W8 (3)

*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: Mon, 29 Nov 2010 10:02:53 +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/Nov/29/t1291025503wlnua7wqlwucc2f.htm/, Retrieved Mon, 29 Nov 2010 11:11:50 +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/Nov/29/t1291025503wlnua7wqlwucc2f.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:

» Textbox « » Textfile « » CSV «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.380859354912001 beta 0.0316088853012633 gamma 0.733581043315084 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 80 65.9535256410257 14.0464743589743 14 42 32.4467148172601 9.55328518273991 15 54 47.1353051316095 6.86469486839045 16 66 60.59089490801 5.40910509199001 17 81 79.7238940940246 1.2761059059754 18 63 69.4231643277681 -6.42316432776809 19 137 111.487769948458 25.5122300515419 20 72 80.1890659314056 -8.18906593140558 21 107 86.456323671552 20.5436763284479 22 58 68.1223642893241 -10.1223642893241 23 36 97.153764642369 -61.1537646423691 24 52 157.471510088699 -105.471510088699 25 79 65.8538039157931 13.1461960842069 26 77 28.6504949782487 48.3495050217513 27 54 56.0480501431291 -2.04805014312910 28 84 64.4949190767423 19.5050809232577 29 48 86.3359268092791 -38.3359268092791 30 96 56.1913729959129 39.8086270040871 31 83 129.664803267216 -46.6648032672161 32 66 53.997391331058 12.002608668942 33 61 79.6754118037384 -18.6754118037384 34 53 30.6746061226849 22.3253938773151 35 30 47.4750331630982 -17.4750331630982 36 74 103.414328539587 -29.4143285395875 37 69 94.6690520639822 -25.6690520639822 38 59 58.2346826816736 0.765317318326439 39 42 43.609557805132 -1.60955780513198 40 65 61.008183141234 3.99181685876599 41 70 49.4788033499318 20.5211966500682 42 100 76.7603341378123 23.2396658621877 43 63 103.965837074180 -40.9658370741803 44 105 56.501549428842 48.498450571158 45 82 81.9715413639356 0.0284586360644283 46 81 58.7674302672568 22.2325697327432 47 75 57.5054384585491 17.4945615414509 48 102 121.811391006691 -19.8113910066906 49 121 119.011021546431 1.98897845356879 50 98 106.036128029648 -8.03612802964805 51 76 87.7937238475118 -11.7937238475118 52 77 104.548576897235 -27.5485768972347 53 63 88.8253943324124 -25.8253943324124 54 37 99.4433230770057 -62.4433230770057 55 35 63.5759025308631 -28.5759025308631 56 23 60.3350961492543 -37.3350961492543 57 40 28.9375786540513 11.0624213459487 58 29 17.9911476535515 11.0088523464485 59 37 8.13783623183913 28.8621637681609 60 51 57.8014044626805 -6.8014044626805 61 20 67.986280314369 -47.9862803143689 62 28 28.951675237226 -0.95167523722598 63 13 9.31321056571396 3.68678943428604 64 22 22.6070517338644 -0.607051733864424 65 25 16.0505737046165 8.94942629538355 66 13 21.8230856739742 -8.82308567397422 67 16 20.9469405271599 -4.94694052715987 68 13 22.1988348562020 -9.19883485620204 69 16 23.3093821664651 -7.30938216646515 70 17 4.93082348472385 12.0691765152762 71 9 3.19217990983756 5.80782009016244 72 17 27.201755489461 -10.2017554894610 73 25 16.6693885647928 8.33061143520722 74 14 20.4077763690616 -6.40777636906155 75 8 0.693902625604984 7.30609737439502 76 7 13.3553977851489 -6.3553977851489 77 10 8.82028766465713 1.17971233534287 78 7 3.33822505002645 3.66177494997355 79 10 8.90454913922412 1.09545086077588 80 3 10.5263066432461 -7.5263066432461 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 13.1518860780379 -37.4465989188957 63.7503710749715 82 6.46657662737189 -47.8972220237203 60.8303752784641 83 -2.75000728509995 -60.8467257368824 55.3467111666825 84 11.6688643515566 -50.1402534266421 73.4779821297553 85 13.4546037022310 -52.0555460762878 78.9647534807497 86 7.24134529398266 -61.965654558537 76.4483451465023 87 -3.81105338954830 -76.7164471374329 69.0943403583363 88 -0.232709452860554 -76.8426607262627 76.3772418205416 89 1.05592991450302 -79.2685090912587 81.3803689202648 90 -3.78144524582828 -87.8334001501179 80.2705096584614 91 -0.852758842772003 -88.647824662595 86.942306977051 92 -3.6547344525488 -95.2106461244885 87.9011772193909

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/1g3b21291024966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/1g3b21291024966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/2g3b21291024966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/2g3b21291024966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/39cam1291024966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025503wlnua7wqlwucc2f/39cam1291024966.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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