Single Exponential Smoothing model_Gem consumptieprijs roze zalm_Dominique Van Santfoort

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 16 Jul 2008 05:00:01 -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/Jul/16/t12162061010y14sqahgv4lf86.htm/, Retrieved Wed, 16 Jul 2008 11:01:45 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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11.73 11.74 11.65 11.38 11.53 11.75 11.82 11.83 11.63 11.55 11.4 11.4 11.63 11.46 11.35 11.7 11.52 11.64 11.9 11.73 11.7 11.54 11.97 11.64 11.98 11.79 11.66 11.96 11.83 12.36 12.53 12.55 12.53 12.24 12.34 12.05 12.22 12.23 11.92 12.13 12.1 12.15 12.23 12.08 12.02 11.93 12.16 11.87 11.93 11.79 11.43 11.63 11.93 11.89 11.83 11.59 12.04 11.81 11.9 11.72 11.91 11.94 11.91 11.84 12.01 11.89 11.8 11.7 11.5 11.76 11.61 11.27 11.64 11.39 11.54 11.62 11.59 11.44 11.31 11.56 11.4 11.51 11.5 11.24 11.8 11.87 11.86 12.11 11.92 12.61 13.34 13.31 13.47 13.3 13.18 13.24

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.779534626319323 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 11.74 11.73 0.00999999999999979 3 11.65 11.7377953462632 -0.087795346263194 4 11.38 11.6693558338213 -0.289355833821338 5 11.53 11.4437929420301 0.0862070579698919 6 11.75 11.5109943287508 0.239005671249243 7 11.82 11.6973075253762 0.122692474623765 8 11.83 11.7929505577343 0.0370494422657348 9 11.63 11.8218318808662 -0.191831880866223 10 11.55 11.6722922872990 -0.122292287299038 11 11.4 11.5769612148176 -0.176961214817647 12 11.4 11.4390138203518 -0.0390138203517605 13 11.63 11.4086011964826 0.221398803517438 14 11.46 11.5811892300501 -0.121189230050073 15 11.35 11.4867180288891 -0.136718028889065 16 11.7 11.3801415913279 0.319858408672086 17 11.52 11.6294822964072 -0.109482296407201 18 11.64 11.5441370553888 0.0958629446111683 19 11.9 11.6188655400942 0.281134459905831 20 11.73 11.8380195862423 -0.108019586242346 21 11.7 11.7538145784458 -0.0538145784457527 22 11.54 11.7118642511465 -0.171864251146511 23 11.97 11.5778901163514 0.392109883648637 24 11.64 11.8835533479775 -0.243553347977517 25 11.98 11.6936950798730 0.286304920126955 26 11.79 11.9168796787976 -0.126879678797595 27 11.66 11.8179725757986 -0.157972575798595 28 11.96 11.6948274829547 0.265172517045265 29 11.83 11.9015386419398 -0.071538641939771 30 12.36 11.8457717934279 0.514228206572138 31 12.53 12.2466304862809 0.283369513719069 32 12.55 12.4675268342682 0.0824731657317876 33 12.53 12.5318175226983 -0.00181752269831392 34 12.24 12.5304007008209 -0.290400700820856 35 12.34 12.3040232990236 0.0359767009764003 36 12.05 12.3320683831754 -0.282068383175440 37 12.22 12.1121863115003 0.107813688499721 38 12.23 12.1962308148770 0.0337691851229831 39 11.92 12.2225550639830 -0.30255506398297 40 12.13 11.986702915240 0.143297084760015 41 12.1 12.0984079546610 0.00159204533896684 42 12.15 12.0996490091294 0.050350990870573 43 12.23 12.1388993499825 0.0911006500174736 44 12.08 12.2099154611513 -0.129915461151345 45 12.02 12.1086418606896 -0.0886418606896289 46 11.93 12.0395424609407 -0.109542460940689 47 12.16 11.9541503195852 0.205849680414810 48 11.87 12.1146172732853 -0.244617273285302 49 11.93 11.9239296385636 0.00607036143640727 50 11.79 11.9286616954975 -0.138661695497547 51 11.43 11.8205701025131 -0.390570102513063 52 11.63 11.5161071835990 0.113892816400959 53 11.93 11.6048905776726 0.325109422327381 54 11.89 11.8583246297195 0.0316753702805155 55 11.83 11.8830166776546 -0.0530166776546341 56 11.59 11.8416883416504 -0.251688341650437 57 12.04 11.6454885642930 0.394511435706967 58 11.81 11.9530238889056 -0.143023888905562 59 11.9 11.8415318151128 0.05846818488717 60 11.72 11.8871097897704 -0.167109789770420 61 11.91 11.7568419222474 0.153158077752565 62 11.94 11.8762339471561 0.063766052843933 63 11.91 11.9259417933316 -0.0159417933316188 64 11.84 11.913514613424 -0.0735146134239955 65 12.01 11.8562074267195 0.153792573280489 66 11.89 11.9760940628624 -0.0860940628624043 67 11.8 11.9089807597406 -0.108980759740648 68 11.7 11.8240264839202 -0.124026483920227 69 11.5 11.7273435451238 -0.227343545123773 70 11.76 11.5501213796296 0.209878620370397 71 11.61 11.7137290315325 -0.103729031532456 72 11.27 11.6328686596983 -0.362868659698339 73 11.64 11.3499999746574 0.2900000253426 74 11.39 11.5760650360454 -0.186065036045438 75 11.54 11.4310208977007 0.108979102299333 76 11.62 11.5159738814882 0.104026118511808 77 11.59 11.5970658429097 -0.00706584290974277 78 11.44 11.5915577736975 -0.151557773697464 79 11.31 11.4734132412124 -0.163413241212423 80 11.56 11.3460269612883 0.213973038711734 81 11.4 11.5128263540628 -0.112826354062827 82 11.51 11.4248743043095 0.0851256956905093 83 11.5 11.4912327316898 0.00876726831023689 84 11.24 11.4980671209158 -0.258067120915825 85 11.8 11.2968948642474 0.503105135752596 86 11.87 11.6890827382456 0.180917261754363 87 11.86 11.8301140082820 0.0298859917179612 88 12.11 11.8534111736681 0.256588826331917 89 11.92 12.0534310485204 -0.133431048520448 90 12.61 11.9494169259727 0.660583074027334 91 13.34 12.4643643057374 0.875635694262566 92 13.31 13.1469526494563 0.163047350543737 93 13.47 13.2740537049347 0.195946295065269 94 13.3 13.4268006268371 -0.126800626837092 95 13.18 13.3279551475786 -0.147955147578585 96 13.24 13.2126189868989 0.0273810131011079 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 13.2339634347149 12.7982583567992 13.6696685126306 98 13.2339634347149 12.6815151275768 13.786411741853 99 13.2339634347149 12.5854579611852 13.8824689082446 100 13.2339634347149 12.5018981600732 13.9660287093566 101 13.2339634347149 12.4269443621557 14.0409825072742 102 13.2339634347149 12.3583836264663 14.1095432429635 103 13.2339634347149 12.2948147682351 14.1731121011947 104 13.2339634347149 12.2352840893347 14.2326427800951 105 13.2339634347149 12.179107685322 14.2888191841078 106 13.2339634347149 12.1257753328272 14.3421515366026 107 13.2339634347149 12.0748943745189 14.3930324949110 108 13.2339634347149 12.0261549633744 14.4417719060555

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/1a0451216205999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/1a0451216205999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/2yrur1216205999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/2yrur1216205999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/3svn61216205999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/16/t12162061010y14sqahgv4lf86/3svn61216205999.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')

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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