Exponential_Smoothing_Reeks_B_Jeroen_Kinne

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 16 Aug 2010 15:24:14 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t.htm/, Retrieved Mon, 16 Aug 2010 17:23:54 +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/2010/Aug/16/t12819722302x93dh1yxkw668t.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:

Jeroen_Kinne

Dataseries X:

» Textbox « » Textfile « » CSV «

430 429 428 426 424 423 424 426 427 427 428 430 432 435 426 411 405 403 402 399 392 387 380 379 386 385 365 356 338 338 343 338 320 316 317 315 317 321 303 303 290 285 300 291 278 273 277 269 275 278 255 254 245 240 261 247 229 213 218 206 217 219 196 193 188 171 190 180 149 135 151 134 145 151 137 124 125 109 131 133 103 85 104 82

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.289075319272455 beta 0.279089476738451 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 432 438.898544293284 -6.89854429328369 14 435 439.588191700283 -4.58819170028295 15 426 429.033615688526 -3.03361568852637 16 411 413.220559235091 -2.2205592350914 17 405 407.049203980354 -2.04920398035432 18 403 405.234879262218 -2.23487926221816 19 402 401.684145910429 0.315854089571133 20 399 399.861758086254 -0.86175808625353 21 392 396.82409187658 -4.82409187658021 22 387 392.119785790203 -5.11978579020285 23 380 388.454794455973 -8.45479445597346 24 379 384.172393304825 -5.17239330482471 25 386 376.185188686141 9.81481131385937 26 385 380.161767893433 4.83823210656709 27 365 372.519373653186 -7.51937365318588 28 356 355.594779872574 0.405220127426162 29 338 348.950662500551 -10.9506625005515 30 338 341.754564225453 -3.75456422545290 31 343 336.676920892576 6.32307910742367 32 338 333.590722901975 4.40927709802457 33 320 327.969073031903 -7.96907303190301 34 316 320.192986655638 -4.19298665563781 35 317 312.632742874520 4.36725712548042 36 315 312.621522250419 2.37847774958055 37 317 315.543876413973 1.45612358602699 38 321 312.228349330538 8.77165066946162 39 303 298.830868400547 4.16913159945295 40 303 292.060983440309 10.9390165596913 41 290 283.260474175589 6.73952582441069 42 285 287.890663970284 -2.89066397028449 43 300 291.604706748857 8.39529325114307 44 291 290.797249982095 0.202750017904634 45 278 279.135422883107 -1.13542288310725 46 273 278.724118657224 -5.72411865722393 47 277 279.089544421879 -2.08954442187934 48 269 277.929911950002 -8.92991195000207 49 275 277.642399308342 -2.64239930834185 50 278 278.721962385085 -0.721962385084964 51 255 261.734565583615 -6.73456558361477 52 254 256.010769194701 -2.01076919470103 53 245 240.88943875154 4.11056124845996 54 240 236.534860652266 3.46513934773409 55 261 246.292875104851 14.7071248951487 56 247 241.935151923681 5.06484807631912 57 229 232.176420030279 -3.17642003027919 58 213 227.642466677343 -14.6424666773428 59 218 225.470770073857 -7.47077007385678 60 206 216.702300550868 -10.7023005508676 61 217 216.335559000485 0.664440999514909 62 219 216.537673568524 2.46232643147644 63 196 198.609369711206 -2.60936971120603 64 193 195.512785156476 -2.51278515647567 65 188 184.868378233240 3.13162176676028 66 171 179.088920736665 -8.08892073666513 67 190 185.594416778149 4.40558322185075 68 180 171.980984239628 8.01901576037173 69 149 158.962083943998 -9.96208394399758 70 135 144.113000044135 -9.1130000441351 71 151 142.144852427581 8.85514757241899 72 134 135.826386053537 -1.82638605353671 73 145 139.664563734048 5.33543626595227 74 151 139.587908211005 11.4120917889950 75 137 126.841887228177 10.1581127718226 76 124 127.743624201119 -3.74362420111891 77 125 122.049819958814 2.95018004118644 78 109 112.628086561266 -3.62808656126597 79 131 122.528786250708 8.4712137492922 80 133 116.707952288599 16.2920477114015 81 103 103.103878543786 -0.103878543786308 82 85 96.424073755864 -11.4240737558641 83 104 103.291671624255 0.70832837574494 84 82 92.6595025076693 -10.6595025076693 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 95.4172368171227 82.2422049101686 108.592268724077 86 96.201243117584 82.0429725652299 110.359513669938 87 83.801513521718 68.7120031848829 98.891023858553 88 74.4484737165014 58.2179844321583 90.6789630008445 89 72.5333453398866 54.2753014124649 90.7913892673083 90 61.8075659592981 42.4970600452776 81.1180718733186 91 70.4602895932986 45.8686018418438 95.0519773447533 92 65.8180551648477 38.1003483617248 93.5357619679706 93 47.9225959710934 22.1667077179168 73.67848422427 94 38.2000015227147 12.5090408447129 63.8909622007166 95 43.5931557867283 9.3545766862781 77.8317348871784 96 32.8446295185282 2.91548640506613 62.7737726319902

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/1oig41281972252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/1oig41281972252.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/2oig41281972252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/2oig41281972252.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/3z9x71281972252.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819722302x93dh1yxkw668t/3z9x71281972252.ps (open in new window)

Parameters (Session):

par1 = 4 ;

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

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