vraag 3: exponential smoothing (single)

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 05 May 2008 09:27:23 -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/05/t121000134985b8nmv1h9o7x3t.htm/, Retrieved Mon, 05 May 2008 17:29:09 +0200

User-defined keywords:

vraag 3

Dataseries X:

» Textbox « » Textfile « » CSV «

56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.587763292802047 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 53152 56421 -3269 3 53536 54499.6017958301 -963.60179583011 4 52408 53933.232031363 -1525.23203136304 5 41454 53036.7566303219 -11582.7566303219 6 38271 46228.8374535592 -7957.83745355917 7 35306 41551.5127082718 -6245.51270827177 8 26414 37880.6295936209 -11466.6295936209 9 31917 31140.9656263329 776.034373667113 10 38030 31597.0901451270 6432.90985487296 11 27534 35378.1184237259 -7844.11842372591 12 18387 30767.6335498676 -12380.6335498676 13 50556 23490.7516076219 27065.2483923781 14 43901 39398.7111232314 4502.28887676863 15 48572 42044.9912585869 6527.00874141307 16 43899 45881.3274085876 -1982.32740858763 17 37532 44716.1881235044 -7184.18812350441 18 40357 40493.5860559241 -136.586055924097 19 35489 40413.3057859433 -4924.3057859433 20 29027 37518.9796024331 -8491.9796024331 21 34485 32527.7057088992 1957.2942911008 22 42598 33678.1314464193 8919.86855358075 23 30306 38920.9027588333 -8614.9027588333 24 26451 33857.379146132 -7406.379146132 25 47460 29504.1813514610 17955.8186485390 26 50104 40057.9524452827 10046.0475547173 27 61465 45962.6504356893 15502.3495643107 28 53726 55074.3624617769 -1348.36246177694 29 39477 54281.8445013523 -14804.8445013523 30 43895 45580.1003478152 -1685.10034781517 31 31481 44589.6602186814 -13108.6602186814 32 29896 36884.8709243260 -6988.87092432604 33 33842 32777.0691368757 1064.93086312432 34 39120 33402.9964075922 5717.00359240784 35 33702 36763.2412640269 -3061.24126402692 36 25094 34963.9560186210 -9869.95601862096 37 51442 29162.7581693049 22279.2418306951 38 45594 42257.6787088474 3336.32129115263 39 52518 44218.6458967808 8299.35410321918 40 48564 49096.7015926191 -532.701592619109 41 41745 48783.5991504604 -7038.59915046041 42 49585 44646.5689370721 4938.43106292789 43 32747 47549.1974398945 -14802.1974398945 44 33379 38849.0091319161 -5470.00913191609 45 35645 35633.9385528838 11.0614471161825 46 37034 35640.440065464 1393.55993453602 47 35681 36459.5234413039 -778.523441303878 48 20972 36001.9359399195 -15029.9359399195 49 58552 27167.8913012686 31384.1086987314 50 54955 45614.3183716923 9340.68162830766 51 65540 51104.428162562 14435.5718374380 52 51570 59589.1273992151 -8019.12739921507 53 51145 54875.7786736533 -3730.77867365331 54 46641 52682.9639157112 -6041.96391571119 55 35704 49131.7193096216 -13427.7193096216 56 33253 41239.3987933768 -7986.39879337679 57 35193 36545.2867409513 -1352.28674095135 58 41668 35750.4622332772 5917.53776672277 59 34865 39228.5737163267 -4363.57371632668 60 21210 36663.8252604340 -15453.8252604340 61 56126 27580.6340389739 28545.3659610261 62 49231 44358.5523304661 4872.44766953393 63 59723 47222.398216717 12500.601783283 64 48103 54569.7930828666 -6466.79308286656 65 47472 50768.8494866114 -3296.84948661141 66 50497 48831.0823764879 1665.91762351205 67 40059 49810.2476044204 -9751.24760442035 68 34149 44078.8222035182 -9929.82220351817 69 36860 38242.4372082394 -1382.43720823945 70 46356 37429.8913626326 8926.10863736744 71 36577 42676.3303672404 -6099.33036724044 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 39091.3678667037 18712.1183588238 59470.6173745835 73 39091.3678667037 15452.6182817948 62730.1174516126 74 39091.3678667037 12591.0442201585 65591.6915132489 75 39091.3678667037 10009.6927979383 68173.0429354691 76 39091.3678667037 7639.49198880313 70543.2437446042 77 39091.3678667037 5435.80119976917 72746.9345336382 78 39091.3678667037 3367.79247025037 74814.943263157 79 39091.3678667037 1413.11803288451 76769.6177005229 80 39091.3678667037 -445.035383633913 78627.7711170413 81 39091.3678667037 -2219.69425238152 80402.4299857889 82 39091.3678667037 -3921.19454058061 82103.930273988 83 39091.3678667037 -5557.90084258356 83740.636575991

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/15wd11210001237.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/15wd11210001237.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/23sst1210001237.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/23sst1210001237.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/3w6oy1210001237.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t121000134985b8nmv1h9o7x3t/3w6oy1210001237.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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