*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 15 Jan 2010 08:25:06 -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/15/t1263569168phq6ou4ia1q08gh.htm/, Retrieved Fri, 15 Jan 2010 16:26:12 +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/15/t1263569168phq6ou4ia1q08gh.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 «

-9 -13 -18 -11 -9 -10 -13 -11 -5 -15 -6 -6 -3 -1 -3 -4 -6 0 -4 -2 -2 -6 -7 -6 -6 -3 -2 -5 -11 -11 -11 -10 -14 -8 -9 -5 -1 -2 -5 -4 -6 -2 -2 -2 -2 2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.70504327667519 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 -13 -9 -4 3 -18 -11.8201731067008 -6.17982689329924 4 -11 -16.1772185088379 5.17721850883791 5 -9 -12.5270554073034 3.52705540730339 6 -10 -10.0403287059233 0.0403287059232618 7 -13 -10.0118952229551 -2.98810477704495 8 -11 -12.1186384060116 1.11863840601161 9 -5 -11.3299499188225 6.32994991882247 10 -15 -6.86706128686603 -8.13293871313397 11 -6 -12.6011350461725 6.6011350461725 12 -6 -7.94704916344361 1.94704916344361 13 -3 -6.57429524140164 3.57429524140164 14 -1 -4.05426241259929 3.05426241259929 15 -3 -1.90087523339442 -1.09912476660558 16 -4 -2.67580576031687 -1.32419423968313 17 -6 -3.60942000601748 -2.39057999398252 18 0 -5.29488235812907 5.29488235812907 19 -4 -1.56176115074409 -2.43823884925590 20 -2 -3.28082505834022 1.28082505834022 21 -2 -2.37778796236034 0.377787962360341 22 -6 -2.11143109948936 -3.88856890051064 23 -7 -4.85304045868262 -2.14695954131738 24 -6 -6.36673984858209 0.366739848582089 25 -6 -6.10817238405041 0.108172384050410 26 -3 -6.03190617195374 3.03190617195374 27 -2 -3.89428110990774 1.89428110990774 28 -5 -2.55873094923447 -2.44126905076553 29 -11 -4.27993128003193 -6.72006871996807 30 -11 -9.01787054984067 -1.98212945015933 31 -11 -10.4153575921754 -0.584642407824605 32 -10 -10.8275557910713 0.827555791071328 33 -14 -10.2440931445029 -3.75590685549713 34 -8 -12.8921700207894 4.89217002078938 35 -9 -9.4429784392799 0.442978439279903 36 -5 -9.13065946895354 4.13065946895354 37 -1 -6.21836578213314 5.21836578213314 38 -2 -2.5391920722083 0.539192072208301 39 -5 -2.15903832686127 -2.84096167313873 40 -4 -4.16203925379963 0.162039253799631 41 -6 -4.04779456735074 -1.95220543264926 42 -2 -5.42418388232888 3.42418388232888 43 -2 -3.00998605799335 1.00998605799335 44 -2 -2.29790217826946 0.297902178269462 45 -2 -2.08786825037368 0.0878682503736838 46 2 -2.02591733121451 4.02591733121451 47 1 0.812528615608405 0.187471384391595 48 -8 0.94470405474269 -8.94470405474269 49 -1 -5.36169940090295 4.36169940090295 50 1 -2.28651256341812 3.28651256341812 51 -1 0.0306210231283678 -1.03062102312837 52 2 -0.696011400028393 2.69601140002839 53 2 1.20479331140129 0.795206688598709 54 1 1.76544844076495 -0.765448440764952 55 -1 1.22577416396212 -2.22577416396212 56 -2 -0.343492945736715 -1.65650705426328 57 -2 -1.51140210711007 -0.488597892889932 58 -1 -1.85588476648978 0.855884766489779 59 -8 -1.25244896626745 -6.74755103373255 60 -4 -6.00976445662331 2.00976445662331 61 -6 -4.59279353878028 -1.40720646121972 62 -3 -5.58493499315713 2.58493499315713 63 -3 -3.76244395558927 0.762443955589267 64 -7 -3.22488797085942 -3.77511202914058 65 -9 -5.88650532570062 -3.11349467429938 66 -11 -8.0816538127794 -2.91834618722059 67 -13 -10.1392141710900 -2.86078582891004 68 -11 -12.1561919857706 1.15619198577064 69 -9 -11.3410265996573 2.34102659965732 70 -17 -9.69050153505114 -7.30949846494886 71 -22 -14.8440142836310 -7.15598571636905 72 -25 -19.8892939009406 -5.11070609905936 73 -20 -23.4925628751453 3.49256287514533 74 -24 -21.0301549016587 -2.96984509834125 75 -24 -23.124024221011 -0.875975778988984 76 -22 -23.7416250545175 1.74162505451751 77 -19 -22.5137040193409 3.51370401934088 78 -18 -20.036390624278 2.03639062427800 79 -17 -18.6006471059464 1.60064710594640 80 -11 -17.4721216255693 6.47212162556929 81 -11 -12.9089957876376 1.90899578763756 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 82 -11.5630711423624 -18.5034914750874 -4.62265080963752 83 -11.5630711423624 -20.0550548281408 -3.07108745658413 84 -11.5630711423624 -21.3639965805111 -1.76214570421382 85 -11.5630711423624 -22.5176360341677 -0.608506250557186 86 -11.5630711423624 -23.5608561251581 0.434713840433171 87 -11.5630711423624 -24.5203546932468 1.39421240852196 88 -11.5630711423624 -25.413542236973 2.28739995224814 89 -11.5630711423624 -26.2525198068722 3.12637752214729 90 -11.5630711423624 -27.0461023246565 3.91996003993162 91 -11.5630711423624 -27.8009468382937 4.67480455356879 92 -11.5630711423624 -28.5222267711412 5.3960844864163 93 -11.5630711423624 -29.2140572951461 6.08791501042124

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/1nws01263569104.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/1nws01263569104.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/2e6mu1263569104.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/2e6mu1263569104.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/355ou1263569104.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/15/t1263569168phq6ou4ia1q08gh/355ou1263569104.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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