*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 16:03:24 +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/06/t12758403013ujazyv8ltrtfbv.htm/, Retrieved Sun, 06 Jun 2010 18:05:01 +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/06/t12758403013ujazyv8ltrtfbv.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 «

25000 25284 12434,5 33955 14980,5 50831 4198,5 34566 35000 11055,5 20807 21887,29 16977,5 19613,5 14570 24416,5 16825,5 13980 21450,5 27239,5 19078,5 20459,1 20373,5 19306,5 16723,16 11638 20917 17903,5 28218,5 15268 21555 23143 16691 17932,5 30512 41931,5 10853,5 25939,5 14900 25127,76 22063,5 25306,5 31217,5 23201,5 38148 26264 16359 27945,5 16218,5 36003,5 20323,5 20100,5 18741 24426,75 19174,5 13766 18999 21745 34469 13248 16218,5 36003,5 20323,5 20100,5 18741 24426,75 19174,5 13766 18999 21745 34469 13248

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0336469139053757 beta 0 gamma 0.609625489191882 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 16977.5 22771.3540372475 -5793.85403724749 14 19613.5 24798.8462292759 -5185.34622927591 15 14570 20549.5419977966 -5979.54199779656 16 24416.5 30466.4280296698 -6049.92802966979 17 16825.5 22298.1124554551 -5472.6124554551 18 13980 19394.0713519956 -5414.07135199558 19 21450.5 5229.8174760041 16220.6825239959 20 27239.5 36713.6350510421 -9474.13505104208 21 19078.5 36976.1513113184 -17897.6513113184 22 20459.1 12737.9089118714 7721.1910881286 23 20373.5 23069.7656636606 -2696.26566366062 24 19306.5 25517.9179783427 -6211.41797834274 25 16723.16 17802.5204593696 -1079.36045936962 26 11638 20347.1209589263 -8709.12095892627 27 20917 15511.3811551864 5405.6188448136 28 17903.5 25769.8773540533 -7866.37735405335 29 28218.5 17880.5482486593 10337.9517513407 30 15268 15542.9711906244 -274.971190624361 31 21555 14296.9571652921 7258.04283470785 32 23143 30342.0463586541 -7199.04635865411 33 16691 25718.7054146535 -9027.7054146535 34 17932.5 16871.3145372803 1061.18546271967 35 30512 20842.0185279488 9669.9814720512 36 41931.5 21635.433307666 20296.066692334 37 10853.5 17835.2950710850 -6981.79507108503 38 25939.5 15686.5021565787 10252.9978434213 39 14900 19803.9625156947 -4903.96251569465 40 25127.76 21896.8613458569 3230.89865414311 41 22063.5 25105.3368709417 -3041.83687094168 42 25306.5 16065.3553257096 9241.14467429043 43 31217.5 19577.3292850326 11640.1707149674 44 23201.5 27252.9975360085 -4051.49753600847 45 38148 21658.2742091317 16489.7257908683 46 26264 19612.9676845156 6651.03231548444 47 16359 28843.3104850334 -12484.3104850334 48 27945.5 35151.2716774774 -7205.77167747736 49 16218.5 14356.0255778618 1862.47442213818 50 36003.5 22658.0637451364 13345.4362548636 51 20323.5 17950.4055583446 2373.09444165539 52 20100.5 25080.5112122902 -4980.01121229021 53 18741 24317.3619506090 -5576.36195060897 54 24426.75 22428.1713732025 1998.57862679745 55 19174.5 27109.7538985344 -7935.25389853443 56 13766 24882.5963448535 -11116.5963448535 57 18999 31151.2656571527 -12152.2656571527 58 21745 22346.1376306901 -601.137630690089 59 34469 20059.5790421567 14409.4209578433 60 13248 30382.0896295068 -17134.0896295068 61 16218.5 14595.0122228692 1623.48777713078 62 36003.5 29653.7767508697 6349.72324913032 63 20323.5 18246.780020073 2076.71997992701 64 20100.5 21035.0999800472 -934.599980047198 65 18741 20056.7480673259 -1315.74806732592 66 24426.75 22773.413548566 1653.33645143401 67 19174.5 21591.2251625127 -2416.72516251267 68 13766 17675.5773732447 -3909.57737324467 69 18999 23576.613887111 -4577.61388711099 70 21745 21831.2746635361 -86.2746635361218 71 34469 28404.9619243286 6064.03807567137 72 13248 19863.9690645763 -6615.96906457627 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 15481.1355231699 -926.59263066812 31888.863677008 74 33269.563690088 16852.5504473886 49686.5769327874 75 19131.6345724171 2705.34148932357 35557.9276555106 76 20076.0701545607 3640.50247065021 36511.6378384712 77 18904.6251735400 2459.78811952451 35349.4622275554 78 23414.6892087322 6960.5880064836 39868.7904109807 79 19779.1430213657 3315.78288394064 36242.5031587907 80 15065.3512252687 -1407.26264306659 31537.965093604 81 20704.3836417496 4222.52123800438 37186.2460454948 82 21758.9754462404 5267.86969384446 38250.0811986364 83 31958.7976800713 15458.4537570670 48459.1416030756 84 15743.8056112086 -765.771313053903 32253.3825354712

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/12idi1275840200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/12idi1275840200.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/22idi1275840200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/22idi1275840200.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/3uru21275840200.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t12758403013ujazyv8ltrtfbv/3uru21275840200.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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