Robin Van Wijnsberghe - Exponential smoothing eigen reeks - 2mar 03

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 16:25:16 -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/t1212013627hlndt3imyb7djxs.htm/, Retrieved Thu, 29 May 2008 00:27:07 +0200

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Dataseries X:

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1,61 1,6 1,59 1,6 1,6 1,59 1,59 1,58 1,59 1,59 1,58 1,58 1,58 1,57 1,57 1,57 1,57 1,58 1,58 1,57 1,58 1,57 1,57 1,57 1,57 1,57 1,57 1,59 1,6 1,6 1,6 1,6 1,61 1,61 1,62 1,62 1,62 1,62 1,62 1,62 1,61 1,59 1,58 1,56 1,56 1,54 1,55 1,56 1,57 1,58 1,59 1,6 1,6 1,61 1,61 1,62 1,61 1,6 1,6 1,6 1,61 1,62 1,63 1,63 1,66 1,66 1,66 1,65 1,65 1,64 1,64 1,65 1,64

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 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 2 1.6 1.61 -0.01 3 1.59 1.6 -0.01 4 1.6 1.59 0.01 5 1.6 1.6 0 6 1.59 1.6 -0.01 7 1.59 1.59 0 8 1.58 1.59 -0.01 9 1.59 1.58 0.01 10 1.59 1.59 0 11 1.58 1.59 -0.01 12 1.58 1.58 0 13 1.58 1.58 0 14 1.57 1.58 -0.01 15 1.57 1.57 0 16 1.57 1.57 0 17 1.57 1.57 0 18 1.58 1.57 0.01 19 1.58 1.58 0 20 1.57 1.58 -0.01 21 1.58 1.57 0.01 22 1.57 1.58 -0.01 23 1.57 1.57 0 24 1.57 1.57 0 25 1.57 1.57 0 26 1.57 1.57 0 27 1.57 1.57 0 28 1.59 1.57 0.02 29 1.6 1.59 0.01 30 1.6 1.6 0 31 1.6 1.6 0 32 1.6 1.6 0 33 1.61 1.6 0.01 34 1.61 1.61 0 35 1.62 1.61 0.01 36 1.62 1.62 0 37 1.62 1.62 0 38 1.62 1.62 0 39 1.62 1.62 0 40 1.62 1.62 0 41 1.61 1.62 -0.01 42 1.59 1.61 -0.02 43 1.58 1.59 -0.01 44 1.56 1.58 -0.02 45 1.56 1.56 0 46 1.54 1.56 -0.02 47 1.55 1.54 0.01 48 1.56 1.55 0.01 49 1.57 1.56 0.01 50 1.58 1.57 0.01 51 1.59 1.58 0.01 52 1.6 1.59 0.01 53 1.6 1.6 0 54 1.61 1.6 0.01 55 1.61 1.61 0 56 1.62 1.61 0.01 57 1.61 1.62 -0.01 58 1.6 1.61 -0.01 59 1.6 1.6 0 60 1.6 1.6 0 61 1.61 1.6 0.01 62 1.62 1.61 0.01 63 1.63 1.62 0.00999999999999979 64 1.63 1.63 0 65 1.66 1.63 0.03 66 1.66 1.66 0 67 1.66 1.66 0 68 1.65 1.66 -0.01 69 1.65 1.65 0 70 1.64 1.65 -0.01 71 1.64 1.64 0 72 1.65 1.64 0.01 73 1.64 1.65 -0.01 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.64 1.62215221290127 1.65784778709873 75 1.64 1.61475941742663 1.66524058257337 76 1.64 1.60908672594232 1.67091327405768 77 1.64 1.60430442580254 1.67569557419746 78 1.64 1.60009113479929 1.67990886520071 79 1.64 1.59628202857028 1.68371797142972 80 1.64 1.59277919388393 1.68722080611607 81 1.64 1.58951883485325 1.69048116514675 82 1.64 1.58645663870381 1.69354336129619 83 1.64 1.58356034157424 1.69643965842576 84 1.64 1.58080558685536 1.69919441314464 85 1.64 1.57817345188465 1.70182654811535

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/1rnsj1212013510.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/1rnsj1212013510.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/2sqir1212013510.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/2sqir1212013510.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/3lwg31212013510.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212013627hlndt3imyb7djxs/3lwg31212013510.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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