iko opgave 10 oplossing 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 14:54:11 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16.htm/, Retrieved Thu, 19 May 2011 16:53:38 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

5939520,00 89948768,00 80953652,00 85942882,00 8944937,00 82975432,00 24940816,00 21973899,00 37950221,00 45949881,00 85950373,00 48960313,00 81954506,00 24960419,00 65973338,00 22950513,00 54963528,00 90995659,00 91967517,00 28999053,00 96990529,00 38979852,00 81496957,00 74982424,00 70976192,00 90990000,00 12998850,00 92986156,00 67994976,00 91022206,00 87992489,00 421022698,00 11018942,00 79100042,00 65996442,00 51000620,00 12996871,00 44994249,00 99996135,00 91977037,00 63974211,00 15998036,00 65974265,00 33984410,00 45939098,00 67935827,00 66921032,00 89911836,00 71890975,00 72880342,00 28871286,00 41844334,00 82847667,00 24871401,00 3867451,00 99896846,00 41890361,00 45884264,00 69884586,00 95896400,00 39904491,00 81900399,00 27909863,00 88900470,00 89917101,00 2945005,00 4934411,00 61957264,00 31946515,00 3938309,00 52933321,00 21947613,00

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0 beta 0 gamma 0.286265298869626 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 81954506 82670206.492058 -715700.492057994 14 24960419 24260878.9253186 699540.074681383 15 65973338 62298285.8615093 3675052.13849071 16 22950513 21293438.8247872 1657074.17521282 17 54963528 52326926.8275468 2636601.17245318 18 90995659 86895100.8807275 4100558.1192725 19 91967517 27317458.6189048 64650058.3810952 20 28999053 24279160.9997002 4719892.00029981 21 96990529 45374218.1875196 51616310.8124804 22 38979852 59576165.711869 -20596313.711869 23 81496957 114931601.835332 -33434644.8353319 24 74982424 63545904.3861768 11436519.6138232 25 70976192 101479198.219442 -30503006.219442 26 90990000 29994766.1720777 60995233.8279223 27 12998850 77416359.0218578 -64417509.0218578 28 92986156 26513226.0448355 66472929.9551645 29 67994976 64447135.8887994 3547840.11120062 30 91022206 106595034.952606 -15572828.9526062 31 87992489 55298053.650113 32694435.349887 32 421022698 30839239.9434361 390183458.056564 33 11018942 72171123.251915 -61152181.2519149 34 79100042 64232338.8345427 14867703.1654573 35 65996442 125737853.013862 -59741411.0138623 36 51000620 79538202.4456177 -28537582.4456177 37 12996871 110125036.648192 -97128165.6481924 38 44994249 56210505.7607682 -11216256.7607682 39 99996135 69691380.0864812 30304754.9135188 40 91977037 53693397.4654222 38283639.5345778 41 63974211 77007309.225137 -13033098.2251369 42 15998036 119888372.911339 -103890336.911339 43 65974265 75734271.9633996 -9760006.96339965 44 33984410 166610301.805772 -132625891.805772 45 45939098 63770534.8285065 -17831436.8285065 46 67935827 79739828.9412088 -11804001.9412088 47 66921032 126241809.09482 -59320777.0948201 48 89911836 82781001.2482031 7130834.75179686 49 71890975 95310850.7855739 -23419875.7855739 50 72880342 61254507.7244933 11625834.2755067 51 28871286 90415968.6659298 -61544682.6659298 52 41844334 74467698.2197461 -32623364.2197461 53 82847667 84261613.9031556 -1413946.90315555 54 24871401 103495984.002679 -78624583.0026795 55 3867451 83608611.813972 -79741160.813972 56 99896846 147233099.632839 -47336253.6328389 57 41890361 67042348.4970693 -25151987.4970693 58 45884264 87135343.8397751 -41251079.8397751 59 69884586 124497918.506727 -54613332.5067266 60 95896400 96515843.4937258 -619443.493725821 61 39904491 100683039.185061 -60778548.1850609 62 81900399 73285908.0271967 8614490.97280332 63 27909863 82499353.0998738 -54589490.0998738 64 88900470 73712889.790602 15187580.209398 65 89917101 94789309.1321042 -4872208.13210419 66 2945005 91433527.4400052 -88488522.4400052 67 4934411 68537080.0952366 -63602669.0952366 68 61957264 150560507.456261 -88603243.4562607 69 31946515 67318949.9976144 -35372434.9976144 70 3938309 84640988.4722276 -80702679.4722276 71 52933321 122188136.380414 -69254815.380414 72 21947613 108010565.90497 -86062952.9049697 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 93273828.0901913 54404802.8448809 132142853.335502 74 84748127.3398675 45879102.0945571 123617152.585178 75 74736105.5196293 35867080.2743189 113605130.76494 76 87150998.1584212 48281972.9131108 126020023.403732 77 104166162.332328 65297137.0870173 143035187.577638 78 73653624.0330558 34784598.7877453 112522649.278366 79 56025123.6480776 17156098.4027671 94894148.893388 80 139231249.065672 100362223.820362 178100274.310983 81 63545164.3658536 24676139.1205432 102414189.611164 82 68310686.3368221 29441661.0915117 107179711.582132 83 113525142.774065 74656117.5287547 152394168.019376 84 92383422.8271286 92383391.1392324 92383454.5150247

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/14bkt1305816848.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/14bkt1305816848.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/2nszd1305816848.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/2nszd1305816848.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/3tlbg1305816848.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816815x7vm4i8wshqqo16/3tlbg1305816848.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=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