inflation in consumer prices (%)

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 19:16:56 +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/May/19/t1305832410ftq0lxdgkw29s9g.htm/, Retrieved Thu, 19 May 2011 21:13:33 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

0.440 0.548 0.163 0.381 0.164 0.109 0.328 0.435 0.325 0.108 0.054 0.270 0.431 0.215 0.214 0.160 0.427 0.372 0.106 0.053 0.317 0.527 0.472 0.001 0.051 0.418 0.364 0.311 0.052 0.052 0.620 0.616 1.377 0.151 0.501 0.001 0.606 0.050 0.150 0.501 0.299 0.248 0.545 0.444 0.491 0.444 0.050 0.545 0.138 0.423 0.495 0.370 0.388 0.169 0.241 0.014 0.376 0.331 0.789 0.289 0.359 0.236 0.367 0.309 0.551 0.901 0.870 0.160 0.032 0.877 1.812 0.784 0.270 0.462 0.146 0.108 0.132 0.680 0.117 0.345 0.204 0.227 0.236 0.092 0.138 0.046 0.023 0.009 0.142 0.207 0.346 0.207 0.165 0.247 0.123 0.433

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0 beta 0 gamma 0.144366894147601 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.431 0.386323806309158 0.0446761936908425 14 0.215 0.212979180505096 0.00202081949490351 15 0.214 0.22752494958839 -0.0135249495883902 16 0.16 0.158485498325249 0.00151450167475148 17 0.427 0.37084819086021 0.0561518091397898 18 0.372 0.316616013728886 0.0553839862711142 19 0.106 0.288834925031666 -0.182834925031666 20 0.053 0.404561238766747 -0.351561238766747 21 0.317 0.316975673160855 2.43268391449947e-05 22 0.527 0.108584514255159 0.418415485744841 23 0.472 0.0539986342485437 0.418001365751456 24 0.001 0.248284557096173 -0.247284557096173 25 0.051 0.401086340442924 -0.350086340442924 26 0.418 0.217776699151086 0.200223300848914 27 0.364 0.230329691722775 0.133670308277225 28 0.311 0.162045323113063 0.148954676886937 29 0.052 0.38691877155086 -0.33491877155086 30 0.052 0.331421745336218 -0.279421745336218 31 0.62 0.267935799520284 0.352064200479716 32 0.616 0.361204195970919 0.254795804029081 33 1.377 0.323594483494426 1.05340551650557 34 0.151 0.172510523248285 -0.0215105232482846 35 0.501 0.116722264178845 0.384277735821155 36 0.001 0.216998433463264 -0.215998433463264 37 0.606 0.357810741599315 0.248189258400685 38 0.05 0.25178614889252 -0.20178614889252 39 0.15 0.254783133690003 -0.104783133690003 40 0.501 0.187334017405296 0.313665982594704 41 0.299 0.345536473558083 -0.0465364735580834 42 0.248 0.297063714700177 -0.0490637147001771 43 0.545 0.325301005053428 0.219698994946572 44 0.444 0.406138302777486 0.0378616972225141 45 0.491 0.485395598713538 0.0056044012864615 46 0.444 0.172862404251645 0.271137595748355 47 0.05 0.175707592952947 -0.125707592952947 48 0.545 0.18959475182542 0.35540524817458 49 0.138 0.401633860459003 -0.263633860459003 50 0.423 0.227168237871728 0.195831762128272 51 0.495 0.244505673565849 0.250494326434151 52 0.37 0.237316389870215 0.132683610129785 53 0.388 0.345651535005459 0.0423484649945405 54 0.169 0.295819141529303 -0.126819141529303 55 0.241 0.364194597344315 -0.123194597344315 56 0.014 0.419863992763976 -0.405863992763976 57 0.376 0.495945130248409 -0.119945130248409 58 0.331 0.216245860261581 0.114754139738419 59 0.789 0.160705563160867 0.628294436839133 60 0.289 0.245705622725122 0.0432943772748776 61 0.359 0.370809243532144 -0.0118092435321445 62 0.236 0.260514884114387 -0.0245148841143871 63 0.367 0.286235809611317 0.0807641903886827 64 0.309 0.261550213030941 0.0474497869690593 65 0.551 0.358719504606986 0.192280495393014 66 0.901 0.282987903032876 0.618012096967124 67 0.87 0.353235254951057 0.516764745048943 68 0.16 0.368377714245271 -0.208377714245271 69 0.032 0.488029374769362 -0.456029374769362 70 0.877 0.237377563378569 0.639622436621431 71 1.812 0.256332111298819 1.55566788870118 72 0.784 0.256880173164005 0.527119826835996 73 0.27 0.3763064984068 -0.1063064984068 74 0.462 0.261981824378854 0.200018175621146 75 0.146 0.303689304048226 -0.157689304048226 76 0.108 0.273612108545154 -0.165612108545154 77 0.132 0.393970839588824 -0.261970839588824 78 0.68 0.379412504742173 0.300587495257827 79 0.117 0.436106489258548 -0.319106489258548 80 0.345 0.344821533458532 0.000178466541468136 81 0.204 0.43032606610757 -0.22632606610757 82 0.227 0.336058667370351 -0.10905866737035 83 0.236 0.490152801987282 -0.254152801987282 84 0.092 0.339361877491228 -0.247361877491228 85 0.138 0.367867749660774 -0.229867749660774 86 0.046 0.29641568201754 -0.25041568201754 87 0.023 0.286283692638016 -0.263283692638016 88 0.009 0.254459507152157 -0.245459507152157 89 0.142 0.362924074480643 -0.220924074480643 90 0.207 0.430835465183252 -0.223835465183252 91 0.346 0.397432245061054 -0.0514322450610543 92 0.207 0.351374448411832 -0.144374448411832 93 0.165 0.405166842631687 -0.240166842631687 94 0.247 0.326357937097361 -0.0793579370973606 95 0.123 0.462004092043866 -0.339004092043866 96 0.433 0.30936237848795 0.12363762151205 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 0.340967642012345 0.248671358820145 0.433263925204545 98 0.265143950175677 0.172847666983477 0.357440233367878 99 0.252922174186256 0.160625890994055 0.345218457378456 100 0.223117218214227 0.130820935022027 0.315413501406427 101 0.337207872202658 0.244911589010458 0.429504155394859 102 0.405946972805201 0.313650689613 0.498243255997401 103 0.39726315699572 0.30496687380352 0.48955944018792 104 0.336671529355768 0.244375246163567 0.428967812547968 105 0.377366393197618 0.285070110005417 0.469662676389818 106 0.320732846364913 0.228436563172713 0.413029129557113 107 0.420700737384418 0.328404454192218 0.512997020576619 108 0.333252451748585 -228.341438594071 229.007943497568

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/19ana1305832615.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/19ana1305832615.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/20rwb1305832615.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/20rwb1305832615.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/3o8om1305832615.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832410ftq0lxdgkw29s9g/3o8om1305832615.ps (open in new window)

Parameters (Session):

par1 = Studio 100 PRIJS 2005 ; par2 = Studio 100 PRIJS 2005 ; par3 = Studio 100 PRIJS 2005 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;

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

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