*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Jun 2010 08:52:21 +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/05/t1275728007unef2paqqzb9lyu.htm/, Retrieved Sat, 05 Jun 2010 10:53:31 +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/05/t1275728007unef2paqqzb9lyu.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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.694939004311082 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 2.4 2 0.4 3 1.5 2.27797560172443 -0.777975601724433 4 1.2 1.73733001168374 -0.53733001168374 5 1.5 1.36391842837778 0.136081571622221 6 0.6 1.45848682026601 -0.858486820266013 7 2.7 0.861890844176163 1.83810915582384 8 3.7 2.13926459073946 1.56073540926054 9 4.9 3.22388050204403 1.67611949795597 10 6.6 4.38868131705994 2.21131868294006 11 7.4 5.9254129207968 1.4745870792032 12 7.2 6.95016099738826 0.249839002611741 13 5.3 7.12378386510134 -1.82378386510134 14 4.7 5.8563653218092 -1.15636532180920 15 6.1 5.05276195645125 1.04723804354875 16 6.6 5.7805285197117 0.819471480288296 17 7 6.35001121428458 0.64998878571542 18 7.5 6.80171377384302 0.698286226156977 19 6.6 7.2869801085727 -0.686980108572696 20 7.8 6.80957083593967 0.990429164060333 21 4.7 7.49785869305241 -2.79785869305241 22 5.4 5.55351755869946 -0.153517558699463 23 4.3 5.44683221931259 -1.14683221931259 24 4.5 4.64985377871163 -0.149853778711630 25 5.8 4.54571454294152 1.25428545705848 26 4.6 5.41736642959161 -0.81736642959161 27 5.2 4.84934661685391 0.350653383146089 28 3.6 5.09302932979577 -1.49302932979577 29 4.8 4.05546501394025 0.744534986059746 30 6.7 4.57287141582738 2.12712858417262 31 6.3 6.05109603615394 0.248903963846057 32 4.8 6.2240691089582 -1.42406910895820 33 8.7 5.23442794030862 3.46557205969138 34 6.8 7.64278913683885 -0.842789136838854 35 7.4 7.05710209323986 0.342897906760136 36 9 7.2953952231441 1.70460477685589 37 7.9 8.47999156951626 -0.579991569516256 38 9.1 8.0769328056878 1.02306719431219 39 8.7 8.78790210304646 -0.0879021030464564 40 9.8 8.7268155030785 1.0731844969215 41 6.4 9.47261326881122 -3.07261326881122 42 6.1 7.33733446315053 -1.23733446315053 43 4.7 6.47746248332891 -1.77746248332891 44 4.8 5.24223447496401 -0.442234474964015 45 4.2 4.93490848926049 -0.734908489260488 46 2.8 4.42419191547404 -1.62419191547404 47 6.1 3.2954776029244 2.8045223970756 48 5.8 5.24444960511625 0.555550394883752 49 4.9 5.63052324338139 -0.73052324338139 50 4.6 5.12285414799983 -0.522854147999825 51 4.1 4.75950240698891 -0.659502406988908 52 3.6 4.30118846093527 -0.701188460935274 53 5.9 3.81390525005849 2.08609474994151 54 4.5 5.26361385848142 -0.763613858481420 55 4.8 4.7329488039902 0.0670511960098015 56 5.7 4.77954529538312 0.920454704616883 57 5 5.41920517132302 -0.419205171323025 58 7 5.12788314696174 1.87211685303826 59 4.6 6.42889016876615 -1.82889016876615 60 2.6 5.15792305588947 -2.55792305588947 61 5 3.38032255432528 1.61967744567472 62 4.1 4.50589958572759 -0.405899585727588 63 3.2 4.22382413177178 -1.02382413177178 64 0 3.51232880904864 -3.51232880904864 65 2.3 1.07147452367525 1.22852547632475 66 3.8 1.92522479496317 1.87477520503683 67 4.5 3.22807920925857 1.27192079074143 68 5.9 4.11198657713898 1.78801342286102 69 5 5.35454684491687 -0.354546844916869 70 4.2 5.1081584135287 -0.908158413528704 71 4.5 4.47704370987433 0.0229562901256655 72 6 4.49299693127694 1.50700306872306 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 5.54027214334909 2.7563313293719 8.32421295732628 74 5.54027214334909 2.15009946085874 8.93044482583943 75 5.54027214334909 1.63691266996215 9.44363161673603 76 5.54027214334909 1.18376442042980 9.89677986626837 77 5.54027214334909 0.77350133899619 10.3070429477020 78 5.54027214334909 0.395853005816942 10.6846912808812 79 5.54027214334909 0.0440923224204841 11.0364519642777 80 5.54027214334909 -0.286471113853737 11.3670154005519 81 5.54027214334909 -0.599262150612824 11.679806437311 82 5.54027214334909 -0.896872076575629 11.9774163632738 83 5.54027214334909 -1.18131770351646 12.2618619902146 84 5.54027214334909 -1.45420528036612 12.5347495670643

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/1d2o11275727939.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/1d2o11275727939.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/2d2o11275727939.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/2d2o11275727939.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/35t641275727939.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275728007unef2paqqzb9lyu/35t641275727939.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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