exponential smoothing prijsindexcijfer ruwe aardolie_Jan De Cleermaecker

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 29 May 2008 12:48:37 -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/29/t1212086952qhywcwr7x14ti9f.htm/, Retrieved Thu, 29 May 2008 18:49:13 +0000

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Dataseries X:

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68.4 70.6 83.9 90.1 90.6 87.1 90.8 94.1 99.8 96.8 87 96.3 107.1 115.2 106.1 89.5 91.3 97.6 100.7 104.6 94.7 101.8 102.5 105.3 110.3 109.8 117.3 118.8 131.3 125.9 133.1 147 145.8 164.4 149.8 137.7 151.7 156.8 180 180.4 170.4 191.6 199.5 218.2 217.5 205 194 199.3 219.3 211.1 215.2 240.2 242.2 240.7 255.4 253 218.2 203.7 205.6 215.6 188.5 202.9 214 230.3 230 241 259.6 247.8 270.3 289.7 322.7 315 320.2

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.904548536281444 beta 0.0104657928757387 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 107.1 97.738763888889 9.36123611111108 14 115.2 114.970133585425 0.229866414575199 15 106.1 107.368912292140 -1.26891229213972 16 89.5 91.1291270188985 -1.6291270188985 17 91.3 92.0897540601084 -0.78975406010845 18 97.6 98.1354915582625 -0.535491558262478 19 100.7 101.718652429370 -1.01865242936979 20 104.6 106.255127444955 -1.6551274449546 21 94.7 96.0668777938087 -1.36687779380865 22 101.8 101.680590626565 0.119409373435005 23 102.5 101.039852767707 1.46014723229324 24 105.3 103.767366990839 1.53263300916115 25 110.3 120.339334296878 -10.0393342968784 26 109.8 119.008708675150 -9.20870867515025 27 117.3 102.495789060092 14.8042109399081 28 118.8 100.681713764846 18.1182862351543 29 131.3 119.693072005650 11.6069279943502 30 125.9 137.201955034841 -11.3019550348411 31 133.1 131.123759764665 1.9762402353349 32 147 138.460411236981 8.53958876301857 33 145.8 137.769705732189 8.03029426781109 34 164.4 152.362861069711 12.0371389302891 35 149.8 163.080462386257 -13.2804623862571 36 137.7 152.791950923431 -15.0919509234309 37 151.7 153.374884340178 -1.67488434017753 38 156.8 159.922049227953 -3.12204922795291 39 180 151.496953240031 28.5030467599689 40 180.4 162.810233960710 17.5897660392897 41 170.4 181.136758741088 -10.7367587410878 42 191.6 176.451239997898 15.1487600021016 43 199.5 196.020061344002 3.4799386559975 44 218.2 205.811235356251 12.3887646437487 45 217.5 209.057995911959 8.4420040880411 46 205 224.914232091180 -19.9142320911795 47 194 204.519397750689 -10.5193977506886 48 199.3 196.787364861647 2.51263513835281 49 219.3 214.973709713729 4.32629028627093 50 211.1 227.266436581910 -16.1664365819098 51 215.2 210.392574235294 4.80742576470561 52 240.2 199.337858353882 40.862141646118 53 242.2 236.339414812687 5.86058518731323 54 240.7 249.622780547128 -8.92278054712844 55 255.4 246.561008829541 8.83899117045928 56 253 262.357889386462 -9.35788938646249 57 218.2 245.658973146754 -27.4589731467545 58 203.7 226.096472012827 -22.3964720128266 59 205.6 204.091666305575 1.50833369442546 60 215.6 208.335675676410 7.26432432358968 61 188.5 230.890702211273 -42.3907022112734 62 202.9 198.424752019992 4.47524798000759 63 214 201.874863053131 12.1251369468687 64 230.3 200.600704914592 29.6992950854079 65 230 223.778155826445 6.22184417355459 66 241 235.594804689704 5.40519531029636 67 259.6 246.942010744540 12.6579892554604 68 247.8 264.245836377464 -16.4458363774642 69 270.3 239.130047652904 31.1699523470957 70 289.7 273.360802277718 16.3391977222819 71 322.7 289.320066023153 33.3799339768466 72 315 323.8886525337 -8.88865253370011 73 320.2 327.885715270535 -7.68571527053547 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 332.40691228315 303.392508708162 361.421315858138 75 333.618149569852 294.310067092635 372.926232047070 76 324.017921375785 276.446301416255 371.589541335314 77 318.773029229436 264.03924131819 373.506817140682 78 325.507934552910 264.324098612851 386.69177049297 79 333.231165731096 266.102687117761 400.359644344431 80 336.760388909931 264.067534979149 409.453242840713 81 331.674509827784 253.715111503978 409.633908151589 82 336.608687879156 253.622942983719 419.594432774593 83 339.574012689299 251.760004064190 427.388021314408 84 339.75732381089 247.281286679227 432.233360942553 85 351.836667044331 254.840085940485 448.833248148177

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/1dn6v1212086910.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/1dn6v1212086910.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/2bfaz1212086910.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/2bfaz1212086910.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/3agqg1212086910.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212086952qhywcwr7x14ti9f/3agqg1212086910.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')

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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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