exponential smoothing(triple&add)-aantal geboortes per maand (2000-2006)-Olivier Percy MAR201

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 08:30:23 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g.htm/, Retrieved Sat, 06 Jun 2009 16:31:57 +0200

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/2009/Jun/06/t1244298717eemma6hys0p1u4g.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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9.733 9.259 9.864 9.215 10.103 9.380 9.896 10.117 9.451 9.700 9.081 9.084 9.743 8.587 9.731 9.563 9.998 9.437 10.038 9.918 9.252 9.737 9.035 9.133 9.487 8.700 9.627 8.947 9.283 8.829 9.947 9.628 9.318 9.605 8.640 9.214 9.567 8.547 9.185 9.470 9.123 9.278 10.170 9.434 9.655 9.429 8.739 9.552 9.687 9.019 9.672 9.206 9.069 9.788 10.312 10.105 9.863 9.656 9.295 9.946 9.701 9.049 10.190 9.706 9.765 9.893 9.994 10.433 10.073 10.112 9.266 9.820 10.097 9.115 10.411 9.678 10.408 10.153 10.368 10.581 10.597 10.680 9.738 9.556

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 0.10425711833567 beta 0.130348249108125 gamma 0.727179362888915 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 9.743 9.74921180555556 -0.00621180555555689 14 8.587 8.59142105170956 -0.00442105170955998 15 9.731 9.74796524912095 -0.016965249120954 16 9.563 9.58113773812208 -0.0181377381220837 17 9.998 10.0105664997834 -0.0125664997834232 18 9.437 9.44390532732481 -0.00690532732481053 19 10.038 9.83615719750635 0.201842802493651 20 9.918 10.1042072025874 -0.186207202587356 21 9.252 9.44822805956723 -0.196228059567231 22 9.737 9.66103748397145 0.0759625160285538 23 9.035 9.03409035705682 0.000909642943176081 24 9.133 9.03345579567608 0.099544204323923 25 9.487 9.68611954459826 -0.199119544598256 26 8.7 8.5058187499709 0.194181250029102 27 9.627 9.67403227136777 -0.0470322713677724 28 8.947 9.50203221802548 -0.555032218025485 29 9.283 9.87054444750937 -0.587544447509369 30 8.829 9.23124105357236 -0.402241053572357 31 9.947 9.69649106157862 0.250508938421376 32 9.628 9.69575706137927 -0.0677570613792717 33 9.318 9.02611433318695 0.291885666813053 34 9.605 9.4542564257478 0.150743574252209 35 8.64 8.77438286347976 -0.134382863479759 36 9.214 8.81021565717309 0.403784342826912 37 9.567 9.29051920324584 0.276480796754155 38 8.547 8.41290900386903 0.134090996130967 39 9.185 9.41384606651053 -0.228846066510531 40 9.47 8.88563267108924 0.584367328910757 41 9.123 9.36087799748514 -0.237877997485139 42 9.278 8.89260191145566 0.38539808854434 43 10.17 9.88972350198546 0.280276498014537 44 9.434 9.70976556212332 -0.275765562123317 45 9.655 9.27484878636274 0.380151213637262 46 9.429 9.6436109406425 -0.214610940642499 47 8.739 8.75831278013992 -0.0193127801399235 48 9.552 9.1766377035185 0.375362296481507 49 9.687 9.5906222075736 0.0963777924263916 50 9.019 8.61860492555353 0.400395074446468 51 9.672 9.43163809278055 0.240361907219448 52 9.206 9.5091554995017 -0.303155499501692 53 9.069 9.37133980882434 -0.302339808824335 54 9.788 9.31649977838275 0.471500221617255 55 10.312 10.2694716023046 0.0425283976953832 56 10.105 9.71465512609808 0.390344873901917 57 9.863 9.7975942248095 0.0654057751904986 58 9.656 9.76302433589962 -0.107024335899615 59 9.295 9.03450554722939 0.260494452770612 60 9.946 9.76123486649888 0.184765133501118 61 9.701 9.99319182522465 -0.29219182522465 62 9.049 9.19297379159361 -0.143973791593615 63 10.19 9.85189863573865 0.338101364261345 64 9.706 9.59379184124023 0.112208158759774 65 9.765 9.51367114412538 0.251328855874622 66 9.893 10.0419911674629 -0.148991167462865 67 9.994 10.6638057580960 -0.669805758095981 68 10.433 10.2645496399226 0.168450360077351 69 10.073 10.1129555017458 -0.0399555017458297 70 10.112 9.95390909308532 0.158090906914678 71 9.266 9.49484565791946 -0.228845657919457 72 9.82 10.1170063573100 -0.297006357310037 73 10.097 9.97729069532818 0.119709304671821 74 9.115 9.31138696974474 -0.196386969744744 75 10.411 10.2729688598946 0.138031140105372 76 9.678 9.83825957821236 -0.160259578212356 77 10.408 9.80804322416032 0.599956775839683 78 10.153 10.1043857912686 0.0486142087313794 79 10.368 10.4026771219723 -0.0346771219723347 80 10.581 10.6193959818708 -0.0383959818707975 81 10.597 10.3114241972789 0.28557580272107 82 10.68 10.3206772680669 0.359322731933105 83 9.738 9.63865102730258 0.099348972697424 84 9.556 10.2631854515408 -0.707185451540758 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 10.3591204222598 9.81037014845646 10.9078706960631 86 9.48019546736412 8.92764784332006 10.0327430914082 87 10.6881030433277 10.1308678894405 11.245338197215 88 10.0508533198912 9.4879638925652 10.6137427472171 89 10.5408485800279 9.97126928479105 11.1104278752648 90 10.4156869980321 9.83832191426582 10.9930520817985 91 10.6541674518087 10.0678694633351 11.2404654402823 92 10.8720611828951 10.2756414713724 11.4684808944178 93 10.7796202367276 10.1718578755293 11.3873825979259 94 10.8037589848034 10.1834103713601 11.4241075982466 95 9.90667245655666 9.27248034011989 10.5408645729934 96 9.98588969137553 9.33659158768095 10.6351877950701

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/14n8q1244298617.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/14n8q1244298617.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/2l8gd1244298617.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/2l8gd1244298617.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/3523q1244298617.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244298717eemma6hys0p1u4g/3523q1244298617.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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