Exponential Smoothing - Ruwe aardolie - Kempenaers Katrijn

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 04:02:10 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t12442826183co41senuus5o6c.htm/, Retrieved Sat, 06 Jun 2009 12:03:38 +0200

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/Jun/06/t12442826183co41senuus5o6c.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 «

88.6 95 96.3 83.3 96.9 103.4 99.3 103.8 113.4 111.5 114.2 90.6 90.8 96.4 90 92.1 97.2 95.1 88.5 91 90.5 75 66.3 66 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 94.7 101.8 102.5 105.3 110.3 109.8 117.3 118.8 131.3 125.9 133.1 147 145.8 164.4 149.8 137.7 151.7 156.8 180 180.4 170.4 191.6 199.5 218.2 217.5 205 194 199.3 219.3 211.1 215.2 240.2 242.2 240.7 255.4 253 218.2 203.7 205.6 215.6 188.5 202.9 214 230.3 230 241 259.6 247.8 270.3 289.7 322.7 315 320.2 329.5 360.6 382.2 435.4 464 468.8 403 351.6 252 188 146.5 152.9

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 96.3 95 1.30000000000000 4 83.3 96.3 -13 5 96.9 83.3 13.6 6 103.4 96.9 6.5 7 99.3 103.4 -4.10000000000001 8 103.8 99.3 4.5 9 113.4 103.8 9.6 10 111.5 113.4 -1.90000000000001 11 114.2 111.5 2.70000000000000 12 90.6 114.2 -23.6 13 90.8 90.6 0.200000000000003 14 96.4 90.8 5.60000000000001 15 90 96.4 -6.4 16 92.1 90 2.09999999999999 17 97.2 92.1 5.10000000000001 18 95.1 97.2 -2.10000000000001 19 88.5 95.1 -6.6 20 91 88.5 2.5 21 90.5 91 -0.5 22 75 90.5 -15.5 23 66.3 75 -8.7 24 66 66.3 -0.299999999999997 25 68.4 66 2.40000000000001 26 70.6 68.4 2.19999999999999 27 83.9 70.6 13.3 28 90.1 83.9 6.19999999999999 29 90.6 90.1 0.5 30 87.1 90.6 -3.5 31 90.8 87.1 3.7 32 94.1 90.8 3.3 33 99.8 94.1 5.7 34 96.8 99.8 -3 35 87 96.8 -9.8 36 96.3 87 9.3 37 107.1 96.3 10.8 38 115.2 107.1 8.10000000000001 39 106.1 115.2 -9.1 40 89.5 106.1 -16.6 41 91.3 89.5 1.80000000000000 42 97.6 91.3 6.3 43 100.7 97.6 3.10000000000001 44 104.6 100.7 3.89999999999999 45 94.7 104.6 -9.9 46 101.8 94.7 7.1 47 102.5 101.8 0.700000000000003 48 105.3 102.5 2.80000000000000 49 110.3 105.3 5 50 109.8 110.3 -0.5 51 117.3 109.8 7.5 52 118.8 117.3 1.5 53 131.3 118.8 12.5000000000000 54 125.9 131.3 -5.40000000000001 55 133.1 125.9 7.19999999999999 56 147 133.1 13.9 57 145.8 147 -1.19999999999999 58 164.4 145.8 18.6 59 149.8 164.4 -14.6 60 137.7 149.8 -12.1000000000000 61 151.7 137.7 14 62 156.8 151.7 5.10000000000002 63 180 156.8 23.2 64 180.4 180 0.400000000000006 65 170.4 180.4 -10 66 191.6 170.4 21.2 67 199.5 191.6 7.9 68 218.2 199.5 18.7 69 217.5 218.2 -0.699999999999989 70 205 217.5 -12.5 71 194 205 -11 72 199.3 194 5.30000000000001 73 219.3 199.3 20 74 211.1 219.3 -8.20000000000002 75 215.2 211.1 4.09999999999999 76 240.2 215.2 25 77 242.2 240.2 2 78 240.7 242.2 -1.5 79 255.4 240.7 14.7000000000000 80 253 255.4 -2.40000000000001 81 218.2 253 -34.8 82 203.7 218.2 -14.5 83 205.6 203.7 1.90000000000001 84 215.6 205.6 10 85 188.5 215.6 -27.1 86 202.9 188.5 14.4 87 214 202.9 11.1 88 230.3 214 16.3 89 230 230.3 -0.300000000000011 90 241 230 11 91 259.6 241 18.6000000000000 92 247.8 259.6 -11.8 93 270.3 247.8 22.5 94 289.7 270.3 19.4000000000000 95 322.7 289.7 33 96 315 322.7 -7.69999999999999 97 320.2 315 5.19999999999999 98 329.5 320.2 9.30000000000001 99 360.6 329.5 31.1 100 382.2 360.6 21.6000000000000 101 435.4 382.2 53.2 102 464 435.4 28.6 103 468.8 464 4.80000000000001 104 403 468.8 -65.8 105 351.6 403 -51.4 106 252 351.6 -99.6 107 188 252 -64 108 146.5 188 -41.5 109 152.9 146.5 6.4 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 152.9 114.429793770068 191.370206229933 111 152.9 98.4949126023395 207.305087397660 112 152.9 86.2676482321042 219.532351767896 113 152.9 75.959587540135 229.840412459865 114 152.9 66.878003761435 238.921996238565 115 152.9 58.6676244370268 247.132375562973 116 152.9 51.1174014302309 254.682598569769 117 152.9 44.089825204679 261.710174795321 118 152.9 37.4893813102025 268.310618689798 119 152.9 31.246526257014 274.553473742986 120 152.9 25.3087603277211 280.491239672279 121 152.9 19.6352964642083 286.164703535792

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/1hga21244282525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/1hga21244282525.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/2ejny1244282525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/2ejny1244282525.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/3nqys1244282525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442826183co41senuus5o6c/3nqys1244282525.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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