Exponential smoothing - Prijen bruin brood 800g - Vanessa Limbourg 2MAR04b

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 07:12:10 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/28/t1211980408cazh87noamks06e.htm/, Retrieved Wed, 28 May 2008 15:13:28 +0200

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Dataseries X:

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1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,44 1,47 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,57 1,58 1,58 1,58 1,58 1,59 1,6 1,6 1,6 1,6 1,61 1,61 1,62 1,63 1,63 1,63 1,63 1,63 1,64 1,64 1,64 1,65 1,65

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0106354671671956 gamma 0.0993629536350756 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.48 1.46645992889509 0.0135400711049085 14 1.48 1.47728349995693 0.00271650004307356 15 1.48 1.47773658423247 0.00226341576752653 16 1.48 1.479430945851 0.000569054148999548 17 1.48 1.48110382317720 -0.00110382317719826 18 1.48 1.48150875016871 -0.00150875016870544 19 1.48 1.48149270390582 -0.00149270390582279 20 1.48 1.48147682830244 -0.001476828302442 21 1.48 1.48146112154352 -0.00146112154351985 22 1.48 1.48144558183332 -0.00144558183331656 23 1.48 1.48143020739519 -0.00143020739519062 24 1.48 1.48141499647140 -0.00141499647139676 25 1.48 1.49190037224011 -0.0119003722401141 26 1.48 1.47709533914180 0.00290466085819596 27 1.48 1.47755089708191 0.00244910291808953 28 1.48 1.47924749224686 0.000752507753144283 29 1.48 1.48092237178651 -0.000922371786510778 30 1.48 1.48132922859833 -0.00132922859832596 31 1.48 1.48131509163121 -0.00131509163121080 32 1.48 1.48130110501735 -0.00130110501734526 33 1.48 1.48128726715765 -0.00128726715765204 34 1.48 1.48127357647006 -0.00127357647006154 35 1.48 1.48126003138933 -0.00126003138932940 36 1.48 1.48124663036686 -0.00124663036685857 37 1.48 1.49173261607148 -0.0117326160714755 38 1.48 1.47692983638352 0.00307016361647827 39 1.48 1.47738757011303 0.00261242988696830 40 1.57 1.47908612986392 0.0909138701360777 41 1.58 1.57169435524082 0.00830564475918494 42 1.58 1.58222469415746 -0.00222469415745841 43 1.58 1.58220103349579 -0.00220103349578982 44 1.58 1.58217762447631 -0.0021776244763112 45 1.59 1.58215446442269 0.00784553557730883 46 1.6 1.59223790535873 0.00776209464126731 47 1.6 1.60232045886144 -0.0023204588614385 48 1.6 1.60229577969740 -0.0022957796974048 49 1.6 1.61362854590409 -0.0136285459040941 50 1.61 1.59761285186013 0.0123871481398714 51 1.61 1.60817615126901 0.00182384873098562 52 1.62 1.61001166315846 0.00998833684153921 53 1.63 1.62192810834392 0.00807189165607691 54 1.63 1.63247003776369 -0.00247003776368926 55 1.63 1.63244376775815 -0.00244376775815169 56 1.63 1.63241777714640 -0.00241777714639579 57 1.63 1.63239206295694 -0.00239206295693761 58 1.64 1.63236662224990 0.00763337775010275 59 1.64 1.64244780678833 -0.00244780678833356 60 1.64 1.64242177321960 -0.00242177321960457 61 1.65 1.65403761006938 -0.00403761006938064 62 1.65 1.64769838697811 0.00230161302188581 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 63 1.64819395826526 1.62098787991760 1.67540003661293 64 1.64825163391080 1.60959879742104 1.68690447040056 65 1.65016535135864 1.60257195286700 1.69775874985028 66 1.65254310361332 1.59728711216743 1.70779909505922 67 1.65492085586800 1.59281089591359 1.71703081582242 68 1.65729860812269 1.58889855965275 1.72569865659262 69 1.65967636037737 1.58540556832412 1.73394715243061 70 1.66205411263205 1.58223828502739 1.74186994023671 71 1.66443186488673 1.57933203275536 1.7495316970181 72 1.66680961714141 1.57663998103245 1.75697925325038 73 1.6810188647845 1.58533967396488 1.77669805560412 74 1.67865403225998 -9.78677292997244 13.1440809944924

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/1dcys1211980324.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/1dcys1211980324.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/2rjdk1211980324.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/2rjdk1211980324.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/39mlu1211980324.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211980408cazh87noamks06e/39mlu1211980324.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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