*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 04:41:42 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw.htm/, Retrieved Sat, 16 Jan 2010 12:42:45 +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/Jan/16/t1263642161tio2ubsnjuw65bw.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 «

2,14 2,45 2,52 2,3 2,25 2,06 1,99 2,25 2,26 2,36 2,3 2,19 2,31 2,21 2,21 2,26 2,18 2,21 2,33 2,12 2,08 1,97 2,09 2,11 2,24 2,45 2,68 2,73 2,76 2,83 3,16 3,22 3,22 3,34 3,35 3,42 3,58 3,71 3,68 3,83 3,94 3,88 4,03 4,15 4,32 4,4 4,37 4,14 4,11 4,16 3,98 4,13 3,76 3,66 3,85 4,03 4,31 4,58 4,46 4,41 3,84 2,84 2,66 2,17 1,43 1,47 1,29 1,23 1,09 0,94 0,76 0,67

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999926825388514 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 2.45 2.14 0.31 3 2.52 2.44997731587044 0.0700226841295604 4 2.3 2.51999487611729 -0.219994876117294 5 2.25 2.30001609803959 -0.0500160980395887 6 2.06 2.25000365990854 -0.190003659908542 7 1.99 2.06001390344399 -0.0700139034439948 8 2.25 1.99000512324018 0.259994876759817 9 2.26 2.24998097497590 0.0100190250240950 10 2.36 2.25999926686174 0.100000733138264 11 2.3 2.35999268248520 -0.0599926824852042 12 2.19 2.30000438994123 -0.110004389941233 13 2.31 2.19000804952850 0.119991950471504 14 2.21 2.30999121963564 -0.0999912196356432 15 2.21 2.21000731681865 -7.31681864918343e-06 16 2.26 2.21000000053541 0.0499999994645943 17 2.18 2.25999634126946 -0.0799963412694646 18 2.21 2.18000585370119 0.0299941462988071 19 2.33 2.20999780519 0.120002194810002 20 2.12 2.32999121888602 -0.209991218886017 21 2.08 2.12001536602586 -0.0400153660258575 22 1.97 2.08000292810886 -0.110002928108863 23 2.09 1.97000804942153 0.119991950578473 24 2.11 2.08999121963563 0.0200087803643649 25 2.24 2.10999853586527 0.130001464134730 26 2.45 2.23999048719337 0.210009512806631 27 2.68 2.44998463263549 0.230015367364508 28 2.73 2.67998316871486 0.0500168312851423 29 2.76 2.72999634003780 0.0300036599621967 30 2.83 2.75999780449384 0.0700021955061612 31 3.16 2.82999487761654 0.330005122383459 32 3.22 3.15997585200338 0.0600241479966188 33 3.22 3.21999560775629 4.39224370918367e-06 34 3.34 3.2199999996786 0.120000000321400 35 3.35 3.3399912190466 0.0100087809534024 36 3.42 3.34999926761134 0.0700007323886576 37 3.58 3.41999487772360 0.160005122276397 38 3.71 3.57998829168734 0.130011708312658 39 3.68 3.70999048644376 -0.0299904864437552 40 3.83 3.68000219454219 0.149997805457806 41 3.94 3.82998902396886 0.110010976031138 42 3.88 3.93999194998957 -0.0599919499895698 43 4.03 3.88000438988763 0.149995610112368 44 4.15 4.02998902412951 0.120010975870495 45 4.32 4.14999121824347 0.170008781756533 46 4.4 4.31998755967345 0.0800124403265547 47 4.37 4.39999414512077 -0.0299941451207655 48 4.14 4.37000219480992 -0.230002194809916 49 4.11 4.14001683032125 -0.0300168303212454 50 4.16 4.1100021964699 0.0499978035301032 51 3.98 4.15999634143015 -0.179996341430151 52 4.13 3.98001317116235 0.149986828837647 53 3.76 4.12998902477207 -0.369989024772072 54 3.66 3.76002707380314 -0.100027073803142 55 3.85 3.66000731944226 0.189992680557736 56 4.03 3.84998609735942 0.180013902640585 57 4.31 4.02998682755261 0.280013172447387 58 4.58 4.3099795101449 0.270020489855106 59 4.46 4.57998024135556 -0.119980241355562 60 4.41 4.46000877950755 -0.0500087795075466 61 3.84 4.41000365937301 -0.570003659373011 62 2.84 3.84004170979632 -1.00004170979632 63 2.66 2.84007317766358 -0.180073177663584 64 2.17 2.66001317678481 -0.490013176784815 65 1.43 2.17003585652383 -0.740035856523834 66 1.47 1.43005415183629 0.0399458481637129 67 1.29 1.46999707697808 -0.17999707697808 68 1.23 1.29001317121618 -0.0600131712161767 69 1.09 1.23000439144049 -0.140004391440488 70 0.94 1.09001024476695 -0.150010244766950 71 0.76 0.94001097694138 -0.180010976941380 72 0.67 0.760013172233301 -0.090013172233301 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.670006586678907 0.228869404737354 1.11114376862046 74 0.670006586678907 0.0461672261290641 1.29384594722875 75 0.670006586678907 -0.0940281522244617 1.43404132558228 76 0.670006586678907 -0.212219357584262 1.55223253094208 77 0.670006586678907 -0.316348395673259 1.65636156903107 78 0.670006586678907 -0.410488524689416 1.75050169804723 79 0.670006586678907 -0.497059486930786 1.8370726602886 80 0.670006586678907 -0.577637895796228 1.91765106915404 81 0.670006586678907 -0.653318879383977 1.99333205274179 82 0.670006586678907 -0.724899798570817 2.06491297192863 83 0.670006586678907 -0.792982599231349 2.13299577258916 84 0.670006586678907 -0.858034935194846 2.19804810855266

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/1utii1263642099.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/1utii1263642099.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/2khnj1263642099.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/2khnj1263642099.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/3rkhz1263642099.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263642161tio2ubsnjuw65bw/3rkhz1263642099.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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