*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: Tue, 01 Dec 2009 12:07:33 -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/01/t1259694532ehe7uc5vk8g7a6l.htm/, Retrieved Tue, 01 Dec 2009 20:08:56 +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/01/t1259694532ehe7uc5vk8g7a6l.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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8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.5 8.26101587988918 0.238984120110819 14 8.6 8.64032888121282 -0.0403288812128242 15 8.5 8.55687786733223 -0.0568778673322257 16 8.2 8.23883422057737 -0.0388342205773693 17 8.1 8.10624963153047 -0.00624963153047275 18 7.9 7.89045517064055 0.00954482935944956 19 8.6 8.85935406035076 -0.259354060350759 20 8.7 9.1230734808869 -0.423073480886906 21 8.7 8.70722563113187 -0.00722563113186858 22 8.5 8.10905124399243 0.390948756007571 23 8.4 7.95461083694412 0.445389163055882 24 8.5 8.45050021454214 0.0494997854578578 25 8.7 8.69852411649443 0.0014758835055666 26 8.7 8.84347614207988 -0.143476142079876 27 8.6 8.65630048952282 -0.0563004895228172 28 8.5 8.3356872492021 0.164312750797901 29 8.3 8.4025910949451 -0.102591094945106 30 8 8.08513102024552 -0.085131020245516 31 8.2 8.97141149469801 -0.771411494698011 32 8.1 8.69908055764248 -0.599080557642484 33 8.1 8.10722563113187 -0.00722563113186858 34 8 7.55027041614762 0.449729583852385 35 7.9 7.48706269874117 0.412937301258835 36 7.9 7.94787077194816 -0.0478707719481557 37 8 8.0849672497312 -0.0849672497311929 38 8 8.13246072904518 -0.132460729045183 39 7.9 7.96034213418867 -0.0603421341886721 40 8 7.65771604882899 0.342283951171013 41 7.7 7.90868865592072 -0.208688655920716 42 7.2 7.50110347143063 -0.301103471430627 43 7.5 8.07495201992 -0.57495201992 44 7.3 7.95709294196475 -0.657092941964749 45 7 7.30722563113187 -0.307225631131868 46 7 6.52583889843212 0.474161101567879 47 7 6.55196642233526 0.448033577664742 48 7.2 7.04313777527898 0.156862224721019 49 7.3 7.36915090517408 -0.0691509051740775 50 7.1 7.42144531601049 -0.321445316010490 51 6.8 7.06553853447334 -0.265538534473342 52 6.4 6.59233273395695 -0.192332733956952 53 6.1 6.32820085104267 -0.228200851042668 54 6.5 5.94369667459092 0.556303325409075 55 7.7 7.29054997948924 0.409450020510757 56 7.9 8.16908940358696 -0.269089403586959 57 7.5 7.90722563113187 -0.407225631131869 58 6.9 6.9914895883028 -0.0914895883027995 59 6.6 6.45845679469467 0.141543205305332 60 6.9 6.6410342212038 0.258965778796208 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 7.06237247179246 6.4456268817051 7.67911806187981 62 7.18007840870063 6.30097896270403 8.05917785469724 63 7.14515458821201 6.07543846346652 8.2148707129575 64 6.9266254060775 5.72089747984573 8.13235333230928 65 6.84840399607044 5.50716832778106 8.18963966435983 66 6.67217759350474 5.22829871123626 8.11605647577322 67 7.48348777329149 5.75195267631735 9.21502287026563 68 7.93959027378621 6.00334243656007 9.87583811101236 69 7.94681590491808 5.91471580648417 9.978916003352 70 7.4076098570434 5.41715202397996 9.39806769010683 71 6.93312088188288 4.9723302125452 8.89391155122056 72 6.97590694755821 -83.4121580322259 97.3639719273423

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/1bpc61259694451.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/1bpc61259694451.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/26r721259694451.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/26r721259694451.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/300sn1259694451.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694532ehe7uc5vk8g7a6l/300sn1259694451.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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