Plantaardige stoffen - Joyce Pauwels - Exponential Smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 31 May 2008 08:16:17 -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/May/31/t1212243501fq7bhj3nw1axgeg.htm/, Retrieved Sat, 31 May 2008 14:18:21 +0000

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Dataseries X:

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79,2 81,5 81,5 82 85,8 88,2 88 88,8 89 90,4 90,9 94,6 97,9 101,7 102,3 103,5 103,6 102,3 101,6 104,3 110,8 112,1 111,1 114,4 115 115,3 114,1 114,8 114,5 114,1 112,3 113 112,2 113,7 113,6 115,8 117,9 120,1 118,8 114,7 110,9 112,9 113,3 114,3 116,5 114,3 115,9 120,1 122,6 122,4 123,1 127,9 130,9 135 134,9 130,2 130,8 132,6 138,6 146,2 149,3 149,9 156,8 158,8 156,7 159,9 158,2 157,5 159,1 160,6 161,6 161,3

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.082827106149464 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 81.5 83.8 -2.30000000000000 4 82 83.6094976558562 -1.60949765585623 5 85.8 83.9761876226673 1.82381237733269 6 88.2 87.9272487240413 0.272751275958655 7 88 90.3498399229276 -2.34983992292759 8 88.8 89.955209482197 -1.15520948219701 9 89 90.6595268237902 -1.65952682379020 10 90.4 90.7220730193983 -0.322073019398246 11 90.9 92.0953966432327 -1.19539664323268 12 94.6 92.496385398573 2.10361460142705 13 97.9 96.3706217084629 1.52937829153711 14 101.7 99.7972956865587 1.90270431344128 15 102.3 103.754891178699 -1.45489117869917 16 103.5 104.234386752605 -0.734386752605133 17 103.6 105.373559623092 -1.77355962309235 18 102.3 105.326660811928 -3.02666081192807 19 101.6 103.77597125558 -2.17597125558009 20 104.3 102.895741853416 1.40425814658403 21 110.8 105.712052491984 5.08794750801566 22 112.1 112.633472460314 -0.533472460313646 23 111.1 113.889286480215 -2.78928648021544 24 114.4 112.658257952837 1.74174204716265 25 115 116.102521406263 -1.10252140626270 26 115.3 116.611202748714 -1.31120274871412 27 114.1 116.802599619463 -2.7025996194629 28 114.8 115.378751113902 -0.578751113902143 29 114.5 116.030814833957 -1.53081483395685 30 114.1 115.604021871210 -1.50402187120955 31 112.3 115.079448092032 -2.77944809203174 32 113 113.049234449876 -0.0492344498761099 33 112.2 113.74515650287 -1.54515650287001 34 113.7 112.817175661189 0.882824338810735 35 113.6 114.390297446411 -0.790297446411273 36 115.8 114.224839395928 1.57516060407229 37 117.9 116.555305390484 1.34469460951635 38 120.1 118.766682553645 1.33331744635531 39 118.8 121.077117379305 -2.27711737930488 40 114.7 119.588510336414 -4.88851033641441 41 110.9 115.083609171867 -4.18360917186746 42 112.9 110.937092930901 1.96290706909868 43 113.3 113.099674843075 0.200325156924890 44 114.3 113.516267196112 0.783732803887872 45 116.5 114.581181516253 1.91881848374744 46 114.3 116.940111698487 -2.64011169848747 47 115.9 114.521438886590 1.37856111340960 48 120.1 116.235621114264 3.86437888573569 49 122.6 120.755696434435 1.84430356556513 50 122.4 123.408454761632 -1.00845476163177 51 123.1 123.124927372043 -0.0249273720431802 52 127.9 123.822862709953 4.07713729004709 53 130.9 128.960560193062 1.93943980693842 54 135 132.121198379821 2.87880162017862 55 134.9 136.459641187199 -1.55964118719916 56 130.2 136.230460621032 -6.03046062103195 57 130.8 131.030975019044 -0.230975019043541 58 132.6 131.611844026623 0.98815597337662 59 138.6 133.493690126322 5.10630987367753 60 146.2 139.916630996262 6.28336900373839 61 149.3 148.037064267710 1.26293573228952 62 149.9 151.241669579669 -1.34166957966880 63 156.8 151.730542970976 5.06945702902394 64 158.8 159.050431426439 -0.250431426439178 65 156.7 161.029688916098 -4.32968891609835 66 159.9 158.571073312650 1.32892668734951 67 158.2 161.881144464448 -3.68114446444847 68 157.5 159.87624592114 -2.37624592114005 69 159.1 158.979428347993 0.120571652007413 70 160.6 160.589414949012 0.0105850509879986 71 161.6 162.090291678154 -0.490291678153795 72 161.3 163.049682237283 -1.74968223728311 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 162.604761120888 157.818930998132 167.390591243644 74 163.909522241776 156.855470759495 170.963573724056 75 165.214283362664 156.220914841431 174.207651883896 76 166.519044483551 155.721751517148 177.316337449955 77 167.823805604439 155.286801307082 180.360809901797 78 169.128566725327 154.881470118865 183.375663331790 79 170.433327846215 154.486364166741 186.380291525689 80 171.738088967103 154.089621506724 189.386556427482 81 173.042850087991 153.683555644829 192.402144531153 82 174.347611208879 153.262983068650 195.432239349107 83 175.652372329766 152.824309524734 198.480435134799 84 176.957133450654 152.36499518454 201.549271716769

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/1aqmd1212243371.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/1aqmd1212243371.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/2mk5p1212243371.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/2mk5p1212243371.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/3s0ct1212243371.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212243501fq7bhj3nw1axgeg/3s0ct1212243371.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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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