Exponential smoothing (Single, Additief) Bel20

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 14:23:51 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068.htm/, Retrieved Sun, 16 Jan 2011 15:23:39 +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/2011/Jan/16/t12951878187bhin2fdlb8a068.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

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 2513,17 2466,92 2502,66

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.99995731091006 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 3080.58 2981.85 98.73 3 3106.22 3080.57578530615 25.6442146938498 4 3119.31 3106.21890527181 13.0910947281877 5 3061.26 3119.30944115308 -58.0494411530794 6 3097.31 3061.26247807781 36.0475219221853 7 3161.69 3097.30846116409 64.3815388359058 8 3257.16 3161.6872516107 95.4727483893016 9 3277.01 3257.15592435526 19.8540756447433 10 3295.32 3277.00915244758 18.3108475524209 11 3363.99 3295.31921832658 68.6707816734179 12 3494.17 3363.98706850682 130.182931493176 13 3667.03 3494.16444260913 172.865557390871 14 3813.06 3667.02262052667 146.037379473327 15 3917.96 3813.05376579717 104.906234202827 16 3895.51 3917.95552164833 -22.4455216483325 17 3801.06 3895.51095817889 -94.4509581788925 18 3570.12 3801.06403202545 -230.944032025448 19 3701.61 3570.12985879055 131.480141209446 20 3862.27 3701.60438723243 160.665612767573 21 3970.1 3862.26314133121 107.836858668793 22 4138.52 3970.09539654264 168.424603457359 23 4199.75 4138.51281010695 61.2371898930451 24 4290.89 4199.74738584009 91.1426141599077 25 4443.91 4290.88610920475 153.023890795253 26 4502.64 4443.90346754936 58.7365324506372 27 4356.98 4502.63749259088 -145.657492590884 28 4591.27 4356.9862179858 234.283782014199 29 4696.96 4591.25999863856 105.700001361442 30 4621.4 4696.95548776314 -75.5554877631357 31 4562.84 4621.40322539501 -58.5632253950125 32 4202.52 4562.8425000108 -360.322500010796 33 4296.49 4202.53538183961 93.9546181603891 34 4435.23 4296.48598916285 138.744010837145 35 4105.18 4435.22407714444 -330.044077144442 36 4116.68 4105.19408928129 11.4859107187067 37 3844.49 4116.67950967692 -272.189509676925 38 3720.98 3844.50161952246 -123.521619522459 39 3674.4 3720.98527302553 -46.5852730255251 40 3857.62 3674.40198868291 183.21801131709 41 3801.06 3857.61217858984 -56.5521785898363 42 3504.37 3801.06241416104 -296.692414161038 43 3032.6 3504.38266552915 -471.782665529153 44 3047.03 3032.62013997264 14.4098600273592 45 2962.34 3047.02938485619 -84.6893848561895 46 2197.82 2962.34361531277 -764.523615312767 47 2014.45 2197.85263681738 -183.402636817376 48 1862.83 2014.45782929166 -151.627829291658 49 1905.41 1862.83647285404 42.5735271459582 50 1810.99 1905.40818257487 -94.4181825748706 51 1670.07 1810.99403062629 -140.924030626288 52 1864.44 1670.07601591862 194.363984081382 53 2052.02 1864.4317027784 187.588297221597 54 2029.6 2052.01199202631 -22.4119920263083 55 2070.83 2029.60095674754 41.2290432524567 56 2293.41 2070.82823996966 222.581760030335 57 2443.27 2293.40049818723 149.869501812773 58 2513.17 2443.26360220736 69.9063977926421 59 2466.92 2513.1670157595 -46.2470157594971 60 2502.66 2466.92197424302 35.7380257569844 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 2502.6584743762 2145.05047372262 2860.26647502979 62 2502.6584743762 1996.93518438748 3008.38176436492 63 2502.6584743762 1883.280875538 3122.03607321441 64 2502.6584743762 1787.465371887 3217.85157686541 65 2502.6584743762 1703.04998408005 3302.26696467236 66 2502.6584743762 1626.73250623777 3378.58444251464 67 2502.6584743762 1556.55125763762 3448.76569111478 68 2502.6584743762 1491.22808652424 3514.08886222817 69 2502.6584743762 1429.87518154585 3575.44176720656 70 2502.6584743762 1371.84613040329 3633.47081834911 71 2502.6584743762 1316.65294269135 3688.66400606106 72 2502.6584743762 1263.91649757368 3741.40045117873

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/1lxa91295187828.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/1lxa91295187828.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/2japd1295187828.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/2japd1295187828.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/3u84b1295187828.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t12951878187bhin2fdlb8a068/3u84b1295187828.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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