Opdracht 10 b

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 16:22:37 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz.htm/, Retrieved Sun, 17 Jan 2010 00:23:43 +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/Jan/17/t1263684218ba3wy94ozpew4dz.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

84.9 81.9 95.9 81 89.2 102.5 89.8 88.8 83.2 90.2 100.4 187.1 87.6 85.4 86.1 86.7 89.1 103.7 86.9 85.2 80.8 91.2 102.8 182.5 80.9 83.1 88.3 86.6 93 105.3 93.8 86.4 87 96.7 100.5 196.7 86.8 88.2 93.8 85 90.4 115.9 94.9 87.7 91.7 95.9 106.8 204.5 90.2 90.5 93.2 97.8 99.4 120 108.2 98.5 104.3 102.9 111.1 188.1 93.8 94.5 112.4 102.5 115.8 136.5 122.1 110.6 116.4 112.6 121.5 199.3 102.1 100.6 119 106.8 121.3 145.5 129.7 117.7 121.3 124.3 135.2 210.1 106.8 110.5 111.5 122.1 126.3 143.2 137.3 121.5 121.9 123.9 131.6 220.9

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 0.0536868572060943 beta 0.0982858832672798 gamma 0.910497809224067 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 87.6 87.4724469700408 0.127553029959202 14 85.4 85.4652147636646 -0.0652147636646419 15 86.1 86.3288295614751 -0.228829561475138 16 86.7 86.914198608956 -0.214198608956039 17 89.1 89.120207340686 -0.0202073406860137 18 103.7 103.751481005857 -0.0514810058570134 19 86.9 89.3286739359633 -2.42867393596329 20 85.2 87.9022547215732 -2.70225472157323 21 80.8 82.3631625078487 -1.5631625078487 22 91.2 89.2616935640018 1.93830643599817 23 102.8 99.139725584336 3.66027441566408 24 182.5 184.890092969064 -2.39009296906366 25 80.9 86.6044003132953 -5.70440031329531 26 83.1 84.1028982193727 -1.00289821937268 27 88.3 84.710934500249 3.58906549975099 28 86.6 85.472508300601 1.12749169939896 29 93 87.8587362932187 5.14126370678134 30 105.3 102.582863709458 2.71713629054153 31 93.8 86.4257536590125 7.37424634098748 32 86.4 85.3550898410494 1.0449101589506 33 87 81.0775597664341 5.92244023356587 34 96.7 91.5842967860673 5.1157032139327 35 100.5 103.381845750047 -2.88184575004691 36 196.7 184.384060613859 12.3159393861415 37 86.8 82.861600028094 3.93839997190599 38 88.2 85.1639160226102 3.03608397738985 39 93.8 90.2886176912111 3.51138230878888 40 85 89.1070000115617 -4.10700001156169 41 90.4 95.0274568479773 -4.62745684797727 42 115.9 107.609946111073 8.29005388892676 43 94.9 95.5695471684893 -0.669547168489245 44 87.7 88.5650001443302 -0.865000144330168 45 91.7 88.4803792008795 3.21962079912046 46 95.9 98.4804238591472 -2.58042385914717 47 106.8 103.141375001151 3.65862499884895 48 204.5 200.181269651242 4.31873034875846 49 90.2 88.4119743213472 1.78802567865283 50 90.5 89.9044717261315 0.595528273868482 51 93.2 95.469114356397 -2.26911435639711 52 97.8 87.2612504706403 10.5387495293597 53 99.4 93.769505363464 5.63049463653603 54 120 119.055160857917 0.94483914208287 55 108.2 98.3339436156351 9.86605638436485 56 98.5 91.5929633324995 6.90703666750055 57 104.3 95.8139715918619 8.48602840813813 58 102.9 101.597992385277 1.30200761472348 59 111.1 112.718341323270 -1.61834132327026 60 188.1 216.162802775936 -28.0628027759363 61 93.8 94.7348742910747 -0.934874291074749 62 94.5 95.2053216060283 -0.705321606028292 63 112.4 98.5187844076512 13.8812155923488 64 102.5 102.556522899516 -0.0565228995160396 65 115.8 104.507939147132 11.2920608528676 66 136.5 127.592138289870 8.90786171012984 67 122.1 114.279153641927 7.82084635807337 68 110.6 104.375022658568 6.22497734143208 69 116.4 110.437212905893 5.96278709410657 70 112.6 110.006025498868 2.59397450113164 71 121.5 119.478867841494 2.02113215850621 72 199.3 206.569975262126 -7.2699752621262 73 102.1 101.896350488685 0.203649511315049 74 100.6 102.917299765070 -2.31729976507039 75 119 120.258732181516 -1.25873218151563 76 106.8 110.923395793423 -4.12339579342331 77 121.3 123.456787301719 -2.15678730171933 78 145.5 145.322284563383 0.177715436617405 79 129.7 129.561281797695 0.138718202305370 80 117.7 117.050044679731 0.649955320269257 81 121.3 122.869961720829 -1.56996172082857 82 124.3 118.822535207939 5.47746479206111 83 135.2 128.404205451201 6.7957945487993 84 210.1 212.482950264386 -2.38295026438641 85 106.8 108.388470443026 -1.58847044302576 86 110.5 107.025154845271 3.47484515472908 87 111.5 126.743431486855 -15.2434314868553 88 122.1 113.433724751907 8.66627524809331 89 126.3 129.244089618442 -2.94408961844211 90 143.2 154.561506283968 -11.3615062839677 91 137.3 137.159577712452 0.140422287548063 92 121.5 124.331045370537 -2.83104537053738 93 121.9 128.184714245078 -6.2847142450776 94 123.9 129.950505473243 -6.05050547324274 95 131.6 140.341352628503 -8.74135262850268 96 220.9 218.230291236717 2.66970876328344 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 110.937461598575 100.093192696182 121.781730500967 98 113.948107193902 103.080285419281 124.815928968524 99 117.172597960547 106.275431725216 128.069764195877 100 125.422001563343 114.481454771639 136.362548355047 101 130.740301880711 119.750622152608 141.729981608815 102 149.318877821006 138.227934500818 160.409821141194 103 142.047444371941 130.927641558720 153.167247185163 104 125.987281168629 114.878706054167 137.095856283091 105 126.925928324180 115.756420840829 138.095435807532 106 129.220367716602 117.974692796636 140.466042636567 107 137.861879301625 126.483067256692 149.240691346559 108 229.713370985837 185.529030909053 273.897711062621

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/1nhdf1263684155.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/1nhdf1263684155.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/27t8h1263684155.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/27t8h1263684155.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/3423l1263684155.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263684218ba3wy94ozpew4dz/3423l1263684155.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=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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