Exponential Smoothing - consumptieprijs bloemkolen

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 18 Aug 2008 07:43:58 -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/18/t1219067142842pcqje0634ng2.htm/, Retrieved Mon, 18 Aug 2008 13:45:46 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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100,58 118,48 79,58 81,97 127,13 120,76 120,26 74,9 67,59 87,73 102,87 144,94 110,48 96,34 100,43 90,88 128,28 101,21 73,76 73,64 66,4 57,34 113,59 123,53 102,87 102,99 95,8 98,43 102,65 129,55 100,37 101,93 101,94 93,87 100,91 92,64 101,67 88,67 129,86 98,07 166,45 176,52 82,07 92,18 95,02 84,69 103,01 107,9 204,13 101,99 119,23 95,65 160,95 111,06 150,41 94,79 160,34 104,08 101,07 111,5 136,9 141,71 153,98 134,27 124,71 72,89 101,2 73,28 174,05 111,9 97,06 105,23 109,13 84,04 118,82 90,84 144,28 110,16 86,09 59,87 108,97 94,93 87,36 143,52 108,7 121,13 210,25 110,2 161,46 99,41 132,72 174,29 69,93 83,43 127,53 187,58

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.069731525720716 beta 0 gamma 0.163517945829889 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 110.48 111.736474939613 -1.25647493961348 14 96.34 99.4988590250444 -3.15885902504442 15 100.43 103.470670299025 -3.04067029902475 16 90.88 95.0244730531934 -4.14447305319345 17 128.28 132.955055957219 -4.67505595721923 18 101.21 106.004473839159 -4.7944738391593 19 73.76 79.4293145299933 -5.66931452999331 20 73.64 78.9539845780263 -5.31398457802625 21 66.4 71.2592656590775 -4.85926565907747 22 57.34 61.738754984121 -4.39875498412105 23 113.59 118.43535642114 -4.84535642114002 24 123.53 127.924565658567 -4.39456565856659 25 102.87 108.020329796908 -5.15032979690821 26 102.99 95.2218071646726 7.7681928353274 27 95.8 99.973556784294 -4.17355678429402 28 98.43 91.2804560281997 7.14954397180034 29 102.65 129.917878039412 -27.2678780394124 30 129.55 101.373698645658 28.1763013543415 31 100.37 76.9645648871014 23.4054351128986 32 101.93 78.5707128129637 23.3592871870363 33 101.94 72.9445947182304 28.9954052817696 34 93.87 65.8548727537672 28.0151272462328 35 100.91 124.743808612160 -23.8338086121603 36 92.64 132.977496410041 -40.3374964100406 37 101.67 110.451941640415 -8.78194164041494 38 88.67 99.3652898654362 -10.6952898654362 39 129.86 101.01302637738 28.84697362262 40 98.07 96.3449177386338 1.72508226136623 41 166.45 129.368657303585 37.0813426964152 42 176.52 113.745571310364 62.774428689636 43 82.07 91.0232946249226 -8.95329462492265 44 92.18 90.3659991368132 1.81400086318679 45 95.02 84.0948367838307 10.9251632161693 46 84.69 75.595933698266 9.094066301734 47 103.01 125.278443640579 -22.268443640579 48 107.9 131.110818519944 -23.2108185199436 49 204.13 114.57962496119 89.55037503881 50 101.99 110.058785561811 -8.06878556181142 51 119.23 117.904666965965 1.3253330340346 52 95.65 107.191769832729 -11.5417698327285 53 160.95 144.668629975369 16.2813700246313 54 111.06 131.503449087175 -20.4434490871753 55 150.41 92.0673578668811 58.3426421331189 56 94.79 97.7405842294255 -2.95058422942544 57 160.34 92.523129925277 67.816870074723 58 104.08 87.7128339723569 16.3671660276431 59 101.07 133.131781552008 -32.0617815520083 60 111.5 138.137902126149 -26.6379021261493 61 136.9 138.520468284303 -1.62046828430348 62 141.71 112.792750670209 28.9172493297908 63 153.98 124.646716610305 29.3332833896947 64 134.27 113.929569643710 20.3404303562896 65 124.71 157.861957583486 -33.1519575834864 66 72.89 135.663297813462 -62.7732978134621 67 101.2 105.260074406501 -4.06007440650085 68 73.28 97.258208845431 -23.9782088454310 69 174.05 101.339299257699 72.7107007423006 70 111.9 89.0439554982013 22.8560445017987 71 97.06 127.548584540667 -30.4885845406669 72 105.23 133.489463161537 -28.2594631615372 73 109.13 137.564497103394 -28.4344971033939 74 84.04 114.612259280672 -30.5722592806718 75 118.82 122.381216287461 -3.56121628746060 76 90.84 108.002332525738 -17.1623325257381 77 144.28 141.182569439872 3.09743056012823 78 110.16 117.005767166331 -6.84576716633123 79 86.09 99.4336524196254 -13.3436524196254 80 59.87 87.7545700279856 -27.8845700279856 81 108.97 106.271154441870 2.69884555813042 82 94.93 81.5101067543454 13.4198932456546 83 87.36 111.242188853492 -23.8821888534922 84 143.52 117.982825638877 25.5371743611229 85 108.7 125.782555802500 -17.0825558025005 86 121.13 103.296719211739 17.8332807882614 87 210.25 118.549869121877 91.700130878123 88 110.2 108.744762619189 1.45523738081117 89 161.46 146.30505690287 15.1549430971299 90 99.41 121.456527986439 -22.0465279864389 91 132.72 101.836011346675 30.8839886533248 92 174.29 91.0290895851693 83.2609104148306 93 69.93 121.948232232915 -52.0182322329146 94 83.43 95.002517722281 -11.5725177222810 95 127.53 117.317612647034 10.2123873529658 96 187.58 133.953171842144 53.6268281578561 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 137.228511023162 78.1162289645769 196.340793081748 98 121.245110194523 61.9892861046106 180.500934284435 99 146.491017708402 87.091998465864 205.890036950940 100 116.563865953365 57.0219959342246 176.105735972506 101 156.106623131848 96.4222442394018 215.791002024294 102 124.542393188877 64.715844883146 184.368941494607 103 114.510771349291 54.5423906759837 174.479152022599 104 109.517608293969 49.407729912961 169.627486674977 105 114.052774029139 53.8017302424929 174.303817815786 106 96.8867939425292 36.4949147220477 157.278673163011 107 123.322681872764 62.7902948871007 183.855068858427 108 145.850128993381 85.1775596347089 206.522698352053

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/1mdk31219067036.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/1mdk31219067036.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/2ifq21219067036.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/2ifq21219067036.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/3hr691219067036.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219067142842pcqje0634ng2/3hr691219067036.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=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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