Glenn Van Passen 2 Mar 01-A opgave 10 oefening 2

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 12:30:05 -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/Jun/01/t1212345064kh4srvidozqj9uz.htm/, Retrieved Sun, 01 Jun 2008 18:31:04 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

11835.70 11542.20 13093.70 11180.20 12035.70 12112.00 10875.20 9897.30 11672.10 12385.70 11405.60 9830.90 11025.10 10853.80 12252.60 11839.40 11669.10 11601.40 11178.40 9516.40 12102.80 12989.00 11610.20 10205.50 11356.20 11307.10 12648.60 11947.20 11714.10 12192.50 11268.80 9097.40 12639.80 13040.10 11687.30 11191.70 11391.90 11793.10 13933.20 12778.10 11810.30 13698.40 11956.60 10723.80 13938.90 13979.80 13807.40 12973.90 12509.80 12934.10 14908.30 13772.10 13012.60 14049.90 11816.50 11593.20 14466.20 13615.90 14733.90 13880.70 13527.50 13584.00 16170.20 13260.60 14741.90 15486.50 13154.50 12621.20 15031.60 15452.40 15428.00 13105.90 14716.80 14180.00 16202.20 14392.40 15140.60 15960.10 14729.90 13705.20 15728.50 17315.60 16152.80

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 0.17805872722291 beta 0.0478690546647562 gamma 0.58355895556279 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 11025.1 11016.3870620836 8.7129379164071 14 10853.8 10863.0373765497 -9.23737654965407 15 12252.6 12273.6993659766 -21.0993659766045 16 11839.4 11825.1308426692 14.2691573308184 17 11669.1 11636.940652566 32.1593474339898 18 11601.4 11564.6848998354 36.7151001646198 19 11178.4 11134.4553086590 43.9446913409683 20 9516.4 9470.64638919494 45.7536108050554 21 12102.8 12033.6303449515 69.1696550485485 22 12989 12921.9563717285 67.0436282714709 23 11610.2 11570.7460974028 39.4539025971972 24 10205.5 10168.1181557252 37.3818442748252 25 11356.2 11256.9999491360 99.200050863983 26 11307.1 11110.8717665178 196.228233482154 27 12648.6 12595.6832158645 52.916784135472 28 11947.2 12171.4217199111 -224.221719911111 29 11714.1 11948.9203377463 -234.820337746269 30 12192.5 11831.5898388765 360.910161123458 31 11268.8 11455.4714702502 -186.671470250218 32 9097.4 9714.8118448612 -617.41184486121 33 12639.8 12194.7233343156 445.076665684384 34 13040.1 13161.7591863968 -121.659186396799 35 11687.3 11742.6771031474 -55.3771031473989 36 11191.7 10302.6732522839 889.02674771613 37 11391.9 11606.5901758006 -214.690175800575 38 11793.1 11450.1689564520 342.93104354804 39 13933.2 12929.1131519386 1004.08684806136 40 12778.1 12530.2145032048 247.885496795167 41 11810.3 12392.0803782404 -581.780378240381 42 13698.4 12518.3033063471 1180.09669365291 43 11956.6 12003.9300753699 -47.3300753699023 44 10723.8 9981.22134570794 742.578654292056 45 13938.9 13514.9818584203 423.918141579677 46 13979.8 14297.4127364848 -317.612736484789 47 13807.4 12785.6110896544 1021.78891034562 48 12973.9 11914.8953314788 1059.00466852118 49 12509.8 12827.3061342329 -317.506134232914 50 12934.1 12974.9410424626 -40.8410424626109 51 14908.3 14927.8086018990 -19.5086018990442 52 13772.1 13919.7558657906 -147.655865790593 53 13012.6 13279.7565899022 -267.156589902186 54 14049.9 14435.3190521728 -385.419052172778 55 11816.5 12961.0793369486 -1144.57933694863 56 11593.2 11013.8774169365 579.32258306352 57 14466.2 14568.3003079413 -102.100307941249 58 13615.9 14918.4772920713 -1302.57729207126 59 14733.9 13823.4566599641 910.443340035932 60 13880.7 12892.6787134222 988.021286577774 61 13527.5 13123.3740067632 404.125993236834 62 13584 13542.7039347324 41.296065267572 63 16170.2 15607.1920689984 563.007931001555 64 13260.6 14584.3120785899 -1323.71207858991 65 14741.9 13642.7457952937 1099.15420470629 66 15486.5 15050.1933174055 436.306682594521 67 13154.5 13238.1520312516 -83.652031251555 68 12621.2 12242.4751487302 378.724851269786 69 15031.6 15701.1610463770 -669.561046376955 70 15452.4 15359.7519949646 92.6480050353839 71 15428 15610.6308813893 -182.630881389294 72 13105.9 14443.2602639418 -1337.36026394177 73 14716.8 13961.0841708753 755.715829124656 74 14180 14274.0196794399 -94.0196794398598 75 16202.2 16673.7299494038 -471.529949403815 76 14392.4 14460.7603890167 -68.3603890166632 77 15140.6 14918.8105645343 221.789435465673 78 15960.1 15877.0702529629 83.0297470370679 79 14729.9 13663.6345116966 1066.26548830342 80 13705.2 13052.2723736871 652.927626312925 81 15728.5 16210.1127280847 -481.612728084703 82 17315.6 16276.6531345611 1038.94686543892 83 16152.8 16578.8065691304 -426.006569130441 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 84 14697.9621533646 13965.1403525942 15430.783954135 85 15534.7538230625 14769.9976848840 16299.5099612411 86 15298.6899504284 14505.7276131855 16091.6522876714 87 17716.4181766161 16863.5028696930 18569.3334835393 88 15635.2966464486 14780.6560577612 16489.9372351359 89 16311.6031963946 15411.4727594712 17211.7336333181 90 17248.7402084333 16293.0810127026 18204.3994041639 91 15351.4301122985 14407.6368428468 16295.2233817502 92 14282.9431585947 13333.1710546621 15232.7152625274 93 16924.0309633257 15853.8143388296 17994.2475878217 94 17857.3644528854 16713.5592184047 19001.169687366 95 17231.9970295433 16334.1984329729 18129.7956261136

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/1fpwb1212344998.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/1fpwb1212344998.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/2hsst1212344998.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/2hsst1212344998.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/3skoc1212344998.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345064kh4srvidozqj9uz/3skoc1212344998.ps (open in new window)

Parameters (Session):

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

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