*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 09:42:27 -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/20/t1264005810hhmytqxdqhg3xbo.htm/, Retrieved Wed, 20 Jan 2010 17:43:34 +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/20/t1264005810hhmytqxdqhg3xbo.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 «

4,26 4,26 4,07 4,26 4,4 4,46 4,34 4,18 4,11 3,98 3,85 3,66 3,59 3,57 3,76 3,6 3,43 3,26 3,3 3,31 3,14 3,3 3,49 3,39 3,37 3,54 3,7 3,96 4,03 4,02 4,04 3,92 3,79 3,83 3,76 3,82 4,06 4,11 4,01 4,22 4,34 4,64 4,62 4,44 4,39 4,42 4,28 4,41 4,25 4,23 4,23 4,37 4,51 4,84 4,85 4,58 4,56 4,46 4,26 3,87 4,13 4,24 4,03 3,93 4,03 4,12 3,92 3,77

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 0.770019236878996 beta 0.0459442665820473 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.59 4.00846955128205 -0.418469551282054 14 3.57 3.66284997093498 -0.0928499709349788 15 3.76 3.77176222129098 -0.0117622212909771 16 3.6 3.58478080858013 0.0152191914198729 17 3.43 3.3836973601118 0.0463026398881983 18 3.26 3.19110352494215 0.0688964750578451 19 3.3 3.55709479485318 -0.257094794853185 20 3.31 3.16463769083862 0.145362309161376 21 3.14 3.16222292221461 -0.0222229222146098 22 3.3 2.96872809975901 0.331271900240985 23 3.49 3.08665081777928 0.403349182220716 24 3.39 3.23684410436798 0.153155895632024 25 3.37 3.22647881180731 0.143521188192688 26 3.54 3.42114828365876 0.118851716341236 27 3.7 3.75187223626913 -0.0518722362691264 28 3.96 3.57894024347777 0.381059756522229 29 4.03 3.71838205633193 0.311617943668066 30 4.02 3.79634096634602 0.223659033653977 31 4.04 4.27306455749515 -0.233064557495147 32 3.92 4.0590526264077 -0.139052626407704 33 3.79 3.85641351993006 -0.0664135199300588 34 3.83 3.76594673576181 0.0640532642381868 35 3.76 3.74098733886507 0.0190126611349264 36 3.82 3.57040240918538 0.249597590814619 37 4.06 3.66820313247483 0.391796867525171 38 4.11 4.09327949150078 0.0167205084992190 39 4.01 4.34738737176980 -0.337387371769804 40 4.22 4.08535846395236 0.134641536047645 41 4.34 4.04155465107101 0.298445348928992 42 4.64 4.11114695829864 0.528853041701364 43 4.62 4.75064071659109 -0.130640716591087 44 4.44 4.67354414644109 -0.233544146441088 45 4.39 4.44793352835303 -0.05793352835303 46 4.42 4.42738453568961 -0.00738453568961361 47 4.28 4.36791404633415 -0.087914046334145 48 4.41 4.19509660330618 0.214903396693819 49 4.25 4.32473082800756 -0.0747308280075609 50 4.23 4.31365233738552 -0.0836523373855202 51 4.23 4.41482300521861 -0.184823005218613 52 4.37 4.39001639067437 -0.0200163906743729 53 4.51 4.27051046934986 0.239489530650142 54 4.84 4.3513250066527 0.488674993347297 55 4.85 4.8104186065169 0.0395813934831004 56 4.58 4.84896122840081 -0.268961228400814 57 4.56 4.6434435574781 -0.0834435574781 58 4.46 4.62095187216924 -0.160951872169243 59 4.26 4.42535366537929 -0.165353665379286 60 3.87 4.26045108029768 -0.39045108029768 61 4.13 3.83382686825878 0.296173131741222 62 4.24 4.09590807066401 0.144091929335993 63 4.03 4.34684431171796 -0.316844311717957 64 3.93 4.25127587092082 -0.321275870920824 65 4.03 3.94181254420326 0.0881874557967421 66 4.12 3.94041349589949 0.179586504100506 67 3.92 4.02426926105732 -0.104269261057318 68 3.77 3.84204523678205 -0.0720452367820461 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 69 3.79874864356221 3.35663752519815 4.24085976192627 70 3.79356322551774 3.22589105872594 4.36123539230953 71 3.69746142328074 3.01891554202909 4.37600730453238 72 3.59053883756575 2.80921304484179 4.3718646302897 73 3.61871576632481 2.73958129734942 4.49785023530021 74 3.60352014260283 2.62979736130801 4.57724292389766 75 3.61815661164457 2.55197876693690 4.68433445635223 76 3.75741477478896 2.60019218552895 4.91463736404897 77 3.79274438739595 2.54538232696154 5.04010644783036 78 3.74457508149109 2.40761268708644 5.08153747589573 79 3.61862676946526 2.19233002433441 5.04492351459612 80 3.52155417355281 2.00598059417063 5.03712775293499

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/1vvdj1264005744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/1vvdj1264005744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/2j2ot1264005744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/2j2ot1264005744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/3y7si1264005744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264005810hhmytqxdqhg3xbo/3y7si1264005744.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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