Michaël Mertens opdracht 10

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Mon, 11 Aug 2008 13:26:29 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34.htm/, Retrieved Mon, 11 Aug 2008 19:27:05 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15.14 15.09 15.17 15.18 15.21 15.27 15.28 15.3 15.34 15.33 15.27 15.35 15.38 15.38 15.39 15.4 15.39 15.43 15.43 15.47 15.48 15.47 15.58 15.56 15.61 15.56 15.62 15.63 15.58 15.65 15.79 15.76 15.77 15.79 15.87 15.79 15.9 15.96 16.05 16.18 16.29 16.43 16.38 16.39 16.35 16.48 16.52 16.44 16.46 16.52 16.47 16.59 16.59 16.59 16.54 16.48 16.47 16.56 16.61 16.57 16.72 16.69 16.72 16.81 16.75 16.85 16.84 16.92 17.02 17.11 17.2 17.3 17.37 17.42 17.51 17.56 17.62 17.59 17.78 17.73 17.79 17.85 17.86 17.79 17.97 17.96 18.03 18.02 18.03 18.14 18.16 18.24 18.28 18.18 18.19 18.32

Text written by user:

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 0.862499742878666 beta 0.0338568524640709 gamma 0.871697167846424 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 15.38 15.2696125 0.110387499999995 14 15.38 15.3729203550379 0.00707964496207936 15 15.39 15.3977486147752 -0.00774861477524169 16 15.4 15.4108112329217 -0.0108112329217409 17 15.39 15.3938333058659 -0.00383330586586617 18 15.43 15.4298452340519 0.00015476594814956 19 15.43 15.4326347258873 -0.00263472588727609 20 15.47 15.4741913437140 -0.00419134371395025 21 15.48 15.4842829854306 -0.00428298543063832 22 15.47 15.4720871831442 -0.00208718314416600 23 15.58 15.5833909774979 -0.00339097749786887 24 15.56 15.5638878945040 -0.00388789450397908 25 15.61 15.5987402444520 0.0112597555480356 26 15.56 15.6034563512448 -0.0434563512447621 27 15.62 15.5807325439382 0.039267456061788 28 15.63 15.6331648819733 -0.00316488197333697 29 15.58 15.6230270321828 -0.0430270321828186 30 15.65 15.6239766065792 0.0260233934208483 31 15.79 15.6477630622646 0.142236937735401 32 15.76 15.8173349762871 -0.0573349762871356 33 15.77 15.7832774869106 -0.0132774869106083 34 15.79 15.7650226843742 0.0249773156257653 35 15.87 15.9017392249009 -0.0317392249009423 36 15.79 15.8591243078315 -0.0691243078315171 37 15.9 15.8390189228894 0.0609810771106343 38 15.96 15.8810064790501 0.0789935209498509 39 16.05 15.9783315541117 0.0716684458883297 40 16.18 16.0590907565419 0.120909243458112 41 16.29 16.1602790399771 0.129720960022883 42 16.43 16.3326345574511 0.0973654425489379 43 16.38 16.4481005577839 -0.0681005577839251 44 16.39 16.4224117075540 -0.0324117075539618 45 16.35 16.425934675581 -0.0759346755809993 46 16.48 16.3671970210661 0.112802978933946 47 16.52 16.5844036434241 -0.06440364342415 48 16.44 16.5197193338504 -0.0797193338503988 49 16.46 16.5163451812626 -0.056345181262639 50 16.52 16.4661469021900 0.0538530978099523 51 16.47 16.5470253433148 -0.0770253433148369 52 16.59 16.507210985151 0.0827890148490056 53 16.59 16.5772364342757 0.0127635657243275 54 16.59 16.6420825014401 -0.0520825014400614 55 16.54 16.6016974185202 -0.061697418520243 56 16.48 16.5788761214078 -0.098876121407752 57 16.47 16.5109833179501 -0.0409833179501504 58 16.56 16.4971600312795 0.0628399687205139 59 16.61 16.6407218417714 -0.0307218417714203 60 16.57 16.5949239270631 -0.0249239270631172 61 16.72 16.6348840676928 0.0851159323072146 62 16.69 16.7173067290362 -0.0273067290361944 63 16.72 16.7075305013812 0.0124694986188345 64 16.81 16.7617064958919 0.0482935041081305 65 16.75 16.7902250548055 -0.0402250548054681 66 16.85 16.7966873741033 0.0533126258967407 67 16.84 16.8442221112176 -0.00422211121762572 68 16.92 16.8663644120368 0.0536355879632175 69 17.02 16.9412527897854 0.0787472102146474 70 17.11 17.0509384008687 0.0590615991312760 71 17.2 17.1877140840098 0.0122859159901552 72 17.3 17.1886480729808 0.111351927019246 73 17.37 17.3722575813102 -0.00225758131021436 74 17.42 17.3762166053562 0.0437833946438069 75 17.51 17.4449698703920 0.065030129607976 76 17.56 17.5627548178179 -0.00275481781785203 77 17.62 17.5491254216809 0.070874578319092 78 17.59 17.6783576375715 -0.088357637571498 79 17.78 17.6084039863123 0.171596013687729 80 17.73 17.8058564838392 -0.0758564838392033 81 17.79 17.7850188275292 0.00498117247082774 82 17.85 17.8395186807054 0.0104813192946338 83 17.86 17.9381657196307 -0.0781657196306895 84 17.79 17.8796960840044 -0.0896960840044052 85 17.97 17.8771507268048 0.092849273195231 86 17.96 17.9723011271238 -0.0123011271238163 87 18.03 17.9972336889866 0.0327663110134502 88 18.02 18.0801299194004 -0.0601299194004454 89 18.03 18.0252276136564 0.0047723863436353 90 18.14 18.0758190585551 0.0641809414448531 91 18.16 18.1704996291990 -0.0104996291989750 92 18.24 18.1778299646626 0.0621700353373811 93 18.28 18.2863544070357 -0.0063544070356798 94 18.18 18.3320307236965 -0.152030723696477 95 18.19 18.2754346170459 -0.0854346170459372 96 18.32 18.2046498415552 0.115350158444805 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 18.4021604026398 18.2748793158208 18.5294414894587 98 18.4032377687556 18.2327033807533 18.5737721567579 99 18.4431535988598 18.2362212811348 18.6500859165849 100 18.4846694873547 18.2449923624976 18.7243466122119 101 18.4891792091889 18.2190273502128 18.759331068165 102 18.5424066255061 18.2433091137492 18.8415041372630 103 18.5705373897666 18.2435746437123 18.8975001358208 104 18.5936976876715 18.2396558773617 18.9477394979812 105 18.6366357397472 18.2560968466046 19.0171746328898 106 18.6667662239642 18.2601644485347 19.0733679993937 107 18.7501522719782 18.3178113226721 19.1824932212842 108 18.7804890114581 18.3226478201896 19.2383302027265

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/1cff01218482787.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/1cff01218482787.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/2rkop1218482787.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/2rkop1218482787.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/357gg1218482787.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/11/t1218482821vrhl6orspatfn34/357gg1218482787.ps (open in new window)

Parameters (Session):

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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