Champagne Exponential Smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 14:37:01 +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/May/31/t127531669365mcx864dhsv212.htm/, Retrieved Mon, 31 May 2010 16:38:14 +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/May/31/t127531669365mcx864dhsv212.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 «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4739 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6922 9858 11331 4016 3975 4510 4276 4968 4677 3523 1821 5222 6873 10803 13916 2639 2899 3370 3740 2927 3986 4217 1738 5221 6424 9842 13076 3934 3162 4286 4676 5010 4874 4633 1659 5951 6981 9851 12670

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.30842644344129 beta 0 gamma 0.632760470780569 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2541 2393.50833868648 147.491661313523 14 2475 2389.75888889292 85.2411111070837 15 3031 2978.35640546918 52.6435945308167 16 3266 3224.57486167209 41.425138327912 17 3776 3723.43585246574 52.5641475342582 18 3230 3145.95647544954 84.0435245504614 19 3028 2495.85826039448 532.141739605515 20 1759 2615.11807012923 -856.118070129231 21 3595 3130.25669910364 464.743300896364 22 4474 4811.13642911062 -337.136429110617 23 6838 6258.72643224635 579.273567753655 24 8357 7934.66214742373 422.337852576273 25 3113 2940.7998191162 172.200180883797 26 3006 2897.56490597696 108.435094023038 27 4047 3580.3024470368 466.697552963203 28 3523 3995.14184564363 -472.141845643626 29 3937 4423.91370452947 -486.913704529466 30 3986 3610.94140603873 375.05859396127 31 3260 3148.77166912909 111.228330870912 32 1573 2417.20206583968 -844.202065839685 33 3528 3625.51605483856 -97.5160548385575 34 5211 4817.81581161119 393.184188388806 35 7614 7041.98015460674 572.019845393255 36 9254 8751.20258405828 502.797415941719 37 5375 3252.83865617398 2122.16134382602 38 3088 3742.2695559007 -654.269555900696 39 3718 4483.8418231847 -765.841823184696 40 4514 4085.64765089121 428.352349108791 41 4520 4861.68281614564 -341.682816145635 42 4539 4410.85001290644 128.149987093557 43 3663 3653.35675591563 9.64324408436505 44 1643 2264.44617605372 -621.446176053724 45 4739 4149.84148853392 589.158511466083 46 5428 6069.71709395816 -641.717093958163 47 8314 8362.0605378331 -48.0605378330911 48 10651 10014.2215488854 636.778451114596 49 3633 4500.74097486828 -867.740974868284 50 4292 3013.42806246447 1278.57193753553 51 4154 4323.7759675356 -169.775967535601 52 4121 4656.04329075914 -535.043290759142 53 4647 4799.98302171796 -152.983021717956 54 4753 4607.07333369408 145.926666305915 55 3965 3775.00500753416 189.994992465839 56 1723 2059.76462237556 -336.764622375558 57 5048 4772.81180891231 275.18819108769 58 6922 6115.09205057554 806.907949424456 59 9858 9486.33781629 371.662183710003 60 11331 11851.8998112841 -520.899811284056 61 4016 4563.38971079182 -547.389710791824 62 3975 3997.45323471011 -22.4532347101144 63 4510 4273.31838761804 236.681612381963 64 4276 4569.22285121982 -293.222851219819 65 4968 4977.49285544872 -9.49285544871782 66 4677 4956.23587445028 -279.23587445028 67 3523 3982.17547180157 -459.175471801574 68 1821 1867.74768227565 -46.7476822756498 69 5222 5011.51465333456 210.485346665436 70 6873 6581.07120783537 291.928792164632 71 10803 9581.4265263545 1221.57347364551 72 13916 11851.0586219917 2064.94137800828 73 2639 4698.03096152302 -2059.03096152302 74 2899 3899.80834532273 -1000.80834532273 75 3370 3949.58307105529 -579.583071055289 76 3740 3765.04537858081 -25.0453785808081 77 2927 4299.35202261117 -1372.35202261117 78 3986 3774.43180886483 211.56819113517 79 4217 3056.30994251208 1160.69005748792 80 1738 1733.49453705188 4.50546294811966 81 5221 4831.36712436927 389.632875630735 82 6424 6427.2259168487 -3.22591684869803 83 9842 9545.7731737953 296.226826204693 84 13076 11678.2599047481 1397.7400952519 85 3934 3307.99996998548 626.00003001452 86 3162 3789.18182936661 -627.181829366613 87 4286 4197.50763059483 88.4923694051668 88 4676 4504.02522974213 171.974770257874 89 5010 4413.97229349209 596.027706507914 90 4874 5413.85440538327 -539.854405383268 91 4633 4676.36618707742 -43.3661870774158 92 1659 2061.05277379123 -402.052773791227 93 5951 5569.97297961752 381.02702038248 94 6981 7130.64581122766 -149.645811227659 95 9851 10661.1481746792 -810.148174679225 96 12670 13072.6379617398 -402.637961739832 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 3630.21995369959 2669.58857082424 4590.85133657494 98 3366.47679616763 2338.43658224513 4394.51701009014 99 4293.27567688428 3113.51173388006 5473.03961988851 100 4610.16644881327 3330.65589931401 5889.67699831253 101 4642.1842342272 3301.71457351402 5982.65389494038 102 4941.06299304759 3499.41380801201 6382.71217808317 103 4592.60029404716 3162.74854334857 6022.45204474576 104 1853.22234945944 790.780915067565 2915.66378385131 105 6031.35494501676 3856.09754514589 8206.61234488763 106 7277.2503070181 4701.79916177352 9852.70145226268 107 10674.8187172446 7013.06511447682 14336.5723200123 108 13682.5704969335 9149.68328683926 18215.4577070277

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/1xg5q1275316616.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/1xg5q1275316616.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/2pp4b1275316616.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/2pp4b1275316616.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/3pp4b1275316616.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t127531669365mcx864dhsv212/3pp4b1275316616.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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