raf mattheussen smoothing eigen reeks

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 11:07:05 -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/Jun/01/t1212340062p87uuc6a25dt5gn.htm/, Retrieved Sun, 01 Jun 2008 17:07:45 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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14,32 14,67 14,8 14,8 14,8 14,8 14,8 14,8 14,8 14,8 14,8 14,8 14,8 15,56 15,56 15,56 15,56 15,56 15,56 15,56 15,56 15,56 15,56 15,56 15,56 16,8 16,8 16,8 16,8 16,8 16,8 16,8 16,8 16,8 16,8 16,8 16,8 17,43 17,43 17,43 17,43 17,43 17,43 17,43 17,43 17,43 17,43 17,43 17,43 18,61 18,61 18,61 18,61 18,61 18,61 18,61 18,61 18,61 18,61 18,61 18,61 20 20 20 20 20 20 20 20 20 20 20 20 20,61 20,61 20,61 20,61 20,61 20,61 20,61 20,61 20,61 20,61 20,61 20,61 19,47 19,47 19,47 19,47 19,47

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 14.8 14.67 0.130000000000001 4 14.8 14.8 0 5 14.8 14.8 0 6 14.8 14.8 0 7 14.8 14.8 0 8 14.8 14.8 0 9 14.8 14.8 0 10 14.8 14.8 0 11 14.8 14.8 0 12 14.8 14.8 0 13 14.8 14.8 0 14 15.56 14.8 0.76 15 15.56 15.56 0 16 15.56 15.56 0 17 15.56 15.56 0 18 15.56 15.56 0 19 15.56 15.56 0 20 15.56 15.56 0 21 15.56 15.56 0 22 15.56 15.56 0 23 15.56 15.56 0 24 15.56 15.56 0 25 15.56 15.56 0 26 16.8 15.56 1.24 27 16.8 16.8 0 28 16.8 16.8 0 29 16.8 16.8 0 30 16.8 16.8 0 31 16.8 16.8 0 32 16.8 16.8 0 33 16.8 16.8 0 34 16.8 16.8 0 35 16.8 16.8 0 36 16.8 16.8 0 37 16.8 16.8 0 38 17.43 16.8 0.629999999999999 39 17.43 17.43 0 40 17.43 17.43 0 41 17.43 17.43 0 42 17.43 17.43 0 43 17.43 17.43 0 44 17.43 17.43 0 45 17.43 17.43 0 46 17.43 17.43 0 47 17.43 17.43 0 48 17.43 17.43 0 49 17.43 17.43 0 50 18.61 17.43 1.18 51 18.61 18.61 0 52 18.61 18.61 0 53 18.61 18.61 0 54 18.61 18.61 0 55 18.61 18.61 0 56 18.61 18.61 0 57 18.61 18.61 0 58 18.61 18.61 0 59 18.61 18.61 0 60 18.61 18.61 0 61 18.61 18.61 0 62 20 18.61 1.39 63 20 20 0 64 20 20 0 65 20 20 0 66 20 20 0 67 20 20 0 68 20 20 0 69 20 20 0 70 20 20 0 71 20 20 0 72 20 20 0 73 20 20 0 74 20.61 20 0.61 75 20.61 20.61 0 76 20.61 20.61 0 77 20.61 20.61 0 78 20.61 20.61 0 79 20.61 20.61 0 80 20.61 20.61 0 81 20.61 20.61 0 82 20.61 20.61 0 83 20.61 20.61 0 84 20.61 20.61 0 85 20.61 20.61 0 86 19.47 20.61 -1.14 87 19.47 19.47 0 88 19.47 19.47 0 89 19.47 19.47 0 90 19.47 19.47 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 91 19.47 18.9036852124955 20.0363147875045 92 19.47 18.6691099469387 20.2708900530613 93 19.47 18.4891140149647 20.4508859850353 94 19.47 18.3373704249910 20.6026295750090 95 19.47 18.2036816384766 20.7363183615234 96 19.47 18.0828177368213 20.8571822631787 97 19.47 17.9716719084847 20.9683280915153 98 19.47 17.8682198938774 21.0717801061226 99 19.47 17.7710556374865 21.1689443625135 100 19.47 17.6791553988516 21.2608446011484 101 19.47 17.5917463366178 21.3482536633822 102 19.47 17.5082280299293 21.4317719700707

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/1ymxc1212340019.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/1ymxc1212340019.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/2jji61212340019.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/2jji61212340019.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/3qr1w1212340019.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212340062p87uuc6a25dt5gn/3qr1w1212340019.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')

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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