*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 05:11:55 -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/t1259928760vzopm2w8phoynd9.htm/, Retrieved Fri, 04 Dec 2009 13:12:44 +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/t1259928760vzopm2w8phoynd9.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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17 14 15 16 16 15 13 12 13 13 12 10 14 14 15 16 16 15 15 13 15 15 15 13 16 16 14 16 15 14 15 15 14 13 12 13 12 9 10 8 11 8 8 8 4 6 8 10 5 6 5 9 8 6 9 11 11 8 11 11 13

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 0.27909312390333 beta 0.261615313687514 gamma 0.364635897888864 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14 14.0102512035019 -0.0102512035018787 14 14 13.9571933384626 0.0428066615374423 15 15 14.9173236916909 0.0826763083090931 16 16 15.8435958771574 0.156404122842602 17 16 15.7612800137760 0.238719986224041 18 15 14.6969363113687 0.30306368863131 19 15 13.7139937524670 1.28600624753303 20 13 13.3134495246946 -0.313449524694612 21 15 14.523827270486 0.476172729513991 22 15 14.8871869333564 0.112813066643646 23 15 13.9914207349320 1.00857926506798 24 13 12.1390736244547 0.860926375545342 25 16 17.6503731751283 -1.65037317512833 26 16 17.3562525620149 -1.35625256201488 27 14 18.257879186246 -4.257879186246 28 16 17.9155792109460 -1.91557921094597 29 15 16.9175619900258 -1.91756199002584 30 14 14.7711881886316 -0.771188188631637 31 15 13.2545566061684 1.74544339383157 32 15 12.1989646828455 2.8010353171545 33 14 14.2497661341261 -0.24976613412608 34 13 14.0482751376354 -1.04827513763537 35 12 12.7987471649270 -0.798747164927015 36 13 10.3374050156026 2.66259498439742 37 12 14.8295877213844 -2.82958772138442 38 9 13.8541932204021 -4.85419322040207 39 10 12.1817400869882 -2.18174008698822 40 8 11.9738044342622 -3.97380443426224 41 11 9.70963700391881 1.29036299608119 42 8 8.61034823859755 -0.610348238597554 43 8 7.41197731589706 0.588022684102945 44 8 6.2388888726614 1.76111112733860 45 4 6.31100840793949 -2.31100840793949 46 6 4.73246179015954 1.26753820984046 47 8 4.1137658064348 3.8862341935652 48 10 4.32989190158651 5.67010809841349 49 5 7.08645151102966 -2.08645151102966 50 6 6.06859837485366 -0.0685983748536616 51 5 6.40780863830277 -1.40780863830277 52 9 6.07559877754733 2.92440122245267 53 8 7.78187997935683 0.218120020643167 54 6 7.01780839356718 -1.01780839356718 55 9 6.82916444849723 2.17083555150277 56 11 7.30991601139381 3.69008398860619 57 11 7.54322144231418 3.45677855768582 58 8 10.6103616524784 -2.61036165247845 59 11 10.9640244053554 0.0359755946446274 60 11 10.8327663850901 0.167233614909858 61 13 9.87267825920092 3.12732174079908 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 11.7333804037677 9.41457357528615 14.0521872322493 63 12.5444281670802 9.77062870312892 15.3182276310314 64 16.3447721044121 12.6041811515812 20.0853630572430 65 17.5532117798871 13.0395353863339 22.0668881734404 66 15.6449013208141 10.9867278944441 20.3030747471841 67 18.7508385451721 12.7038317840475 24.7978453062966 68 19.6709250681894 12.7188865015583 26.6229636348205 69 17.5985935295977 10.7343765603987 24.4628104987967 70 17.9861237997251 10.3911479052626 25.5810996941876 71 21.2650404984640 11.6964520110012 30.8336289859267 72 20.8751798299709 10.8170542396425 30.9333054202994 73 20.1302809450564 9.63112987139291 30.6294320187199

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/1cri41259928713.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/1cri41259928713.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/2qrdf1259928713.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/2qrdf1259928713.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/3fxsc1259928713.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928760vzopm2w8phoynd9/3fxsc1259928713.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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