Tijdreeks 1 - Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 Jul 2010 14:45:56 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu.htm/, Retrieved Wed, 28 Jul 2010 16:49:45 +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/2010/Jul/28/t1280328581gd06i6x7m8lgcyu.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:

Patrick Fieremans

Dataseries X:

» Textbox « » Textfile « » CSV «

136 135 134 132 152 151 136 126 127 127 128 130 125 118 111 104 126 131 122 116 115 115 113 122 114 106 93 89 114 122 115 116 120 120 120 121 118 112 99 96 120 135 128 134 134 132 130 125 124 114 101 101 123 143 133 136 137 135 141 136 133 124 110 104 130 160 142 142 137 135 139 135 134 120 103 101 127 159 141 140 135 127 130 128 126 110 101 102 129 169 146 145 138 123 124 137 132 112 105 106 137 175 151 142 140 122 127 135 128 117 107 108 134 171 154 146 148 122 124 135

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 0.206674112244381 beta 0.156145216303958 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 125 136.497707249167 -11.497707249167 14 118 125.868466827844 -7.86846682784406 15 111 115.829465823458 -4.82946582345791 16 104 106.517461771267 -2.51746177126746 17 126 127.127195352308 -1.12719535230811 18 131 130.336377069246 0.663622930753945 19 122 117.326137698583 4.67386230141722 20 116 108.433819474594 7.56618052540635 21 115 110.361495776654 4.63850422334642 22 115 111.355941877338 3.64405812266216 23 113 113.273838994097 -0.273838994097034 24 122 114.965256489656 7.03474351034428 25 114 104.112777485435 9.88722251456544 26 106 101.894963219054 4.10503678094598 27 93 98.2124211486975 -5.21242114869752 28 89 92.1233403863731 -3.12334038637309 29 114 111.830786669907 2.16921333009276 30 122 117.596665005009 4.40333499499071 31 115 110.541878156574 4.45812184342579 32 116 105.528235318581 10.4717646814189 33 120 107.029892660232 12.9701073397680 34 120 110.494493199738 9.5055068002625 35 120 112.308917268727 7.6910827312734 36 121 123.663846534212 -2.66384653421156 37 118 114.595993170302 3.40400682969825 38 112 107.755031686656 4.24496831334436 39 99 97.6588251140776 1.34117488592241 40 96 95.8752952217872 0.124704778212759 41 120 124.446887300445 -4.44688730044543 42 135 133.207648979929 1.79235102007070 43 128 126.706194912045 1.29380508795455 44 134 127.222212879329 6.77778712067129 45 134 131.369433412117 2.63056658788315 46 132 130.728257439174 1.271742560826 47 130 129.952663178631 0.0473368213690435 48 125 132.14519310741 -7.14519310740994 49 124 127.014338051243 -3.01433805124296 50 114 119.134346479543 -5.134346479543 51 101 103.923333356148 -2.92333335614836 52 101 99.8862219572254 1.11377804277460 53 123 125.771961793655 -2.77196179365495 54 143 140.180102773959 2.81989722604084 55 133 132.949390419299 0.0506095807014333 56 136 137.394194343486 -1.39419434348619 57 137 135.994819057389 1.00518094261091 58 135 133.318218875344 1.68178112465566 59 141 131.076384087444 9.92361591255647 60 136 129.216539914763 6.78346008523744 61 133 130.405324525263 2.59467547473665 62 124 121.806190773239 2.19380922676073 63 110 109.463847125284 0.536152874716379 64 104 109.946623474011 -5.946623474011 65 130 133.486170377532 -3.4861703775322 66 160 154.249954231527 5.75004576847334 67 142 145.131414581241 -3.13141458124142 68 142 148.535983295595 -6.53598329559478 69 137 148.363336605893 -11.3633366058930 70 135 143.435306155354 -8.43530615535431 71 139 145.300218303875 -6.3002183038752 72 135 136.499747085003 -1.49974708500298 73 134 131.512780408953 2.48721959104736 74 120 121.599293388196 -1.5992933881964 75 103 106.460309284893 -3.4603092848927 76 101 100.042096228068 0.95790377193218 77 127 124.906187861806 2.09381213819428 78 159 151.989770662127 7.01022933787294 79 141 135.859115598457 5.14088440154296 80 140 137.505210337323 2.49478966267679 81 135 134.911431998035 0.0885680019652568 82 127 134.539329979635 -7.53932997963528 83 130 138.113277855539 -8.11327785553866 84 128 132.699208207592 -4.69920820759233 85 126 130.026352503398 -4.02635250339841 86 110 115.626259796421 -5.62625979642135 87 101 98.461966970452 2.53803302954793 88 102 96.6151552203016 5.38484477969838 89 129 122.320837513975 6.67916248602478 90 169 153.420600807372 15.579399192628 91 146 138.083670415765 7.9163295842352 92 145 138.547422449867 6.45257755013265 93 138 135.312671755108 2.68732824489229 94 123 129.816666734662 -6.81666673466157 95 124 133.592182462144 -9.5921824621443 96 137 131.016504740961 5.98349525903944 97 132 131.849065171388 0.150934828611526 98 112 117.160761905490 -5.16076190548961 99 105 106.839523079279 -1.83952307927935 100 106 106.952241870461 -0.952241870460966 101 137 134.057920517065 2.94207948293533 102 175 173.322657341209 1.67734265879105 103 151 148.291843001298 2.70815699870235 104 142 146.257365484352 -4.25736548435154 105 140 137.310720799050 2.68927920095015 106 122 123.797097441325 -1.79709744132461 107 127 126.016400504588 0.983599495412335 108 135 138.187228930160 -3.1872289301603 109 128 132.225310477006 -4.22531047700616 110 117 112.140293426311 4.8597065736893 111 107 106.434032035451 0.565967964548932 112 108 107.823958537440 0.176041462560207 113 134 138.899016279422 -4.89901627942174 114 171 175.614202884575 -4.61420288457478 115 154 149.824044485801 4.17595551419856 116 146 142.308382497310 3.69161750268964 117 148 140.484395652935 7.51560434706499 118 122 124.278204568723 -2.27820456872307 119 124 128.792888611097 -4.79288861109745 120 135 136.432504114121 -1.43250411412075 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 129.920542091987 119.61912351386 140.221960670115 122 117.809395866572 107.269169687027 128.349622046116 123 107.571174468567 96.7773312182415 118.365017718892 124 108.470298979205 97.2599351972896 119.680662761120 125 135.477907013571 123.077610847703 147.87820317944 126 173.907459891797 159.306299443702 188.508620339891 127 155.923697153213 141.23034115805 170.617053148375 128 147.094206191856 131.965590877942 162.222821505770 129 147.414793932782 131.332818210342 163.496769655222 130 121.720603655513 106.470496083891 136.970711227135 131 124.483372343429 108.152042446747 140.814702240111 132 135.774713610729 -40.0558894088902 311.605316630347

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/1g1ls1280328353.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/1g1ls1280328353.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/2rakd1280328353.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/2rakd1280328353.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/3rakd1280328353.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280328581gd06i6x7m8lgcyu/3rakd1280328353.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=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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