*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 15:24:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv.htm/, Retrieved Tue, 19 Jan 2010 23:25:39 +0100

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/2010/Jan/19/t1263939934h1xfnpvnwc5amfv.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

161.88 162.05 162.16 162.61 162.53 162.53 162.53 162.53 162.83 161.61 161.79 161.79 161.79 161.79 161.85 161.77 161.86 161.89 161.89 161.89 162.18 162.43 162.58 162.57 162.57 162.57 162.44 162.79 163.15 163.23 163.23 163.23 163.38 163.71 163.73 163.73 163.73 163.73 163.93 164.27 164.57 164.73 164.73 164.76 165.75 165.86 165.99 166.13 166.13 166.13 166.15 166.45 166.48 166.51 166.51 166.51 166.58 166.82 167.35 167.5 167.5 167.6 167.72 167.29 166.98 166.98 166.98 166.98 167.63 167.83 167.85 167.87 167.87 167.96 167.7 169.25 168.79 168.77 168.77 169 168.92 169.23 169.28 169.29 169.29 170.29 170.59 171.98 172.31 172.28 172.28 172.45 172.27 172.65 172.08 172.2 172.2 172.2 172.36 172.53 173.18 173.17 173.17 173.17 173.4 174.47 174.56 174.59 174.59 175.22 175.3 175.25 175.54 175.58 175.58 175.68 176.05 176.4 176.58 176.49

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.752503278433036 beta 0.0380281280298083 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 161.79 162.070066773504 -0.280066773504331 14 161.79 161.872791520583 -0.0827915205832994 15 161.85 161.882014022659 -0.0320140226591263 16 161.77 161.727697302471 0.0423026975287542 17 161.86 161.740514704170 0.119485295829747 18 161.89 161.756498156793 0.133501843207085 19 161.89 162.237682768199 -0.347682768198950 20 161.89 161.945991657381 -0.0559916573813553 21 162.18 162.181363456848 -0.00136345684839512 22 162.43 160.9619708059 1.46802919409987 23 162.58 162.305310492733 0.274689507267198 24 162.57 162.570185414485 -0.000185414485059709 25 162.57 162.557645142323 0.0123548576772805 26 162.57 162.673035602884 -0.103035602884120 27 162.44 162.722804819364 -0.282804819364173 28 162.79 162.434196833075 0.355803166924517 29 163.15 162.747034512509 0.402965487491315 30 163.23 163.032926646595 0.197073353405301 31 163.23 163.497796453228 -0.267796453228129 32 163.23 163.395637739183 -0.165637739182699 33 163.38 163.616108228195 -0.236108228195491 34 163.71 162.631109131358 1.07889086864171 35 163.73 163.422507497087 0.307492502913021 36 163.73 163.681209043474 0.0487909565259201 37 163.73 163.747201754240 -0.0172017542402898 38 163.73 163.849520633067 -0.119520633066571 39 163.93 163.879649404472 0.050350595528073 40 164.27 164.046585901296 0.223414098703728 41 164.57 164.314474966689 0.255525033311045 42 164.73 164.477242922606 0.252757077393738 43 164.73 164.909337497808 -0.179337497807893 44 164.76 164.941936088549 -0.181936088548639 45 165.75 165.175142106944 0.574857893055906 46 165.86 165.191503788618 0.668496211382006 47 165.99 165.537064438065 0.452935561935249 48 166.13 165.899250794797 0.230749205203182 49 166.13 166.149107891066 -0.0191078910658575 50 166.13 166.287887448449 -0.157887448448946 51 166.15 166.393308361539 -0.243308361538595 52 166.45 166.43581547379 0.0141845262098172 53 166.48 166.601935870345 -0.121935870344544 54 166.51 166.516906587067 -0.00690658706668046 55 166.51 166.676159190015 -0.166159190015321 56 166.51 166.747906249489 -0.237906249488674 57 166.58 167.154571800821 -0.574571800820991 58 166.82 166.324539864892 0.495460135108402 59 167.35 166.476968913472 0.873031086527845 60 167.5 167.102738878487 0.397261121513253 61 167.5 167.423273622585 0.0767263774152411 62 167.6 167.609779414124 -0.00977941412364203 63 167.72 167.819707133685 -0.0997071336846886 64 167.29 168.052309041777 -0.762309041776575 65 166.98 167.596511520489 -0.616511520489212 66 166.98 167.149714278442 -0.169714278442115 67 166.98 167.124312579372 -0.144312579372269 68 166.98 167.172640808570 -0.192640808569678 69 167.63 167.509239146999 0.120760853001485 70 167.83 167.466368564985 0.363631435014867 71 167.85 167.608363064942 0.241636935058409 72 167.87 167.618506603400 0.251493396600239 73 167.87 167.723099275631 0.146900724369345 74 167.96 167.916089640378 0.0439103596216057 75 167.7 168.120786723988 -0.420786723988186 76 169.25 167.915219729843 1.33478027015667 77 168.79 169.10102045958 -0.311020459580106 78 168.77 169.030876376209 -0.260876376208614 79 168.77 168.976742297021 -0.206742297021179 80 169 168.997924933841 0.00207506615905118 81 168.92 169.595979589385 -0.675979589385435 82 169.23 169.028235228113 0.201764771886957 83 169.28 169.028165613955 0.251834386045488 84 169.29 169.058648342201 0.231351657798712 85 169.29 169.131847697186 0.158152302814159 86 170.29 169.317786863128 0.97221313687183 87 170.59 170.142560136861 0.447439863138641 88 171.98 171.086215307758 0.893784692242264 89 172.31 171.581597212847 0.728402787153328 90 172.28 172.384539543148 -0.104539543148036 91 172.28 172.544427747400 -0.264427747399623 92 172.45 172.655213059747 -0.20521305974691 93 172.27 173.004864152603 -0.734864152603336 94 172.65 172.683760494379 -0.0337604943787824 95 172.08 172.585822229125 -0.505822229124533 96 172.2 172.086387958819 0.113612041180943 97 172.2 172.094793491164 0.105206508835892 98 172.2 172.482775274142 -0.28277527414167 99 172.36 172.237779988784 0.122220011215518 100 172.53 173.04236245027 -0.512362450269876 101 173.18 172.393631238984 0.786368761015837 102 173.17 172.990650127469 0.179349872531247 103 173.17 173.289325572315 -0.119325572315148 104 173.17 173.492839805206 -0.322839805206229 105 173.4 173.58840705326 -0.188407053259908 106 174.47 173.833190161929 0.636809838071315 107 174.56 174.123368925541 0.436631074459001 108 174.59 174.513755712087 0.0762442879128287 109 174.59 174.518206124398 0.071793875602026 110 175.22 174.810309004881 0.409690995118751 111 175.3 175.231736111872 0.0682638881279729 112 175.25 175.88221956009 -0.632219560089851 113 175.54 175.504857556805 0.0351424431949567 114 175.58 175.40497404162 0.175025958379905 115 175.58 175.644983847259 -0.064983847259299 116 175.68 175.859085673376 -0.179085673375710 117 176.05 176.120278124767 -0.070278124767043 118 176.4 176.685750608855 -0.285750608854613 119 176.58 176.233314259917 0.346685740083132 120 176.49 176.465406673471 0.0245933265290148 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 176.426994380779 175.644288517035 177.209700244523 122 176.743752364600 175.750564381066 177.736940348134 123 176.755711529035 175.577532508447 177.933890549623 124 177.162833325453 175.814248094876 178.511418556030 125 177.425854805415 175.916167856869 178.935541753961 126 177.33260783522 175.668117873330 178.997097797111 127 177.374960436864 175.560076989025 179.189843884704 128 177.605034633421 175.642897195861 179.567172070981 129 178.028355560677 175.921207162871 180.135503958484 130 178.595831337892 176.345258428167 180.846404247617 131 178.525573811711 176.132667872911 180.918479750512 132 178.417771022660 175.883241686965 180.952300358355

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/1235m1263939851.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/1235m1263939851.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/29j181263939851.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/29j181263939851.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/3bhmn1263939851.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263939934h1xfnpvnwc5amfv/3bhmn1263939851.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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