*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Dec 2009 02:50:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6.htm/, Retrieved Fri, 04 Dec 2009 10:53:04 +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/2009/Dec/04/t12599203801qhvw1b2uve15w6.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:

ws9p2.2es

Dataseries X:

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2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.960596258085363 beta 0.155180585289121 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3295.32 2962.76559155129 332.554408448710 14 3363.99 3392.98879678833 -28.9987967883330 15 3494.17 3546.58680895763 -52.4168089576297 16 3667.03 3722.78042621769 -55.7504262176926 17 3813.06 3855.97632952237 -42.9163295223652 18 3917.96 3947.54155853685 -29.5815585368532 19 3895.51 3794.2083205011 101.301679498902 20 3801.06 3854.59220615474 -53.5322061547413 21 3570.12 3873.8904436771 -303.770443677099 22 3701.61 3632.87127883522 68.7387211647838 23 3862.27 3788.57541742667 73.6945825733328 24 3970.1 3865.00887974193 105.091120258073 25 4138.52 3998.12875106984 140.391248930162 26 4199.75 4217.02339826659 -17.2733982665886 27 4290.89 4391.40027088035 -100.510270880351 28 4443.91 4533.88370146698 -89.9737014669781 29 4502.64 4632.48542203175 -129.845422031752 30 4356.98 4613.6483417335 -256.668341733503 31 4591.27 4158.21487503664 433.055124963359 32 4696.96 4491.69926816083 205.260731839172 33 4621.4 4765.9242492627 -144.524249262704 34 4562.84 4747.24615518697 -184.406155186975 35 4202.52 4678.39475203288 -475.874752032879 36 4296.49 4150.75837033177 145.731629668234 37 4435.23 4255.07810908536 180.151890914637 38 4105.18 4445.09564869543 -339.91564869543 39 4116.68 4193.94661730321 -77.2666173032057 40 3844.49 4241.83793067068 -397.347930670677 41 3720.98 3867.54902688718 -146.569026887182 42 3674.4 3653.15282874672 21.2471712532843 43 3857.62 3402.43741968196 455.182580318040 44 3801.06 3663.70342094598 137.356579054023 45 3504.37 3746.06217649642 -241.69217649642 46 3032.6 3487.58628066273 -454.986280662727 47 3047.03 2954.27508070904 92.7549192909573 48 2962.34 2912.93021982351 49.4097801764929 49 2197.82 2832.39247361421 -634.572473614209 50 2014.45 2011.17217036097 3.27782963902678 51 1862.83 1867.95929153018 -5.12929153018263 52 1905.41 1721.00559015236 184.404409847640 53 1810.99 1769.78587813698 41.2041218630247 54 1670.07 1654.48280602717 15.5871939728315 55 1864.44 1433.03442239943 431.40557760057 56 2052.02 1674.65573155100 377.364268448996 57 2029.6 1967.70100363557 61.8989963644285 58 2070.83 2001.80549300778 69.0245069922157 59 2293.41 2076.08781223182 217.322187768176 60 2443.27 2274.38036988952 168.889630110483 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 2416.71570394995 1956.86969699156 2876.56171090834 62 2455.79179358273 1767.76260019310 3143.82098697235 63 2550.31272869058 1634.17344113523 3466.45201624593 64 2680.65977059481 1519.48977957618 3841.82976161344 65 2783.78612207790 1377.61431506305 4189.95792909274 66 2854.02988129776 1208.61907367176 4499.44068892377 67 2797.38145038882 980.660744445978 4614.10215633167 68 2716.01911918143 749.098026106781 4682.94021225608 69 2697.94865330974 539.53298718693 4856.36431943255 70 2743.24951877555 339.458614270698 5147.0404232804 71 2826.65811423442 134.022440995286 5519.29378747356 72 2834.39557499779 -47.7551012753402 5716.54625127091

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/1rjxm1259920203.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/1rjxm1259920203.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/211mb1259920203.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/211mb1259920203.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/33k341259920203.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599203801qhvw1b2uve15w6/33k341259920203.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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