Exponentional Smoothing Lederen Laarzen - Christine Van Bergen

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 31 May 2008 14:19:36 -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/31/t1212265545d3ku7xfnhilngm9.htm/, Retrieved Sat, 31 May 2008 20:25:46 +0000

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Dataseries X:

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101,22 101,25 101,25 101,26 101,26 101,26 101,29 101,31 101,31 101,31 101,32 101,34 101,34 101,34 101,34 101,34 101,34 101,34 101,34 101,39 102,16 102,19 102,31 102,32 102,32 102,32 102,36 102,36 102,37 102,37 102,37 102,37 103,45 103,8 103,81 103,81 103,81 103,84 103,9 103,91 103,92 103,92 103,93 104 104,51 105 105,01 105,01 105,01 105,01 105,13 105,14 105,15 105,22 105,23 105,23 105,57 106,05 106,09 106,09 106,19 106,2 106,2 106,22 106,22 106,23 106,23 106,61 106,95 107,74 107,8 107,8

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.564996882250498 beta 0.0602692712103975 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 101.34 101.055322222222 0.284677777777773 14 101.34 101.285402859038 0.0545971409617465 15 101.34 101.354014459186 -0.0140144591858444 16 101.34 101.350050166162 -0.0100501661623724 17 101.34 101.342150125245 -0.00215012524522251 18 101.34 101.334473700191 0.00552629980882102 19 101.34 101.331739279313 0.00826072068720407 20 101.39 101.380831091356 0.00916890864405673 21 102.16 102.149081579318 0.0109184206817048 22 102.19 102.177025662979 0.0129743370205802 23 102.31 102.296156467775 0.0138435322246977 24 102.32 102.305833097757 0.014166902243403 25 102.32 102.315010562329 0.00498943767085791 26 102.32 102.290667839546 0.0293321604544445 27 102.36 102.317983697548 0.0420163024515574 28 102.36 102.352134199747 0.00786580025264527 29 102.37 102.363136349787 0.006863650212793 30 102.37 102.369542068591 0.000457931409172829 31 102.37 102.370611049142 -0.000611049141767239 32 102.37 102.420260834585 -0.0502608345845914 33 103.45 103.158846478537 0.291153521463443 34 103.8 103.358711134622 0.441288865378027 35 103.81 103.747495644399 0.0625043556006943 36 103.81 103.813742379996 -0.00374237999585603 37 103.81 103.837135309402 -0.027135309402297 38 103.84 103.832463833858 0.00753616614248642 39 103.9 103.879472937100 0.020527062899518 40 103.91 103.912385033261 -0.00238503326063721 41 103.92 103.942569017299 -0.0225690172989061 42 103.92 103.953966084705 -0.0339660847046162 43 103.93 103.958355610351 -0.0283556103509142 44 104 103.993022254074 0.00697774592559597 45 104.51 104.936703172511 -0.426703172511296 46 105 104.796085302426 0.203914697574348 47 105.01 104.877693576527 0.132306423472713 48 105.01 104.948649494638 0.0613505053624408 49 105.01 104.994949012119 0.0150509878813381 50 105.01 105.026936696687 -0.0169366966870825 51 105.13 105.062678274329 0.0673217256708938 52 105.14 105.110564310335 0.0294356896646093 53 105.15 105.149532299847 0.000467700153194528 54 105.22 105.169357218309 0.0506427816913231 55 105.23 105.227242097804 0.00275790219559724 56 105.23 105.299168409326 -0.0691684093262381 57 105.57 106.012892020798 -0.442892020798439 58 106.05 106.138614564618 -0.0886145646178278 59 106.09 106.015000026336 0.07499997366439 60 106.09 106.011965668201 0.0780343317992163 61 106.19 106.037372912807 0.152627087192570 62 106.2 106.127682508202 0.0723174917983727 63 106.2 106.248050965841 -0.0480509658406874 64 106.22 106.207888447256 0.0121115527439457 65 106.22 106.217494467209 0.00250553279082055 66 106.23 106.253393743378 -0.0233937433779658 67 106.23 106.239193728807 -0.0091937288066788 68 106.61 106.263247843612 0.346752156387566 69 106.95 107.053725855553 -0.103725855552668 70 107.74 107.541068806443 0.19893119355703 71 107.8 107.676761836326 0.123238163674145 72 107.8 107.729616741881 0.0703832581187811 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 107.810203582369 107.551132399128 108.069274765611 74 107.801201522479 107.499201909271 108.103201135686 75 107.847744714236 107.504079577628 108.191409850844 76 107.881932499667 107.497251582135 108.266613417200 77 107.901135234431 107.475717246965 108.326553221896 78 107.944885661203 107.478769211744 108.411002110663 79 107.971409726603 107.464470577782 108.478348875424 80 108.177138541015 107.629138191005 108.725138891025 81 108.585578440489 107.996196183743 109.174960697236 82 109.276550118507 108.645405020626 109.907695216387 83 109.273514127294 108.600180551164 109.946847703424 84 109.236144493104 108.520163343796 109.952125642412

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/1s2ag1212265167.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/1s2ag1212265167.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/2xyjn1212265167.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/2xyjn1212265167.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/3ekeh1212265167.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212265545d3ku7xfnhilngm9/3ekeh1212265167.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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