*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 08:44:16 +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/Jun/02/t12754684248yswnn6xaoafvx4.htm/, Retrieved Wed, 02 Jun 2010 10:47:06 +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/Jun/02/t12754684248yswnn6xaoafvx4.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 «

40801 49081 52431 59650 75428 78705 68870 70641 80074 76464 69976 92917 92559 73981 71107 96942 86270 69610 57768 80077 71454 70382 69881 84530 79322 80181 82137 88439 91575 82909 73282 94089 108112 95653 85273 105093 102275 99308 79687 93263 114918 103374 65124 104045 101183 95492 85035 90692 107486 98179 82551 106804 110898 89950 65184 95357 98280 92146 77874 100039 104777 102341 71316 88838 85457 70784 70522 88629 88452 98886 79601 108135 113835 101617 68698 79182 86003 84165 68550 90385 100368 99081 81288 103491 111695 82504 62237 78249 92341 84412 75102 90461 106451 98379 72615 98367 116949 95832 68060 83923 87653 78054 57566 78784 88916 84662 63442 77773 88102 87972 61790 95276 104418 95420 82141 104064 96287 78426 59111 76837 76615 65860 57703 68656 77955 65856 60947 69885 80550 73694 67538 76326 84727

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 184.73.236.201 @ 184.73.236.201 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.548527818590737 beta 0.000644959083758779 gamma 0.777318754607708 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 92559 85982.6856303419 6576.3143696581 14 73981 71586.9604668322 2394.03953316779 15 71107 70498.5715023652 608.428497634843 16 96942 97786.5237936756 -844.523793675617 17 86270 87414.9842268457 -1144.98422684574 18 69610 70986.2703504739 -1376.27035047389 19 57768 77316.5777070669 -19548.5777070669 20 80077 65669.0780938773 14407.9219061227 21 71454 81693.1770129404 -10239.1770129404 22 70382 70634.7007984483 -252.700798448277 23 69881 62502.4118639836 7378.58813601641 24 84530 89920.4992505915 -5390.4992505915 25 79322 90255.6905370996 -10933.6905370996 26 80181 64778.6985396935 15402.3014603065 27 82137 70194.8430185478 11942.1569814522 28 88439 103189.552725928 -14750.5527259283 29 91575 85079.5948009386 6495.40519906138 30 82909 72758.2513081145 10150.7486918855 31 73282 79035.7491092813 -5753.74910928126 32 94089 86878.245386985 7210.754613015 33 108112 90308.8827063547 17803.1172936453 34 95653 98150.921087073 -2497.92108707299 35 85273 91478.2838988088 -6205.28389880882 36 105093 106972.388389777 -1879.388389777 37 102275 107297.752646559 -5022.75264655927 38 99308 94317.0069144006 4990.99308559937 39 79687 92815.9178297424 -13128.9178297424 40 93263 102690.049489015 -9427.04948901468 41 114918 94957.1587042393 19960.8412957607 42 103374 91310.5113770731 12063.4886229269 43 65124 93062.119251958 -27938.1192519581 44 104045 93284.1657418708 10760.8342581292 45 101183 102379.196874525 -1196.19687452525 46 95492 92668.2757189951 2823.72428100491 47 85035 87608.6324510824 -2573.63245108243 48 90692 106609.180934283 -15917.1809342834 49 107486 98122.5958088848 9363.4041911152 50 98179 96543.6443028818 1635.35569711824 51 82551 86838.131213733 -4287.13121373301 52 106804 102859.680348468 3944.3196515321 53 110898 112777.735604522 -1879.73560452218 54 89950 94374.7745724244 -4424.77457242443 55 65184 73033.5320266145 -7849.5320266145 56 95357 97852.2563509315 -2495.25635093151 57 98280 95471.6927177199 2808.30728228015 58 92146 89361.4262838443 2784.57371615572 59 77874 82379.4880579576 -4505.48805795761 60 100039 95630.2377650423 4408.7622349577 61 104777 107164.734780101 -2387.73478010108 62 102341 96423.5591683452 5917.44083165479 63 71316 86985.646123207 -15669.646123207 64 88838 99645.4512239981 -10807.4512239981 65 85457 99415.8046599267 -13958.8046599267 66 70784 73477.6505399322 -2693.65053993219 67 70522 51868.3759639063 18653.6240360937 68 88629 93097.4877013623 -4468.48770136235 69 88452 91488.725954073 -3036.72595407293 70 98886 82154.85259344 16731.14740656 71 79601 80260.4592153847 -659.459215384675 72 108135 98746.3901054685 9388.60989453146 73 113835 110626.266227334 3208.73377266599 74 101617 105870.431017513 -4253.43101751289 75 68698 83275.1106313527 -14577.1106313527 76 79182 98238.2397860906 -19056.2397860906 77 86003 92372.765956804 -6369.76595680404 78 84165 74548.2556034055 9616.74439659451 79 68550 67184.9722859613 1365.02771403872 80 90385 90812.1005252403 -427.100525240254 81 100368 91919.7565422856 8448.24345771439 82 99081 95824.2105580484 3256.78944195157 83 81288 80432.1772399301 855.822760069917 84 103491 103272.507087103 218.492912897287 85 111695 107947.300102278 3747.69989772202 86 82504 100862.271080889 -18358.2710808893 87 62237 66896.0181375353 -4659.01813753534 88 78249 85720.0439735783 -7471.04397357826 89 92341 90658.0768001031 1682.92319989686 90 84412 82860.3513339137 1551.64866608626 91 75102 68173.836344098 6928.16365590201 92 90461 94222.0789336987 -3761.07893369869 93 106451 96612.97425354 9838.02574646 94 98379 99455.7023418756 -1076.70234187559 95 72615 80840.3224286113 -8225.32242861128 96 98367 98468.7998254973 -101.799825497321 97 116949 104199.393604992 12749.6063950084 98 95832 94290.4828376276 1541.51716237245 99 68060 76050.5858463905 -7990.58584639052 100 83923 92062.3122483282 -8139.31224832825 101 87653 99848.022238282 -12195.022238282 102 78054 84388.6465854162 -6334.6465854162 103 57566 67257.1697219225 -9691.16972192255 104 78784 80426.1750096974 -1642.1750096974 105 88916 88740.7260864393 175.273913560726 106 84662 82438.2951417569 2223.7048582431 107 63442 63111.2467866248 330.753213375188 108 77773 88273.5351006883 -10500.5351006883 109 88102 92796.2129153977 -4694.21291539774 110 87972 69365.4041120282 18606.5958879718 111 61790 57126.9038036889 4663.09619631115 112 95276 80017.7111681615 15258.2888318385 113 104418 99213.0099491208 5204.99005087925 114 95420 95359.4637510156 60.5362489844265 115 82141 80565.0655957316 1575.9344042684 116 104064 102750.147274705 1313.85272529542 117 96287 113336.078986117 -17049.078986117 118 78426 98310.4952321351 -19884.4952321351 119 59111 66190.3665165909 -7079.36651659092 120 76837 83482.4587396106 -6645.45873961064 121 76615 92154.3440649274 -15539.3440649274 122 65860 70944.9097820315 -5084.90978203154 123 57703 40802.3732135801 16900.6267864199 124 68656 74113.1041187262 -5457.10411872623 125 77955 78399.0665012763 -444.066501276335 126 65856 69621.1892586357 -3765.18925863574 127 60947 53238.448154569 7708.55184543097 128 69885 78675.9997528165 -8790.99975281647 129 80550 77251.8501785946 3298.14982140542 130 73694 72376.3892805472 1317.6107194528 131 67538 56371.6664970912 11166.3335029088 132 76326 83822.4196999445 -7496.41969994445 133 84727 88904.1400319154 -4177.14003191541 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 134 77597.8778022822 59479.768657828 95715.9869467364 135 57963.7412902554 37295.8224081766 78631.6601723341 136 74155.4863106948 51216.7114796307 97094.2611417589 137 83193.6678936945 58186.8784027714 108200.457384618 138 73493.6045085956 46574.8500283783 100412.358988813 139 63203.8144075576 34497.9449852659 91909.6838298492 140 78621.0380878178 48230.8687499474 109011.207425688 141 86262.9894207008 54275.0888296753 118250.890011726 142 78883.642268976 45372.1935242394 112395.091013713 143 65612.282951652 30641.7709050069 100582.794998297 144 80384.3963127775 44011.5436078764 116757.249017679 145 90741.4942934366 53016.6963164359 128466.292270437

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/12hsa1275468252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/12hsa1275468252.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/2d8rv1275468252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/2d8rv1275468252.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/3d8rv1275468252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t12754684248yswnn6xaoafvx4/3d8rv1275468252.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=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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