ws 9

*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: Fri, 04 Dec 2009 08:14:43 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf.htm/, Retrieved Fri, 04 Dec 2009 16:15:29 +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/2009/Dec/04/t125993972548a6kdg5gcbylmf.htm/}, year = {2009}, } @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 = {2009}, 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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8.2 8 7.5 6.8 6.5 6.6 7.6 8 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8 8.1

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 1 beta 0 gamma 0.668258580403658 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7.8 7.53561935176154 0.264380648238461 14 7.8 7.838265199013 -0.0382651990129999 15 7.8 7.85558974755393 -0.0555897475539346 16 7.5 7.53297162445567 -0.0329716244556737 17 7.5 7.50408923805517 -0.0040892380551707 18 7.1 7.09218930660449 0.00781069339551177 19 7.5 7.726775108697 -0.226775108697007 20 7.5 7.93452869210363 -0.434528692103629 21 7.6 7.60303279772518 -0.00303279772517673 22 7.7 7.19740015671231 0.50259984328769 23 7.7 7.44227605124198 0.257723948758016 24 7.9 7.75127791758613 0.148722082413871 25 8.1 8.10295103420125 -0.00295103420124754 26 8.2 8.13924719573968 0.0607528042603231 27 8.2 8.2577839329626 -0.057783932962602 28 8.2 7.91864480715856 0.281355192841441 29 7.9 8.20332000728594 -0.303320007285938 30 7.3 7.46981853034878 -0.169818530348782 31 6.9 7.94407445538895 -1.04407445538895 32 6.6 7.30083508308107 -0.700835083081073 33 6.7 6.69229102416132 0.00770897583868368 34 6.9 6.34658977894686 0.553410221053142 35 7 6.67033370787107 0.32966629212893 36 7.1 7.04774294937541 0.0522570506245881 37 7.2 7.2836842702277 -0.0836842702276916 38 7.1 7.23630120555964 -0.136301205559645 39 6.9 7.15174992308877 -0.251749923088767 40 7 6.66520696337418 0.334793036625819 41 6.8 7.00463868860462 -0.204638688604619 42 6.4 6.43133816505198 -0.0313381650519773 43 6.7 6.96622739527521 -0.266227395275208 44 6.6 7.08960388007355 -0.489603880073554 45 6.4 6.69229102416132 -0.292291024161316 46 6.3 6.06298631969171 0.237013680308293 47 6.2 6.09137695034288 0.108623049657117 48 6.5 6.24370298570602 0.256297014293979 49 6.8 6.66923419724753 0.130765802752474 50 6.8 6.83499187659074 -0.0349918765907411 51 6.4 6.85010428403227 -0.450104284032268 52 6.1 6.18311548499557 -0.0831154849955738 53 5.8 6.10562769959363 -0.305627699593630 54 6.1 5.48726510569125 0.612734894308752 55 7.2 6.6402783752373 0.559721624762706 56 7.3 7.61768188759235 -0.317681887592351 57 6.9 7.40064573693321 -0.500645736933206 58 6.1 6.53565875178363 -0.435658751783627 59 5.8 5.89839136450015 -0.098391364500154 60 6.2 5.84168300387132 0.358316996128676 61 7.1 6.36200916075744 0.737990839242557 62 7.7 7.13597387331742 0.564026126682581 63 7.9 7.75504120120177 0.144958798798232 64 7.7 7.6293899201314 0.0706100798686062 65 7.4 7.70386945783539 -0.303869457835389 66 7.5 6.99778200066842 0.502217999331584 67 8 8.1613738020809 -0.161373802080893 68 8.1 8.46260669962242 -0.362606699622425 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 69 8.21019398010108 7.5258390960881 8.89454886411406 70 7.77424390195676 6.83249675503644 8.71599104887708 71 7.51391606581386 6.37632640484586 8.65150572678187 72 7.56425426798303 6.23175464610015 8.8967538898659 73 7.7591193849669 6.23253833444812 9.28570043548569 74 7.79725076854608 6.11973090054358 9.47477063654858 75 7.85282543529116 6.03255837254869 9.67309249803363 76 7.58390500884669 5.7001284848726 9.46768153282078 77 7.58790204359543 5.5856131700397 9.59019091715117 78 7.17517525782569 5.16480163691102 9.18554887874037 79 7.80845278076161 5.51948959740797 10.0974159641153 80 8.26030295186008 -49.0911171148197 65.6117230185399

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/10tpr1259939682.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/10tpr1259939682.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/2o9141259939682.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/2o9141259939682.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/395my1259939682.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t125993972548a6kdg5gcbylmf/395my1259939682.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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