 1.2114 1.2614 1.2812 1.2786 1.2772 1.2815 1.2679 1.2765 1.3247 1.3191 1.3029 1.3234 1.3354 1.3651 1.3453 1.3534 1.3706 1.3638 1.4268 1.4485 1.4635 1.4587 1.4876 1.5189 1.5783 1.5633 1.5554 1.5757 1.5593 1.4660 1.4065 1.2759 1.2705 1.3954 1.2793 1.2694 1.3282 1.3230 1.4135 1.4042 1.4253 1.4322 1.4632 1.4713 1.5016 1.4318

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 0.824124154937339 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.2159 1.21481549145299 0.00108450854700815 14 1.1922 1.19014760613116 0.00205239386883771 15 1.2114 1.20910237848226 0.0022976215177386 16 1.2614 1.25777591552895 0.00362408447105467 17 1.2812 1.27404678940275 0.00715321059724694 18 1.2786 1.26838443469631 0.0102155653036904 19 1.2772 1.23867917380777 0.0385208261922347 20 1.2815 1.30482596212927 -0.0233259621292741 21 1.2679 1.26379915162306 0.00410084837693625 22 1.2765 1.27232543814791 0.0041745618520892 23 1.3247 1.25737080706151 0.0673291929384907 24 1.3191 1.31476343294957 0.00433656705043250 25 1.3029 1.34844971978419 -0.045549719784195 26 1.3234 1.28551966809666 0.0378803319033416 27 1.3354 1.33404423922357 0.00135576077642630 28 1.3651 1.38217485887561 -0.0170748588756138 29 1.3453 1.38200792159553 -0.0367079215955290 30 1.3534 1.34073714260800 0.0126628573920033 31 1.3706 1.31802696592211 0.0525730340778903 32 1.3638 1.38487716203193 -0.0210771620319317 33 1.4268 1.35052735548072 0.0762726445192803 34 1.4485 1.41854512693142 0.029954873068579 35 1.4635 1.43594404715227 0.0275559528477276 36 1.4587 1.44947970385063 0.0092202961493677 37 1.4876 1.47841699694778 0.00918300305221598 38 1.5189 1.47526683505939 0.0436331649406088 39 1.5783 1.52210866503914 0.0561913349608576 40 1.5633 1.6121891051201 -0.0488891051200999 41 1.5554 1.58235029754178 -0.0269502975417761 42 1.5757 1.55780413970757 0.0178958602924271 43 1.5593 1.54642584316601 0.0128741568339867 44 1.466 1.56760594513540 -0.101605945135396 45 1.4065 1.48401190275479 -0.0775119027547904 46 1.2759 1.41714593694552 -0.141245936945515 47 1.2705 1.29303222216783 -0.0225322221678332 48 1.3954 1.26206420484254 0.133335795157462 49 1.2793 1.39328151971938 -0.113981519719385 50 1.2694 1.29468745091825 -0.0252874509182524 51 1.3282 1.28693881536031 0.0412611846396893 52 1.323 1.34623384672595 -0.0232338467259532 53 1.4135 1.34139666361391 0.0721033363860906 54 1.4042 1.40637035404089 -0.00217035404088617 55 1.4253 1.37757180922969 0.0477281907703144 56 1.4322 1.40734167778628 0.0248583222137231 57 1.4632 1.4322074529292 0.0309925470708017 58 1.4713 1.44355334801683 0.0277466519831659 59 1.5016 1.47958938268773 0.0220106173122729 60 1.4318 1.51274361457281 -0.0809436145728115 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 1.42387095023263 1.32541206914885 1.52232983131641 62 1.43481094935116 1.30722477863904 1.56239712006327 63 1.45960661042826 1.30840373132310 1.61080948953342 64 1.47355418472723 1.30195467906826 1.64515369038619 65 1.50463208355988 1.31481514534015 1.69444902177960 66 1.49712072474974 1.29068780652248 1.70355364297700 67 1.47888676986446 1.25707912928251 1.70069441044642 68 1.46530042607692 1.22911679177250 1.70148406038134 69 1.47075871941284 1.2210252839142 1.72049215491148 70 1.45599203329487 1.19340705943181 1.71857700715793 71 1.46815255190275 1.19331633123419 1.74298877257130 72 1.46506013986014 1.17849596225923 1.75162431746105

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/1pb9q1292181692.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/1pb9q1292181692.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/202rb1292181692.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/202rb1292181692.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/302rb1292181692.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t12921815647x0vcvs9ampg23l/302rb1292181692.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 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=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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