Exponential Smoothing

*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: Thu, 03 Dec 2009 06:33:46 -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/03/t12598472619khg0oezoew9snf.htm/, Retrieved Thu, 03 Dec 2009 14:34:25 +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/03/t12598472619khg0oezoew9snf.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:

JSSHWWS9P10

Dataseries X:

» Textbox « » Textfile « » CSV «

11.1 10.9 10 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9 9 9 9.8 10 9.8 9.3 9 9 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8 7.9 7.6 7.1 6.8 6.5 6.9 8.2 8.7 8.3 7.9 7.5 7.8 8.3 8.4 8.2 7.7 7.2 7.3 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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0.428593928188172 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10.3 10.3771634615385 -0.077163461538472 14 10.2 10.2079399766900 -0.00793997668997548 15 9.6 9.60377331002331 -0.00377331002331083 16 9.2 9.18710664335664 0.0128933566433567 17 9.3 9.28293997668998 0.0170600233100231 18 9.4 9.39960664335664 0.000393356643355602 19 9.4 9.40793997668998 -0.00793997668997726 20 9.2 9.34960664335664 -0.149606643356645 21 9 8.83293997668998 0.167060023310022 22 9 8.80377331002331 0.196226689976690 23 9 9.08293997668998 -0.0829399766899783 24 9.8 10.0871066433566 -0.287106643356640 25 10 9.99960664335665 0.000393356643353826 26 9.8 9.90793997668997 -0.107939976689973 27 9.3 9.20377331002331 0.0962266899766906 28 9 8.88710664335664 0.112893356643356 29 9 9.08293997668998 -0.0829399766899783 30 9.1 9.09960664335664 0.000393356643357379 31 9.1 9.10793997668998 -0.00793997668997548 32 9.1 9.04960664335664 0.0503933566433563 33 9.2 8.73293997668998 0.467060023310021 34 8.8 9.00377331002331 -0.203773310023308 35 8.3 8.88293997668998 -0.582939976689978 36 8.4 9.38710664335664 -0.987106643356642 37 8.1 8.59960664335665 -0.499606643356646 38 7.7 8.00793997668997 -0.307939976689974 39 7.9 7.10377331002331 0.796226689976692 40 7.9 7.48710664335664 0.412893356643358 41 8 7.98293997668998 0.0170600233100213 42 7.9 8.09960664335664 -0.199606643356642 43 7.6 7.90793997668997 -0.307939976689975 44 7.1 7.54960664335664 -0.449606643356643 45 6.8 6.73293997668998 0.067060023310022 46 6.5 6.60377331002331 -0.103773310023309 47 6.9 6.58293997668998 0.317060023310023 48 8.2 7.98710664335664 0.212893356643360 49 8.7 8.39960664335664 0.300393356643355 50 8.3 8.60793997668997 -0.307939976689973 51 7.9 7.70377331002331 0.196226689976691 52 7.5 7.48710664335664 0.0128933566433576 53 7.8 7.58293997668998 0.217060023310022 54 8.3 7.89960664335664 0.400393356643360 55 8.4 8.30793997668998 0.0920600233100242 56 8.2 8.34960664335664 -0.149606643356645 57 7.7 7.83293997668998 -0.132939976689978 58 7.2 7.50377331002331 -0.303773310023311 59 7.3 7.28293997668998 0.0170600233100222 60 8.1 8.38710664335664 -0.287106643356639 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 8.29960664335665 7.72361476753616 8.87559851917713 62 8.20754662004662 7.39297109744457 9.02212214264867 63 7.61131993006993 6.61367273640194 8.60896712373791 64 7.19842657342657 6.0464428217856 8.35041032506754 65 7.28136655011655 5.99340956129432 8.56932353893877 66 7.38097319347319 5.97008700172447 8.79185938522191 67 7.38891317016316 5.86498190954856 8.91284443077777 68 7.33851981351981 5.7093687683157 8.96767085872391 69 6.97145979020979 5.24348416274832 8.69943541767125 70 6.7752331002331 4.95378685888749 8.5966793415787 71 6.85817307692307 4.94782414253354 8.76852201131261 72 7.94527972027971 5.94998533294374 9.94057410761569

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/1b5961259847224.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/1b5961259847224.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/2twrs1259847224.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/2twrs1259847224.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/3cf551259847224.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598472619khg0oezoew9snf/3cf551259847224.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; 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=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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