ws 9: 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: Fri, 04 Dec 2009 08:35:15 -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/t1259940945k20r5bfoclolf27.htm/, Retrieved Fri, 04 Dec 2009 16:35:49 +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/t1259940945k20r5bfoclolf27.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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79.8 83.4 113.6 112.9 104 109.9 99 106.3 128.9 111.1 102.9 130 87 87.5 117.6 103.4 110.8 112.6 102.5 112.4 135.6 105.1 127.7 137 91 90.5 122.4 123.3 124.3 120 118.1 119 142.7 123.6 129.6 151.6 110.4 99.2 130.5 136.2 129.7 128 121.6 135.8 143.8 147.5 136.2 156.6 123.3 104.5 139.8 136.5 112.1 118.5 94.4 102.3 111.4 99.2 87.8 115.8

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 0.39496296829087 beta 0.183094101313385 gamma 0.644958687350449 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 87 86.241006491056 0.758993508944016 14 87.5 87.0197904141963 0.480209585803749 15 117.6 117.087414200422 0.512585799578034 16 103.4 103.528359905879 -0.128359905879265 17 110.8 110.539593772998 0.260406227002349 18 112.6 111.568291084604 1.03170891539605 19 102.5 102.798455794746 -0.298455794746488 20 112.4 110.275273260498 2.12472673950171 21 135.6 135.113841067739 0.48615893226085 22 105.1 117.588315576490 -12.4883155764899 23 127.7 104.279381310879 23.4206186891212 24 137 144.820228932451 -7.82022893245136 25 91 95.8538749386248 -4.85387493862478 26 90.5 94.5640330111002 -4.06403301110021 27 122.4 124.620095482164 -2.22009548216366 28 123.3 108.699680783219 14.6003192167807 29 124.3 123.256255182409 1.04374481759140 30 120 125.899247386699 -5.89924738669933 31 118.1 113.235832873777 4.86416712622336 32 119 125.486247188026 -6.48624718802567 33 142.7 148.720876219639 -6.02087621963935 34 123.6 121.249329572109 2.35067042789126 35 129.6 128.616348044054 0.983651955945533 36 151.6 147.910207043899 3.6897929561014 37 110.4 100.960965706053 9.43903429394676 38 99.2 106.547012121165 -7.34701212116492 39 130.5 141.209642796919 -10.7096427969186 40 136.2 127.440007325703 8.75999267429725 41 129.7 134.368655182123 -4.66865518212265 42 128 131.245203197272 -3.24520319727154 43 121.6 122.873339460583 -1.27333946058297 44 135.8 127.521580902507 8.27841909749326 45 143.8 159.071824885082 -15.2718248850821 46 147.5 129.390922685289 18.1090773147115 47 136.2 143.773351668667 -7.57335166866687 48 156.6 162.566569237088 -5.96656923708829 49 123.3 110.606574321782 12.6934256782176 50 104.5 110.280899047444 -5.78089904744392 51 139.8 146.549107503577 -6.74910750357657 52 136.5 141.830251885327 -5.33025188532682 53 112.1 136.981192390721 -24.8811923907206 54 118.5 124.184618141031 -5.68461814103101 55 94.4 113.651172273622 -19.2511722736216 56 102.3 109.882769188564 -7.58276918856379 57 111.4 116.459249243814 -5.05924924381364 58 99.2 101.296471086083 -2.09647108608323 59 87.8 92.9228304871463 -5.12283048714626 60 115.8 99.2950172286432 16.5049827713568 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 73.7425102127098 59.7731440957264 87.7118763296932 62 62.3882162021922 46.5983806080871 78.1780517962973 63 80.3150544297715 59.0357735748043 101.594335284739 64 75.2384578542102 50.9620636175961 99.5148520908242 65 65.5014374443539 39.4639906216041 91.5388842671037 66 65.1284624867358 34.4455041007752 95.8114208726964 67 55.0502235694466 23.5333061905507 86.5671409483424 68 57.8464616334233 19.0941644722557 96.5987587945908 69 61.9243348543234 13.4042716986218 110.444398010025 70 53.8094264967576 3.76331594632744 103.855537047188 71 47.6698718636309 -4.86453787945371 100.204281606715 72 54.9485875501871 -14.6951939996628 124.592369100037

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/1nvjp1259940913.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/1nvjp1259940913.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/2jlq21259940913.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/2jlq21259940913.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/32c001259940913.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940945k20r5bfoclolf27/32c001259940913.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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