*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: Sun, 19 Dec 2010 17:21:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy.htm/, Retrieved Sun, 19 Dec 2010 18:18:56 +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/2010/Dec/19/t129277913633funkupnq6hxzy.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:

Dataseries X:

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41,85 41,75 41,75 41,75 41,58 41,61 41,42 41,37 41,37 41,33 41,37 41,34 41,33 41,29 41,29 41,27 41,04 40,90 40,89 40,72 40,72 40,58 40,24 40,07 40,12 40,10 40,10 40,08 40,06 39,99 40,05 39,66 39,66 39,67 39,56 39,64 39,73 39,70 39,70 39,68 39,76 40,00 39,96 40,01 40,01 40,01 40,00 39,91 39,86 39,79 39,79 39,80 39,64 39,55 39,36 39,28

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.000564574695315228 gamma 0.192386515790093 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 41.33 41.6101522435898 -0.280152243589754 14 41.29 41.2865186979343 0.00348130206570829 15 41.29 41.2915206633893 -0.00152066338934986 16 41.27 41.275686471528 -0.00568647152795876 17 41.04 41.06568326109 -0.0256832610900091 18 40.9 40.9473354276374 -0.0473354276373854 19 40.89 40.7627253699194 0.127274630080592 20 40.72 40.8282138926216 -0.108213892621571 21 40.72 40.7056527977961 0.0143472022038793 22 40.58 40.6664942311968 -0.0864942311967667 23 40.24 40.6097787320759 -0.369778732075865 24 40.07 40.2091532976942 -0.139153297694222 25 40.12 40.0586580685969 0.0613419314030992 26 40.1 40.0761927006991 0.0238072993008842 27 40.1 40.1012061416979 -0.00120614169787814 28 40.08 40.0853721274075 -0.00537212740748316 29 40.06 39.8753690944403 0.184630905559743 30 39.99 39.9671399990442 0.0228600009558022 31 40.05 39.8525695718889 0.197430428111069 32 39.66 39.9880977027794 -0.328097702779388 33 39.66 39.6454124671188 0.0145875328811869 34 39.67 39.6062540362041 0.0637459637959239 35 39.56 39.6996233588955 -0.139623358895491 36 39.64 39.5291278644135 0.110872135586462 37 39.73 39.628773793349 0.101226206650971 38 39.7 39.6863309431038 0.0136690568962123 39 39.7 39.7013386603074 -0.00133866030743945 40 39.68 39.6855045712004 -0.00550457120038317 41 39.76 39.4755014634587 0.28449853654125 42 40 39.6673287508 0.332671249199983 43 39.96 39.8629332352358 0.0970667647641648 44 40.01 39.8984047033416 0.111595296658358 45 40.01 39.9959677072222 0.0140322927777490 46 40.01 39.956808962833 0.0531910371669895 47 40 40.0401723264799 -0.040172326479933 48 39.91 39.9697329795343 -0.0597329795343029 49 39.86 39.8992825891389 -0.0392825891388995 50 39.79 39.8167604111831 -0.0267604111831048 51 39.79 39.7917453029321 -0.00174530293212172 52 39.8 39.7759109842449 0.0240890157550666 53 39.64 39.5959245842936 0.0440754157063665 54 39.55 39.5476161348247 0.00238386517528255 55 39.36 39.4130341473613 -0.0530341473613234 56 39.28 39.2984208722904 -0.0184208722903989 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 57 39.2659104723320 39.0097388057074 39.5220821389567 58 39.2126542779974 38.8502705508625 39.5750380051323 59 39.2427314169961 38.7987785247121 39.6866843092801 60 39.2123918893282 38.6996145699768 39.7251692086796 61 39.2016356949936 38.6281714558744 39.7750999341127 62 39.1583795006589 38.5300036773465 39.7867553239714 63 39.1601233063243 38.4812084026721 39.8390382099765 64 39.1460337786564 38.4200385385787 39.8720290187341 65 38.9419442509884 38.1716928999339 39.712195602043 66 38.8495213899871 38.0373762959348 39.6616664840395 67 38.7125151956525 37.8604901605592 39.5645402307458 68 38.6509256679846 37.760763769489 39.5410875664801

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/121l61292779274.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/121l61292779274.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/262nm1292779275.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/262nm1292779275.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/362nm1292779275.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129277913633funkupnq6hxzy/362nm1292779275.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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