tijdreeks - evolutie graan - marie-laure van thielen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 Jan 2009 14:26:35 -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/Jan/26/t1233005240sj05g0f4uaequ1g.htm/, Retrieved Mon, 26 Jan 2009 22:27:20 +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/Jan/26/t1233005240sj05g0f4uaequ1g.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:

» Textbox « » Textfile « » CSV «

273,9 284,7 314,1 333,2 315,1 321 310,9 289 259,3 244,7 215,9 215,3 211,4 184,6 177,7 184,8 172,3 169,6 180,3 180,9 175,8 175 170,4 159,3 139,9 134,5 143 137,3 140,3 131,3 127,8 126,5 119,2 116 110,8 115,4 115,1 114,1 119,1 114 112,1 111,2 116 109,5 109,5 110,2 108,8 108,2 111,4 110,8 117,2 130,7 137,4 141,4 137,1 129,8 127,3 121,7 117,6 111,2 113 111,1 103,7 110,8 115,3 111,4 112,5 115,5 114,9 119,9 125,6 131,8 134,2 124,5 114,4 103,8 98,5 97 98,1 99 99,7 98,6 97,4 97,8 100,3 101,2 100,7 96,3 98,4 99,5 101,4 101,1 104,7 102,3 100,8 98,5

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.425593260268888 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 314.1 295.5 18.6000000000000 4 333.2 332.816034641001 0.383965358998637 5 315.1 352.079447709968 -36.9794477099678 6 321 318.24124399614 2.75875600386019 7 310.9 325.315351958109 -14.4153519581091 8 289 309.080275320334 -20.0802753203339 9 259.3 278.634245479656 -19.3342454796561 10 244.7 240.705720911130 3.99427908886972 11 215.9 227.805659170986 -11.9056591709862 12 215.3 193.938690868756 21.361309131244 13 211.4 202.429920065534 8.9700799344663 14 184.6 202.347525629716 -17.7475256297157 15 177.7 167.994298335259 9.70570166474062 16 184.8 165.224979549954 19.5750204500465 17 172.3 180.655976323119 -8.35597632311897 18 169.6 164.599729117033 5.00027088296687 19 180.3 164.027810704343 16.2721892956574 20 180.9 181.653144798394 -0.753144798393919 21 175.8 181.932611448191 -6.13261144819089 22 175 174.222613347993 0.777386652006953 23 170.4 173.753463867710 -3.35346386771019 24 159.3 167.726252247058 -8.4262522470575 25 139.9 153.040096081384 -13.1400960813843 26 134.5 128.047759749861 6.45224025013852 27 143 125.393789713956 17.6062102860439 28 137.3 141.386874150573 -4.08687415057312 29 140.3 133.947528056522 6.35247194347792 30 131.3 139.651097301713 -8.35109730171348 31 127.8 127.096926574255 0.703073425745458 32 126.5 123.896149885726 2.60385011427405 33 119.2 123.704330945111 -4.50433094511136 34 116 114.487318052851 1.51268194714862 35 110.8 111.931105294488 -1.13110529448825 36 115.4 106.249714504500 9.15028549550041 37 115.1 114.744014340921 0.355985659079252 38 114.1 114.595519438177 -0.49551943817724 39 119.1 113.384629704957 5.71537029504321 40 114 120.817052782468 -6.81705278246818 41 112.1 112.815761063352 -0.71576106335246 42 111.2 110.611137978827 0.588862021173256 43 116 109.961753686266 6.0382463137336 44 109.5 117.331590621235 -7.83159062123488 45 109.5 107.498518435652 2.00148156434771 46 110.2 108.350335499991 1.8496645000089 47 108.8 109.837540244954 -1.03754024495352 48 108.2 107.995970109444 0.204029890556441 49 111.4 107.482803855758 3.91719614424221 50 110.8 112.349936133899 -1.54993613389856 51 117.2 111.090293761464 6.10970623853591 52 130.7 120.090543558808 10.6094564411922 53 137.4 138.105856715295 -0.705856715295482 54 141.4 144.505448854550 -3.10544885455022 55 137.1 147.183790751944 -10.0837907519439 56 129.8 138.592197369955 -8.7921973699548 57 127.3 127.550297426348 -0.25029742634824 58 121.7 124.943772528632 -3.24377252863177 59 117.6 117.963244802601 -0.363244802600732 60 111.2 113.708650262786 -2.50865026278613 61 113 106.240985618573 6.7590143814274 62 111.1 110.917576585369 0.182423414631415 63 103.7 109.095214761151 -5.39521476115094 64 110.8 99.3990477211019 11.4009522788981 65 115.3 111.351216171648 3.94878382835186 66 111.4 117.531791955253 -6.13179195525346 67 112.5 111.022142625727 1.47785737427338 68 115.5 112.751108763856 2.74889123614396 69 114.9 116.921018347171 -2.02101834717111 70 119.9 115.460886559735 4.43911344026468 71 125.6 122.350143321481 3.24985667851898 72 131.8 129.433260420699 2.36673957930151 73 134.2 136.640528834461 -2.44052883446088 74 124.5 138.001856211022 -13.5018562110224 75 114.4 122.555557206492 -8.15555720649166 76 103.8 108.984607025671 -5.18460702567147 77 98.5 96.178073218403 2.32192678159704 78 97 91.8662696074885 5.13373039251151 79 98.1 92.551150662579 5.54884933742106 80 99 96.0127035428328 2.98729645716718 81 99.7 98.1840767814283 1.5159232185717 82 98.6 99.5292434863375 -0.92924348633754 83 97.4 98.0337637214035 -0.633763721403497 84 97.8 96.5640381529713 1.23596184702873 85 100.3 97.4900551850162 2.80994481498382 86 101.2 101.185948760001 0.0140512399992048 87 100.7 102.091928873043 -1.39192887304289 88 96.3 100.999533325902 -4.69953332590217 89 98.4 94.5994436159892 3.80055638401085 90 99.5 98.316934798296 1.18306520170391 91 101.4 99.9204393746 1.47956062540008 92 101.1 102.450130404929 -1.35013040492943 93 104.7 101.575524004107 3.12447599589267 94 102.3 106.505279929831 -4.20527992983119 95 100.8 102.315541134151 -1.51554113415101 96 98.5 100.170537041796 -1.67053704179607 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 97.1595677357781 80.4723783283844 113.846757143172 98 95.8191354715563 66.7608199947369 124.877450948376 99 94.4787032073344 52.0682591689816 136.889147245687 100 93.1382709431126 36.1986711439238 150.077870742301 101 91.7978386788907 19.1639758939002 164.431701463881 102 90.4574064146688 1.01356204125629 179.901250788081 103 89.116974150447 -18.1982781877222 196.432226488616 104 87.7765418862251 -38.4202878157595 213.973371588210 105 86.4361096220033 -59.6060286909149 232.478247934921 106 85.0956773577814 -81.7139084949872 251.90526321055 107 83.7552450935596 -104.706715721756 272.217205908875 108 82.4148128293377 -128.551061018514 293.380686677189

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/1pyyd1233005182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/1pyyd1233005182.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/2or891233005182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/2or891233005182.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/3xuzy1233005182.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233005240sj05g0f4uaequ1g/3xuzy1233005182.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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