gaelle.wauters-exponental smoothing- werkloosheid

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 03:28:26 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep.htm/, Retrieved Mon, 26 May 2008 11:29:26 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

9.8 9.7 9.5 9.3 9.1 9 9.5 10 10.2 10.1 10 9.9 10 9.9 9.7 9.5 9.2 9 9.3 9.8 9.8 9.6 9.4 9.3 9.2 9.2 9 8.8 8.7 8.7 9.1 9.7 9.8 9.6 9.4 9.4 9.5 9.4 9.3 9.2 9 8.9 9.2 9.8 9.9 9.6 9.2 9.1 9.1 9.1 8.9 8.7 8.5 8.4 8.4 8.7 8.5 8.1 7.8 7.7 7.4 7.2 7 6.6 6.4 6.4 6.8 7.3 7 7 6.7 6.7 6.3 6.2 6 6.3 6.2 6.1 6.2 6.6 6.6 7.8 7.4 7.4 7.5 7.4 7.4 7 6.9 6.9 7.6 7.7 7.6 8.2 8 8.1 8.3 8.2 8.1 7.7 7.6 7.7 8.2 8.4 8.4 8.6 8.4 8.5 8.7 8.7 8.6 7.4 7.3 7.4 9 9.2 9.2 8.5 8.3 8.3 8.6 8.6 8.5 8.1 8.1 8 8.6 8.7 8.7 8.6 8.4 8.4 8.7 8.7 8.5 8.3 8.3 8.3 8.1 8.2 8.1 8.1 7.9 7.7 8.1 8 7.7 7.8 7.6 7.4 7.3 7.4 7.1 7.3 7.1 7.1

Text written by user:

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 9.5 9.7 -0.199999999999999 4 9.3 9.5 -0.199999999999999 5 9.1 9.3 -0.200000000000001 6 9 9.1 -0.0999999999999996 7 9.5 9 0.5 8 10 9.5 0.5 9 10.2 10 0.199999999999999 10 10.1 10.2 -0.0999999999999996 11 10 10.1 -0.0999999999999996 12 9.9 10 -0.0999999999999996 13 10 9.9 0.0999999999999996 14 9.9 10 -0.0999999999999996 15 9.7 9.9 -0.200000000000001 16 9.5 9.7 -0.199999999999999 17 9.2 9.5 -0.300000000000001 18 9 9.2 -0.199999999999999 19 9.3 9 0.300000000000001 20 9.8 9.3 0.5 21 9.8 9.8 0 22 9.6 9.8 -0.200000000000001 23 9.4 9.6 -0.199999999999999 24 9.3 9.4 -0.0999999999999996 25 9.2 9.3 -0.100000000000001 26 9.2 9.2 0 27 9 9.2 -0.199999999999999 28 8.8 9 -0.199999999999999 29 8.7 8.8 -0.100000000000001 30 8.7 8.7 0 31 9.1 8.7 0.4 32 9.7 9.1 0.6 33 9.8 9.7 0.100000000000001 34 9.6 9.8 -0.200000000000001 35 9.4 9.6 -0.199999999999999 36 9.4 9.4 0 37 9.5 9.4 0.0999999999999996 38 9.4 9.5 -0.0999999999999996 39 9.3 9.4 -0.0999999999999996 40 9.2 9.3 -0.100000000000001 41 9 9.2 -0.199999999999999 42 8.9 9 -0.0999999999999996 43 9.2 8.9 0.299999999999999 44 9.8 9.2 0.600000000000001 45 9.9 9.8 0.0999999999999996 46 9.6 9.9 -0.300000000000001 47 9.2 9.6 -0.4 48 9.1 9.2 -0.0999999999999996 49 9.1 9.1 0 50 9.1 9.1 0 51 8.9 9.1 -0.199999999999999 52 8.7 8.9 -0.200000000000001 53 8.5 8.7 -0.199999999999999 54 8.4 8.5 -0.0999999999999996 55 8.4 8.4 0 56 8.7 8.4 0.299999999999999 57 8.5 8.7 -0.199999999999999 58 8.1 8.5 -0.4 59 7.8 8.1 -0.3 60 7.7 7.8 -0.0999999999999996 61 7.4 7.7 -0.3 62 7.2 7.4 -0.2 63 7 7.2 -0.2 64 6.6 7 -0.4 65 6.4 6.6 -0.199999999999999 66 6.4 6.4 0 67 6.8 6.4 0.399999999999999 68 7.3 6.8 0.5 69 7 7.3 -0.3 70 7 7 0 71 6.7 7 -0.3 72 6.7 6.7 0 73 6.3 6.7 -0.4 74 6.2 6.3 -0.0999999999999996 75 6 6.2 -0.2 76 6.3 6 0.3 77 6.2 6.3 -0.0999999999999996 78 6.1 6.2 -0.100000000000001 79 6.2 6.1 0.100000000000001 80 6.6 6.2 0.399999999999999 81 6.6 6.6 0 82 7.8 6.6 1.2 83 7.4 7.8 -0.399999999999999 84 7.4 7.4 0 85 7.5 7.4 0.0999999999999996 86 7.4 7.5 -0.0999999999999996 87 7.4 7.4 0 88 7 7.4 -0.4 89 6.9 7 -0.0999999999999996 90 6.9 6.9 0 91 7.6 6.9 0.700 92 7.7 7.6 0.100000000000001 93 7.6 7.7 -0.100000000000001 94 8.2 7.6 0.6 95 8 8.2 -0.199999999999999 96 8.1 8 0.0999999999999996 97 8.3 8.1 0.200000000000001 98 8.2 8.3 -0.100000000000001 99 8.1 8.2 -0.0999999999999996 100 7.7 8.1 -0.399999999999999 101 7.6 7.7 -0.100000000000001 102 7.7 7.6 0.100000000000001 103 8.2 7.7 0.499999999999999 104 8.4 8.2 0.200000000000001 105 8.4 8.4 0 106 8.6 8.4 0.199999999999999 107 8.4 8.6 -0.199999999999999 108 8.5 8.4 0.0999999999999996 109 8.7 8.5 0.199999999999999 110 8.7 8.7 0 111 8.6 8.7 -0.0999999999999996 112 7.4 8.6 -1.2 113 7.3 7.4 -0.100000000000001 114 7.4 7.3 0.100000000000001 115 9 7.4 1.6 116 9.2 9 0.199999999999999 117 9.2 9.2 0 118 8.5 9.2 -0.700 119 8.3 8.5 -0.199999999999999 120 8.3 8.3 0 121 8.6 8.3 0.299999999999999 122 8.6 8.6 0 123 8.5 8.6 -0.0999999999999996 124 8.1 8.5 -0.4 125 8.1 8.1 0 126 8 8.1 -0.0999999999999996 127 8.6 8 0.6 128 8.7 8.6 0.0999999999999996 129 8.7 8.7 0 130 8.6 8.7 -0.0999999999999996 131 8.4 8.6 -0.199999999999999 132 8.4 8.4 0 133 8.7 8.4 0.299999999999999 134 8.7 8.7 0 135 8.5 8.7 -0.199999999999999 136 8.3 8.5 -0.199999999999999 137 8.3 8.3 0 138 8.3 8.3 0 139 8.1 8.3 -0.200000000000001 140 8.2 8.1 0.0999999999999996 141 8.1 8.2 -0.0999999999999996 142 8.1 8.1 0 143 7.9 8.1 -0.199999999999999 144 7.7 7.9 -0.2 145 8.1 7.7 0.399999999999999 146 8 8.1 -0.0999999999999996 147 7.7 8 -0.3 148 7.8 7.7 0.0999999999999996 149 7.6 7.8 -0.2 150 7.4 7.6 -0.199999999999999 151 7.3 7.4 -0.100000000000001 152 7.4 7.3 0.100000000000001 153 7.1 7.4 -0.300000000000001 154 7.3 7.1 0.2 155 7.1 7.3 -0.2 156 7.1 7.1 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 157 7.1 6.50046464838099 7.699535351619 158 7.1 6.25212897461828 7.94787102538172 159 7.1 6.06157431006221 8.1384256899378 160 7.1 5.90092929676199 8.29907070323801 161 7.1 5.75939819886566 8.44060180113434 162 7.1 5.63144430577334 8.56855569422666 163 7.1 5.51377855742444 8.68622144257556 164 7.1 5.40425794923655 8.79574205076344 165 7.1 5.30139394514298 8.89860605485702 166 7.1 5.20410275109402 8.99589724890598 167 7.1 5.11156619012596 9.08843380987404 168 7.1 5.02314862012441 9.17685137987558

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/161ri1211794099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/161ri1211794099.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/2ejnh1211794099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/2ejnh1211794099.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/3k3nx1211794099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211794162x2y1fc7y1o0pbep/3k3nx1211794099.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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