Mattias Dierckx Opg 10 Exponential smoothing Biefstuk

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 13:44:00 -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/04/t1244144855qecivcinlfh1b0x.htm/, Retrieved Thu, 04 Jun 2009 21:47:35 +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/04/t1244144855qecivcinlfh1b0x.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:

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9,3700 9,3300 9,3100 9,2600 9,3500 9,3800 9,4300 9,2700 9,2900 9,2700 9,2900 9,3100 9,3300 9,3500 9,3400 9,4700 9,6300 9,6200 9,6300 9,5000 9,5500 9,5800 9,6100 9,5700 9,6100 9,6500 9,6200 9,6500 9,9600 10,0300 10,0300 9,7200 9,7500 9,7700 9,7800 9,8200 9,8400 9,9000 9,9400 10,1200 10,5200 10,5700 10,5700 10,1200 10,0500 10,1400 10,1700 10,2000 10,2000 10,3500 10,4300 10,5700 10,8200 10,9000 10,8300 10,6500 10,5700 10,6100 10,6300 10,6100 10,7200 10,7700 10,7900 10,9200 10,9000 11,0000 10,9900 10,9100 10,8800 10,8700 11,0000 10,9900 11,0300 11,0400 10,9900

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 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 9.31 9.33 -0.0199999999999996 4 9.26 9.31 -0.0500000000000007 5 9.35 9.26 0.0899999999999999 6 9.38 9.35 0.0300000000000011 7 9.43 9.38 0.0499999999999989 8 9.27 9.43 -0.16 9 9.29 9.27 0.0199999999999996 10 9.27 9.29 -0.0199999999999996 11 9.29 9.27 0.0199999999999996 12 9.31 9.29 0.0200000000000014 13 9.33 9.31 0.0199999999999996 14 9.35 9.33 0.0199999999999996 15 9.34 9.35 -0.00999999999999979 16 9.47 9.34 0.130000000000001 17 9.63 9.47 0.16 18 9.62 9.63 -0.0100000000000016 19 9.63 9.62 0.0100000000000016 20 9.5 9.63 -0.130000000000001 21 9.55 9.5 0.0500000000000007 22 9.58 9.55 0.0299999999999994 23 9.61 9.58 0.0299999999999994 24 9.57 9.61 -0.0399999999999991 25 9.61 9.57 0.0399999999999991 26 9.65 9.61 0.0400000000000009 27 9.62 9.65 -0.0300000000000011 28 9.65 9.62 0.0300000000000011 29 9.96 9.65 0.310000000000000 30 10.03 9.96 0.0699999999999985 31 10.03 10.03 0 32 9.72 10.03 -0.309999999999999 33 9.75 9.72 0.0299999999999994 34 9.77 9.75 0.0199999999999996 35 9.78 9.77 0.00999999999999979 36 9.82 9.78 0.0400000000000009 37 9.84 9.82 0.0199999999999996 38 9.9 9.84 0.0600000000000005 39 9.94 9.9 0.0399999999999991 40 10.12 9.94 0.180000000000000 41 10.52 10.12 0.4 42 10.57 10.52 0.0500000000000007 43 10.57 10.57 0 44 10.12 10.57 -0.450000000000001 45 10.05 10.12 -0.0699999999999985 46 10.14 10.05 0.0899999999999999 47 10.17 10.14 0.0299999999999994 48 10.2 10.17 0.0299999999999994 49 10.2 10.2 0 50 10.35 10.2 0.150000000000000 51 10.43 10.35 0.08 52 10.57 10.43 0.140000000000001 53 10.82 10.57 0.25 54 10.9 10.82 0.08 55 10.83 10.9 -0.0700000000000003 56 10.65 10.83 -0.180000000000000 57 10.57 10.65 -0.08 58 10.61 10.57 0.0399999999999991 59 10.63 10.61 0.0200000000000014 60 10.61 10.63 -0.0200000000000014 61 10.72 10.61 0.110000000000001 62 10.77 10.72 0.0499999999999989 63 10.79 10.77 0.0199999999999996 64 10.92 10.79 0.130000000000001 65 10.9 10.92 -0.0199999999999996 66 11 10.9 0.0999999999999996 67 10.99 11 -0.00999999999999979 68 10.91 10.99 -0.08 69 10.88 10.91 -0.0299999999999994 70 10.87 10.88 -0.0100000000000016 71 11 10.87 0.130000000000001 72 10.99 11 -0.00999999999999979 73 11.03 10.99 0.0399999999999991 74 11.04 11.03 0.00999999999999979 75 10.99 11.04 -0.0499999999999989 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 10.99 10.7675284921980 11.2124715078020 77 10.99 10.6753777764248 11.3046222235752 78 10.99 10.6046680452505 11.3753319547495 79 10.99 10.5450569843960 11.4349430156040 80 10.99 10.4925385854979 11.4874614145021 81 10.99 10.4450583235775 11.5349416764225 82 10.99 10.4013957165584 11.5786042834416 83 10.99 10.3607555528497 11.6192444471503 84 10.99 10.3225854765941 11.6574145234059 85 10.99 10.2864833208538 11.6935166791462 86 10.99 10.2521454820762 11.7278545179238 87 10.99 10.2193360905010 11.7606639094990

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/1qwqx1244144634.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/1qwqx1244144634.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/2ppvp1244144634.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/2ppvp1244144634.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/3ztc21244144634.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244144855qecivcinlfh1b0x/3ztc21244144634.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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