*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 07:56:57 -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/16/t1263653911oomg26k81ahrc82.htm/, Retrieved Sat, 16 Jan 2010 15:58:36 +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/16/t1263653911oomg26k81ahrc82.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 «

100,7 105,9 115,4 113,9 121,5 119,5 115,8 116,3 113,5 110,7 116,9 141,1 101,8 102,9 119 112,8 120,9 123,1 121,9 119,4 110,9 116,8 120,6 143,3 106,4 106,9 125,6 110,9 127 124,3 121,3 124,4 113,2 120,2 122,6 143,3 106,5 105,9 114 121,6 119,7 122,5 126,5 118,2 115,5 120,1 115,3 146,5 107,7 106,3 121,8 115,8 115,4 124,3 121,7 118,7 113,5 113,4 115,1 144,2 100,9 103,2 121,3 111,9 117,3 124,2 122 119,6 114,9 112,2 115,3 143 104 105,3 124,3 114,1 124,8 131,9 125,8 125,2 119,8 116,2 120,2 148,6 109,4 109,6 135,2 115,2 129,1 138,8 126 130,7 120,5 126,5 128 151,7 114,8 118,9 131,5 124,8 137 137,1 137 131,3 126 129,7 125,1 157,8

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 0.0963474453290963 beta 0.343443065425805 gamma 0.235170688807855 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 101.8 101.277287425462 0.522712574538346 14 102.9 102.252139067473 0.647860932527124 15 119 118.518061280529 0.481938719470818 16 112.8 112.466915237244 0.333084762755533 17 120.9 120.404675682050 0.49532431794988 18 123.1 122.655194166115 0.444805833884828 19 121.9 117.395196072577 4.50480392742267 20 119.4 118.839009955928 0.560990044072028 21 110.9 116.433708685718 -5.5337086857179 22 116.8 113.178578254901 3.62142174509883 23 120.6 120.337964576642 0.262035423357545 24 143.3 145.590981100622 -2.29098110062182 25 106.4 104.913320222304 1.48667977769622 26 106.9 106.203322696405 0.696677303595152 27 125.6 123.228854121050 2.37114587895019 28 110.9 117.316165731205 -6.41616573120494 29 127 124.942719534639 2.05728046536133 30 124.3 127.481482263572 -3.18148226357204 31 121.3 122.520167586333 -1.22016758633264 32 124.4 122.333551608785 2.06644839121475 33 113.2 118.472074619633 -5.27207461963347 34 120.2 116.988041226851 3.21195877314879 35 122.6 123.352083403192 -0.75208340319216 36 143.3 148.268458737549 -4.96845873754907 37 106.5 107.073400127399 -0.573400127398642 38 105.9 107.676024966410 -1.77602496641025 39 114 124.512357215434 -10.5123572154341 40 121.6 114.672142810139 6.92785718986075 41 119.7 124.946482739439 -5.24648273943873 42 122.5 124.973556227158 -2.47355622715817 43 126.5 119.920465493495 6.57953450650491 44 118.2 120.795164474322 -2.59516447432230 45 115.5 114.524973804509 0.97502619549131 46 120.1 115.121695811683 4.97830418831667 47 115.3 120.451306748820 -5.15130674882023 48 146.5 142.944858182845 3.55514181715455 49 107.7 104.290950679179 3.40904932082121 50 106.3 104.995350736643 1.30464926335661 51 121.8 120.065442417401 1.73455758259944 52 115.8 115.619359551648 0.180640448352392 53 115.4 122.844863691546 -7.44486369154588 54 124.3 123.427368486299 0.872631513700611 55 121.7 120.924668764043 0.77533123595687 56 118.7 119.402754965216 -0.702754965215661 57 113.5 114.257885189853 -0.757885189853411 58 113.4 115.626155831230 -2.22615583122963 59 115.1 117.932674009311 -2.83267400931095 60 144.2 142.163025097462 2.03697490253779 61 100.9 103.687844119812 -2.78784411981181 62 103.2 103.046644107937 0.153355892062962 63 121.3 117.375343143529 3.92465685647123 64 111.9 112.625617659283 -0.725617659282904 65 117.3 117.637213121795 -0.337213121795472 66 124.2 120.473389731657 3.72661026834345 67 122 118.257337941230 3.74266205876971 68 119.6 116.817228224179 2.78277177582108 69 114.9 112.263465188583 2.63653481141705 70 112.2 113.92404484476 -1.72404484475999 71 115.3 116.440135139821 -1.14013513982114 72 143 142.163290190717 0.836709809283263 73 104 102.998584803698 1.00141519630225 74 105.3 103.777631362056 1.52236863794367 75 124.3 119.706660516196 4.59333948380412 76 114.1 114.493415203007 -0.393415203007493 77 124.8 120.294008143440 4.50599185656037 78 131.9 125.327666993841 6.57233300615901 79 125.8 124.137266206681 1.66273379331872 80 125.2 122.96485063182 2.23514936818000 81 119.8 118.800987089810 0.999012910189592 82 116.2 120.045641988447 -3.84564198844703 83 120.2 123.226948746746 -3.02694874674629 84 148.6 151.385830782402 -2.7858307824018 85 109.4 109.894663681849 -0.494663681848593 86 109.6 111.022121009392 -1.42212100939206 87 135.2 128.629941140805 6.5700588591946 88 115.2 122.398097210631 -7.19809721063108 89 129.1 129.104716185616 -0.00471618561613241 90 138.8 134.364285581255 4.43571441874542 91 126 131.598390430252 -5.59839043025167 92 130.7 129.39422936014 1.30577063985996 93 120.5 124.253997514669 -3.75399751466911 94 126.5 123.459716653618 3.04028334638184 95 128 127.299860757428 0.700139242571694 96 151.7 156.800869115537 -5.10086911553734 97 114.8 113.774958224513 1.02504177548667 98 118.9 114.705292845492 4.19470715450844 99 131.5 135.345341936157 -3.84534193615750 100 124.8 124.532732914897 0.267267085102603 101 137 133.739601269251 3.2603987307493 102 137.1 140.527534084171 -3.42753408417053 103 137 134.473150154057 2.52684984594291 104 131.3 134.56431364795 -3.26431364794996 105 126 127.594985554761 -1.59498555476145 106 129.7 128.467604706045 1.23239529395485 107 125.1 131.654687024155 -6.55468702415473 108 157.8 159.60355805447 -1.80355805446990 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 116.875154931201 114.788675712536 118.961634149867 110 118.172143695526 115.906233084753 120.438054306299 111 136.601904778109 133.952754809723 139.251054746495 112 126.569537428808 123.665702292737 129.473372564879 113 136.218444136065 132.757197211304 139.679691060827 114 140.881517332329 136.82945040822 144.933584256437 115 136.059447407979 131.574283642735 140.544611173223 116 134.271964059335 129.261572316064 139.282355802606 117 127.665606808959 122.282097997682 133.049115620235 118 129.078457649881 123.020688463827 135.136226835936 119 130.224076872719 123.456852988829 136.991300756609 120 159.889159926174 116.120048171011 203.658271681337

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/1hpg01263653815.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/1hpg01263653815.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/20zfc1263653815.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/20zfc1263653815.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/3rt5a1263653815.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263653911oomg26k81ahrc82/3rt5a1263653815.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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