*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 03:02:15 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t124427896164cki81k0vc1118.htm/, Retrieved Sat, 06 Jun 2009 11:02:45 +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/2009/Jun/06/t124427896164cki81k0vc1118.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,73 1,75 1,75 1,75 1,73 1,74 1,75 1,75 1,34 1,24 1,24 1,26 1,25 1,26 1,26 1,22 1,01 1,03 1,01 1,01 1 0,98 1 1,01 1 1 1 1,03 1,26 1,43 1,61 1,76 1,93 2,16 2,28 2,5 2,63 2,79 3 3,04 3,26 3,5 3,62 3,78 4 4,16 4,29 4,49 4,59 4,79 4,94 4,99 5,24 5,25 5,25 5,25 5,25 5,24 5,25 5,26 5,26 5,25 5,25 5,25 5,26 5,02 4,94 4,76 4,49 4,24 3,94 2,98 2,61 2,28 1,98 2 2,01 2 1,81 0,97 0,39 0,16 0,15 0,22

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.932952155499902 beta 0.189496457771257 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.25 1.55613514957265 -0.306135149572649 14 1.26 1.24174026172699 0.0182597382730081 15 1.26 1.20655177680316 0.0534482231968443 16 1.22 1.15364163644576 0.066358363554239 17 1.01 0.95034094268985 0.0596590573101498 18 1.03 0.98092064214776 0.0490793578522398 19 1.01 1.22114011659760 -0.211140116597604 20 1.01 0.970426238588068 0.0395737614119325 21 1 0.55102937009633 0.44897062990367 22 0.98 0.904620883616097 0.0753791163839029 23 1 1.03257908172319 -0.0325790817231904 24 1.01 1.08155775357132 -0.0715577535713181 25 1 1.03182804490521 -0.0318280449052057 26 1 1.07706301749370 -0.0770630174936968 27 1 1.02041453445696 -0.0204145344569628 28 1.03 0.951513552203646 0.0784864477963538 29 1.26 0.81327672442798 0.44672327557202 30 1.43 1.3268871123142 0.103112887685801 31 1.61 1.73225041648978 -0.122250416489781 32 1.76 1.72917139777662 0.0308286022233808 33 1.93 1.47541402205550 0.454585977944496 34 2.16 1.95653775495551 0.203462245044488 35 2.28 2.36673885446528 -0.0867388544652825 36 2.5 2.52298648122298 -0.0229864812229752 37 2.63 2.69023307474055 -0.0602330747405508 38 2.79 2.86991068644488 -0.0799106864448795 39 3 2.97787626093149 0.0221237390685056 40 3.04 3.12628557745283 -0.0862855774528297 41 3.26 3.00087661391343 0.259123386086571 42 3.5 3.42512374325458 0.0748762567454193 43 3.62 3.89273831067774 -0.272738310677737 44 3.78 3.83662479299525 -0.0566247929952528 45 4 3.5913285059267 0.4086714940733 46 4.16 4.06630054730212 0.0936994526978783 47 4.29 4.38875739711791 -0.0987573971179065 48 4.49 4.57005852830135 -0.080058528301354 49 4.59 4.70346426753753 -0.113464267537532 50 4.79 4.84465151794328 -0.0546515179432818 51 4.94 4.99998060954632 -0.0599806095463196 52 4.99 5.06696329871044 -0.0769632987104432 53 5.24 4.97750001053091 0.262499989469089 54 5.25 5.39723043875835 -0.147230438758349 55 5.25 5.59974324735948 -0.349743247359479 56 5.25 5.438083932831 -0.188083932830997 57 5.25 5.0299050405674 0.220094959432600 58 5.24 5.20305271218159 0.0369472878184061 59 5.25 5.34485212237757 -0.094852122377568 60 5.26 5.41693425669915 -0.156934256699154 61 5.26 5.34867173961789 -0.0886717396178938 62 5.25 5.39360850247778 -0.143608502477775 63 5.25 5.32653687580434 -0.0765368758043357 64 5.25 5.23495690327119 0.0150430967288102 65 5.26 5.12837957159404 0.131620428405959 66 5.02 5.24968385364721 -0.229683853647209 67 4.94 5.19826625598185 -0.258266255981847 68 4.76 4.98553455906218 -0.225534559062178 69 4.49 4.41590765348667 0.0740923465133312 70 4.24 4.26087436358426 -0.0208743635842579 71 3.94 4.14998186561459 -0.209981865614586 72 2.98 3.90022685977977 -0.920226859779767 73 2.61 2.77921823239927 -0.169218232399271 74 2.28 2.38587818868410 -0.105878188684096 75 1.98 2.00572714136778 -0.0257271413677773 76 2 1.62389616393725 0.376103836062746 77 2.01 1.58202552582611 0.427974474173886 78 2 1.72802008633794 0.271979913662062 79 1.81 2.00383490291067 -0.193834902910672 80 0.97 1.72592056673923 -0.75592056673923 81 0.39 0.460302090557214 -0.0703020905572139 82 0.16 -0.0825954090470405 0.242595409047040 83 0.15 -0.160567141812935 0.310567141812935 84 0.22 -0.0804714551562155 0.300471455156215 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 0.095358954104449 -0.369196950475911 0.55991485868481 86 0.0016869236061966 -0.692280948000863 0.695654795213256 87 -0.118043874765269 -1.03390272773684 0.797814978206305 88 -0.288115419315582 -1.42869454772222 0.852463709091057 89 -0.583071609198795 -1.95473184411114 0.788588625713548 90 -0.828154427966192 -2.43870745679227 0.782398600859889 91 -0.866737945478451 -2.72461280360688 0.991136912649974 92 -0.996654140072004 -3.11051223698863 1.11720395684462 93 -1.37257951964057 -3.75112166124944 1.00596262196830 94 -1.67799450997325 -4.32985978736562 0.973870767419127 95 -1.86971259109484 -4.80342469497206 1.06399951278237 96 -2.02691739513862 -5.25085674953783 1.19702195926059

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/1ldeh1244278932.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/1ldeh1244278932.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/2rr1l1244278932.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/2rr1l1244278932.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/3qell1244278932.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t124427896164cki81k0vc1118/3qell1244278932.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=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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by