ws9 exponential smoothing

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Dec 2009 14:50:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5.htm/, Retrieved Wed, 02 Dec 2009 22:51:48 +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/2009/Dec/02/t1259790703n9jcszml6488hp5.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 «

216234 213587 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186412 189226 191563 188906 186005 195309 223532 226899 214126

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.719322263189433 beta 0.175883227652681 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 235243 226737.096173609 8505.90382639144 14 230354 229123.663657679 1230.33634232086 15 227184 228466.606944256 -1282.60694425550 16 221678 223800.799736545 -2122.79973654507 17 217142 219569.963404597 -2427.96340459693 18 219452 221777.488382775 -2325.48838277528 19 256446 253078.86492726 3367.13507274029 20 265845 275261.348592982 -9416.34859298158 21 248624 249812.961546658 -1188.96154665813 22 241114 248787.113109431 -7673.11310943082 23 229245 230323.758223731 -1078.75822373136 24 231805 230951.619090012 853.3809099879 25 219277 230021.713136055 -10744.7131360545 26 219313 213007.912949720 6305.08705027957 27 212610 212302.915434283 307.084565716534 28 214771 205964.418159997 8806.58184000323 29 211142 208148.332026315 2993.66797368464 30 211457 213328.520399341 -1871.52039934113 31 240048 244474.550451757 -4426.55045175678 32 240636 254512.147891949 -13876.147891949 33 230580 227069.630096231 3510.36990376926 34 208795 225903.193603848 -17108.1936038479 35 197922 200792.922646433 -2870.92264643265 36 194596 197141.523346073 -2545.52334607317 37 194581 187540.072309868 7040.9276901315 38 185686 187093.073748093 -1407.07374809266 39 178106 177822.535574330 283.464425669546 40 172608 172111.618182285 496.381817715155 41 167302 164666.660612638 2635.33938736227 42 168053 164733.29100947 3319.70899053002 43 202300 189312.370753273 12987.6292467267 44 202388 206422.384439344 -4034.38443934402 45 182516 192976.209422581 -10460.2094225812 46 173476 176004.181549568 -2528.18154956779 47 166444 166722.951638836 -278.951638836093 48 171297 165447.794630753 5849.20536924707 49 169701 166504.988684226 3196.01131577438 50 164182 162870.492996047 1311.50700395295 51 161914 158194.423186792 3719.57681320762 52 159612 157313.046426763 2298.95357323682 53 151001 154302.302218677 -3301.30221867724 54 158114 151651.041667999 6462.9583320012 55 186530 181293.236881336 5236.76311866372 56 187069 188881.128254835 -1812.12825483538 57 174330 177306.013959189 -2976.01395918918 58 169362 170383.00391962 -1021.00391961989 59 166827 165305.241737241 1521.75826275870 60 178037 169696.530607771 8340.46939222876 61 186412 174725.036040875 11686.9639591248 62 189226 180249.057187600 8976.9428124004 63 191563 186117.340911741 5445.65908825921 64 188906 190545.546284782 -1639.54628478200 65 186005 186419.699256824 -414.699256823573 66 195309 194188.497080277 1120.50291972345 67 223532 230249.192150284 -6717.1921502841 68 226899 230891.317106715 -3992.31710671465 69 214126 217945.224671812 -3819.22467181191 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 70 212749.177448599 201158.928045624 224339.426851573 71 211087.295561823 196017.170010025 226157.421113621 72 220331.805448108 201147.479503513 239516.131392704 73 221516.021217242 198492.334928469 244539.707506015 74 216743.438960666 190321.804979516 243165.072941816 75 213364.77811028 183397.841609235 243331.714611325 76 209566.740699672 176100.354199004 243033.12720034 77 204836.148573866 168029.552205537 241642.744942196 78 212386.963886877 170027.002367126 254746.925406628 79 246091.041662252 192384.317915784 299797.765408720 80 251602.164189145 191711.285210845 311493.043167446 81 239704.508944503 178808.146533843 300600.871355164

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/1wvlr1259790647.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/1wvlr1259790647.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/2k4ap1259790647.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/2k4ap1259790647.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/3o3a81259790647.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790703n9jcszml6488hp5/3o3a81259790647.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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=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