exponential smoothing mndlijkse bezoekers VS

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 05:47:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu.htm/, Retrieved Wed, 20 Jan 2010 13:49:15 +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/2010/Jan/20/t12639917515n7ho4csehly7cu.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 «

2357402 2199181 2603060 2629720 2638792 2717481 3810804 3871664 2998364 2923432 2712359 2996099 2395029 2483862 3120231 3360606 3177203 3062783 4242509 4026394 3192481 3118695 2782482 3209833 2630190 2592882 3785309 3231539 3421369 3312134 4647303 4289177 3463853 3304422 3006121 3464238 2921118 2624018 3500718 3939351 3467672 3343628 4852445 4597807 3653145 3572079 3334861 3695369 3075704 2852998 3942704 4004560 3822145 3760085 5267816 5271333 4144142 4109749 3896808 4211074 3402318 3279817 4706628 4079499 4344530 4048625 5394915 5611967 4145481 4025610 3552218 3910443

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.322318927826622 beta 0 gamma 0.338239344476265 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2395029 2203500.6160181 191528.383981902 14 2483862 2354144.51729817 129717.482701827 15 3120231 3024971.32671285 95259.6732871505 16 3360606 3305337.8863403 55268.1136596985 17 3177203 3160208.73307108 16994.2669289159 18 3062783 3068546.80818926 -5763.80818926031 19 4242509 4251562.93097811 -9053.9309781082 20 4026394 4335650.44624688 -309256.446246878 21 3192481 3272999.23247284 -80518.2324728402 22 3118695 3139278.4121909 -20583.4121909016 23 2782482 2881878.36115006 -99396.3611500566 24 3209833 3138729.54666279 71103.4533372121 25 2630190 2572471.79654668 57718.2034533215 26 2592882 2671481.48897259 -78599.488972587 27 3785309 3320809.75094113 464499.249058865 28 3231539 3737656.90952928 -506117.909529283 29 3421369 3388407.38733092 32961.6126690833 30 3312134 3287221.1879598 24912.8120402023 31 4647303 4565262.47939346 82040.5206065373 32 4289177 4606439.06063027 -317262.060630268 33 3463853 3516916.71738083 -53063.7173808296 34 3304422 3395459.5595987 -91037.5595986987 35 3006121 3074556.92854807 -68435.9285480664 36 3464238 3404200.55155149 60037.4484485136 37 2921118 2783641.23042907 137476.769570934 38 2624018 2879134.50493975 -255116.504939751 39 3500718 3640546.3209408 -139828.320940798 40 3939351 3634876.18096818 304474.819031818 41 3467672 3663130.60759224 -195458.607592242 42 3343628 3478396.57140973 -134768.571409733 43 4852445 4768456.26608866 83988.7339113439 44 4597807 4712411.15555613 -114604.155556130 45 3653145 3696038.55611583 -42893.5561158336 46 3572079 3561063.10409942 11015.8959005778 47 3334861 3257637.3131016 77223.6868984029 48 3695369 3692096.49054781 3272.50945219304 49 3075704 3022407.60464566 53296.3953543375 50 2852998 2995061.36786489 -142063.367864885 51 3942704 3883588.37537769 59115.6246223105 52 4004560 4052379.9997273 -47819.9997273041 53 3822145 3838502.99915632 -16357.9991563158 54 3760085 3714367.88751018 45717.1124898195 55 5267816 5241009.38965736 26806.6103426442 56 5271333 5105758.50216002 165574.497839981 57 4144142 4087212.2634823 56929.736517698 58 4109749 3980562.71638617 129186.283613828 59 3896808 3689704.6973044 207103.302695602 60 4211074 4199356.89940781 11717.1005921895 61 3402318 3449644.37776311 -47326.3777631079 62 3279817 3330476.98177587 -50659.9817758738 63 4706628 4424002.23306473 282625.766935269 64 4079499 4654716.02486776 -575217.024867761 65 4344530 4253790.12636495 90739.873635048 66 4048625 4162635.76029505 -114010.760295053 67 5394915 5785139.51096908 -390224.510969085 68 5611967 5535331.23696055 76635.7630394455 69 4145481 4384473.44600513 -238992.446005126 70 4025610 4192393.20272735 -166783.202727349 71 3552218 3815830.19195126 -263612.191951261 72 3910443 4121881.72220775 -211438.722207753 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 3315247.21085082 3119057.91779925 3511436.50390239 74 3214540.73794767 2989427.67937013 3439653.79652520 75 4368723.17218181 4077817.83488473 4659628.50947889 76 4310497.42994896 4001622.09142496 4619372.76847296 77 4248056.03945433 3923094.05599499 4573018.02291366 78 4083022.85264373 3748926.58617268 4417119.11911478 79 5670625.30932799 5220459.54405919 6120791.07459679 80 5652529.9648649 5191774.79468588 6113285.13504393 81 4386470.6409973 3999729.44905311 4773211.83294148 82 4283465.14089223 3889287.06706244 4677643.21472202 83 3920467.14972206 3538392.91773748 4302541.38170663 84 4348079.37232493 3965400.05443253 4730758.69021734

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/1r73f1263991637.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/1r73f1263991637.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/2jjho1263991637.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/2jjho1263991637.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/3f1er1263991637.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t12639917515n7ho4csehly7cu/3f1er1263991637.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=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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