datareeks-cinemaprijs-seda hovhannesian

*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 06:39:05 -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/t124429211466w3822ls9n8omw.htm/, Retrieved Sat, 06 Jun 2009 14:41:58 +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/t124429211466w3822ls9n8omw.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:

» Textbox « » Textfile « » CSV «

5.44 5.44 5.44 5.44 5.44 5.49 5.49 5.49 5.49 5.49 5.49 5.60 5.60 5.60 5.60 5.60 5.60 5.60 5.67 5.67 5.67 5.67 5.67 5.67 5.67 5.67 5.67 5.82 5.82 5.95 5.95 5.95 5.95 5.95 5.95 6.02 6.02 6.05 6.05 6.05 6.12 6.12 6.12 6.12 6.12 6.12 6.12 6.12 6.17 6.17 6.17 6.17 6.17 6.28 6.27 6.28 6.28 6.27 6.27 6.28 6.59 6.59 6.59 6.59 6.59 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.63 6.79 6.79 6.79 6.81 6.80 6.80 6.85 6.85 6.85 6.85 6.85 6.85 6.86 6.86 6.88 6.88 6.88 6.91 6.91 6.91 6.91 6.99 6.99 6.99 7.02 7.02 7.05 7.05 7.05 7.05 7.10 7.10 7.10 7.10 7.12 7.13 7.18

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.800021697608403 beta 0 gamma 0.938182298582948 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5.6 5.52588995089906 0.074110049100943 14 5.6 5.5836960661993 0.0163039338007014 15 5.6 5.59522900432491 0.00477099567508521 16 5.6 5.59753321270797 0.00246678729202543 17 5.6 5.59799681111868 0.00200318888132411 18 5.6 5.60264896463026 -0.00264896463025988 19 5.67 5.65124590981136 0.0187540901886427 20 5.67 5.66597157942531 0.00402842057468789 21 5.67 5.66890994253915 0.00109005746084989 22 5.67 5.66949681982731 0.000503180172692907 23 5.67 5.6696145865947 0.000385413405301627 24 5.67 5.78540913247381 -0.115409132473809 25 5.67 5.70846222126103 -0.0384622212610317 26 5.67 5.66499221198552 0.00500778801447943 27 5.67 5.66511130783521 0.00488869216478616 28 5.82 5.66688706778091 0.153112932219088 29 5.82 5.78727543430731 0.0327245656926864 30 5.95 5.8152043030481 0.134795696951902 31 5.95 5.98014370904363 -0.0301437090436343 32 5.95 5.95215353141279 -0.00215353141279451 33 5.95 5.94888916380895 0.00111083619105035 34 5.95 5.94870191697253 0.00129808302746781 35 5.95 5.94875895718062 0.00124104281937587 36 6.02 6.04710204611742 -0.0271020461174167 37 6.02 6.05621048990421 -0.0362104899042102 38 6.05 6.02155855303841 0.028441446961585 39 6.05 6.03925205883379 0.0107479411662101 40 6.05 6.07368537555861 -0.0236853755586131 41 6.12 6.02846456461447 0.0915354353855315 42 6.12 6.12247130456343 -0.0024713045634277 43 6.12 6.14699180601871 -0.0269918060187146 44 6.12 6.12641899140255 -0.00641899140254765 45 6.12 6.11994126287854 5.87371214564314e-05 46 6.12 6.11853484868824 0.00146515131176095 47 6.12 6.11830524031134 0.00169475968865918 48 6.12 6.21391319226207 -0.09391319226207 49 6.17 6.16813412705065 0.00186587294935325 50 6.17 6.17587698996837 -0.0058769899683675 51 6.17 6.16235272343768 0.00764727656232367 52 6.17 6.18794569341074 -0.0179456934107405 53 6.17 6.16835408334248 0.00164591665751601 54 6.28 6.17272422982617 0.107275770173833 55 6.27 6.28061659094706 -0.0106165909470644 56 6.28 6.27679027483096 0.00320972516904305 57 6.28 6.2788781994558 0.00112180054420463 58 6.27 6.27820520653592 -0.00820520653592283 59 6.27 6.26991719974773 8.28002522705873e-05 60 6.28 6.34761656413826 -0.0676165641382624 61 6.59 6.34179518934648 0.248204810653516 62 6.59 6.54463503626821 0.0453649637317906 63 6.59 6.57332283222538 0.0166771677746222 64 6.59 6.60140796860466 -0.0114079686046589 65 6.59 6.5896932922136 0.00030670778639319 66 6.63 6.61315267193653 0.0168473280634744 67 6.63 6.62582945499342 0.00417054500658409 68 6.63 6.63607188217895 -0.00607188217894716 69 6.63 6.62954255504114 0.000457444958857245 70 6.63 6.62565504698584 0.0043449530141606 71 6.63 6.62818735823105 0.00181264176895457 72 6.63 6.6974052631018 -0.0674052631018025 73 6.63 6.75492951073505 -0.124929510735055 74 6.63 6.62066105398888 0.00933894601112062 75 6.63 6.61498292594439 0.0150170740556073 76 6.63 6.63644494323795 -0.00644494323795097 77 6.63 6.63081202185839 -0.00081202185839313 78 6.63 6.65655126741056 -0.0265512674105643 79 6.63 6.63211560629388 -0.00211560629387808 80 6.63 6.63540589045668 -0.00540589045668405 81 6.63 6.63063226754273 -0.00063226754272705 82 6.63 6.626601560358 0.00339843964199371 83 6.79 6.62790285951553 0.162097140484475 84 6.79 6.81305631113353 -0.0230563111335300 85 6.79 6.89705711743291 -0.107057117432912 86 6.81 6.80165988098065 0.00834011901935128 87 6.8 6.7955533858772 0.00444661412279768 88 6.8 6.80432465670647 -0.00432465670646565 89 6.85 6.80111241569742 0.0488875843025749 90 6.85 6.86202239722673 -0.0120223972267288 91 6.85 6.85338976835674 -0.00338976835674210 92 6.85 6.85474010811502 -0.00474010811502357 93 6.85 6.85096214536677 -0.000962145366766087 94 6.85 6.84688656604298 0.00311343395702046 95 6.86 6.87762543910154 -0.0176254391015398 96 6.86 6.88432842658235 -0.024328426582346 97 6.88 6.9520991608042 -0.0720991608041954 98 6.88 6.9062923434223 -0.0262923434223046 99 6.88 6.87144898690064 0.00855101309935957 100 6.91 6.88174328435744 0.0282567156425646 101 6.91 6.91447689719075 -0.00447689719075051 102 6.91 6.92123518754496 -0.011235187544961 103 6.91 6.9147531730619 -0.00475317306189993 104 6.99 6.91467313862054 0.0753268613794598 105 6.99 6.97542760721591 0.0145723927840855 106 6.99 6.98422543358631 0.00577456641369167 107 7.02 7.01341712155786 0.00658287844214289 108 7.02 7.03835766823982 -0.0183576682398172 109 7.05 7.10336775614203 -0.0533677561420314 110 7.05 7.08130525442563 -0.0313052544256349 111 7.05 7.04845503023365 0.00154496976635166 112 7.05 7.05666647299218 -0.00666647299217793 113 7.1 7.05512388374282 0.0448761162571767 114 7.1 7.09997911473098 2.0885269019999e-05 115 7.1 7.10344992850955 -0.00344992850954551 116 7.1 7.11945656199515 -0.0194565619951472 117 7.12 7.09257914899669 0.0274208510033080 118 7.13 7.10968511823511 0.0203148817648904 119 7.18 7.15087995737546 0.0291200426245446 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 120 7.18919858120288 7.09505600011893 7.28334116228684 121 7.26369897882036 7.14213715935736 7.38526079828335 122 7.28878837141537 7.14515708534149 7.43241965748926 123 7.28663309257369 7.12424543629639 7.44902074885099 124 7.29179564697852 7.11254244382039 7.47104885013665 125 7.30521059402036 7.11041247391562 7.5000087141251 126 7.30537293316067 7.09648427113101 7.51426159519033 127 7.30786698923388 7.0857679274736 7.52996605099415 128 7.32368925656306 7.08879966057436 7.55857885255175 129 7.32065375460443 7.0741701124099 7.56713739679895 130 7.31392774424587 7.0565319494421 7.57132353904964 131 7.34084400377227 0.369393019297254 14.3122949882473

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/1d03w1244291941.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/1d03w1244291941.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/2zyqh1244291941.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/2zyqh1244291941.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/3ezkd1244291941.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124429211466w3822ls9n8omw/3ezkd1244291941.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=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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