*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 11:48:14 +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/02/t1275479417l96mp1zlr49pc9n.htm/, Retrieved Wed, 02 Jun 2010 13:50:21 +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/02/t1275479417l96mp1zlr49pc9n.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 «

127,87 127,94 122,44 120,25 118,13 114,93 112,57 110,81 109,02 106,39 103,75 102,60 101,63 100,00 97,98 96,56 94,32 91,79 89,61 86,83 83,94 81,41 80,47 79,24 78,23 74,60 70,14 65,15 59,92 55,67 52,20 49,97 47,83 44,66 40,91 36,28 32,20 30,10 28,55 27,36 26,33 25,38 24,69 24,01 23,05 22,15 21,26 20,81 20,52 20,32 20,26 20,02 19,76 19,15 18,63 18,73 18,48 18,53 18,37 16,80 16,94 17,21 15,26 14,99 15,80 4,71 4,65 4,50

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.129014448423179 gamma 2.56496888259109e-14 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 101.63 113.672174302484 -12.0421743024838 14 100 98.385400054189 1.61459994581089 15 97.98 96.6620992181513 1.31790078184866 16 96.56 95.446231988679 1.113768011321 17 94.32 93.276115115031 1.04388488496906 18 91.79 90.8184727040291 0.971527295970887 19 89.61 87.6765461835445 1.93345381645551 20 86.83 87.4766585208546 -0.646658520854558 21 83.94 84.5226792203938 -0.582679220393757 22 81.41 80.7760065854546 0.63399341454543 23 80.47 78.3096429549786 2.16035704502141 24 79.24 78.7732200401001 0.466779959899881 25 78.23 77.7054069122023 0.524593087797655 26 74.6 76.277301457744 -1.67730145774398 27 70.14 72.1979065027617 -2.05790650276172 28 65.15 67.9223532678424 -2.77235326784243 29 59.92 61.9451427862315 -2.02514278623153 30 55.67 56.2470571238373 -0.577057123837342 31 52.2 51.5168832339972 0.683116766002762 32 49.97 49.1679465061719 0.802053493828105 33 47.83 46.9807651615694 0.849234838430561 34 44.66 44.5122123901705 0.147787609829479 35 40.91 41.372090749097 -0.462090749097008 36 36.28 38.1410288239702 -1.86102882397022 37 32.2 33.265134134704 -1.06513413470397 38 30.1 28.8050072876653 1.29499271233467 39 28.55 26.7750628933280 1.77493710667197 40 27.36 25.6230522542151 1.73694774578493 41 26.33 24.4026278157112 1.92737218428882 42 25.38 23.5349644387672 1.84503556123281 43 24.69 22.6446108626465 2.04538913735349 44 24.01 22.6905916963092 1.31940830369079 45 23.05 22.1518803387645 0.898119661235519 46 22.15 21.0989418428601 1.05105815713993 47 21.26 20.3371538979161 0.922846102083863 48 20.81 19.8603253813924 0.94967461860763 49 20.52 19.5507445037173 0.969255496282724 50 20.32 19.2556408903534 1.06435910964662 51 20.26 19.1319156593876 1.12808434061241 52 20.02 19.3459619346969 0.674038065303144 53 19.76 19.0086983719909 0.751301628009081 54 19.15 18.7729283105054 0.377071689494571 55 18.63 18.0617094891898 0.568290510810204 56 18.73 17.9749106448497 0.755089355150297 57 18.48 18.1555474303080 0.324452569692035 58 18.53 17.7767523741009 0.753247625899107 59 18.37 17.9155390737877 0.454460926212253 60 16.8 18.0712783598503 -1.27127835985025 61 16.94 16.3476916800632 0.592308319936777 62 17.21 16.4620771127601 0.74792288723987 63 15.26 16.7785493403617 -1.51854934036171 64 14.99 14.7298204384497 0.260179561550283 65 15.8 14.3545490858381 1.44545091416191 66 4.71 15.2890253348108 -10.5790253348108 67 4.65 2.88741574822219 1.76258425177781 68 4.5 3.13781223550201 1.36218776449799 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 69 3.15453720120978 -1.73856607783734 8.04764048025691 70 1.78273530557923 -5.5728598082169 9.13833041937534 71 0.426634442942795 -9.11455849971161 9.9678273855972 72 -0.924958824678932 -12.6951024502224 10.8451848008645 73 -2.30107192827578 -16.3293307291427 11.7271868725911 74 -3.68076902624497 -19.9249155986382 12.5633775461482 75 -5.05472174846452 -23.5083158472719 13.3988723503428 76 -6.47285116523605 -27.3105614833601 14.3648591528880 77 -7.83840903211632 -30.9294481546044 15.2526300903717 78 -9.16146505824447 -34.4506812516890 16.1277511352 79 -10.3769578920506 -37.6615653076719 16.9076495235708 80 -11.7782884699307 -41.4209308812682 17.8643539414067

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/1idw71275479291.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/1idw71275479291.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/2t4es1275479291.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/2t4es1275479291.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/3t4es1275479291.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479417l96mp1zlr49pc9n/3t4es1275479291.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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