Alexander De Raeymaeker - Opdracht 9.2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 10 May 2011 19:36:39 +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/10/t13050559735ztx5f7z43bvgz8.htm/, Retrieved Tue, 10 May 2011 21:32:56 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

2435 1379 1511 2021 1614 1680 1630 870 1877 2428 1711 127 3192 1934 2075 1700 1198 1582 1705 911 1817 1168 920 84 2254 1485 1886 1358 1167 1781 1218 779 1418 1641 1196 132 2926 1777 2094 1648 1646 1537 1917 977 1475 2124 1209 135 2917 1981 1398 1171 903 1390 1280 781 1828 1631 1063 186 2275 1342 1070 950 1121 1305 1586 548 1225 1419 880 124 2044 1143 897 1264 1326 1529 1373 587 1137 1426 1016 176 2614

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.241318956657905 beta 0 gamma 0.491116881078373 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3192 3211.64289529915 -19.6428952991455 14 1934 1932.20878204341 1.79121795659466 15 2075 2062.57212663543 12.4278733645729 16 1700 1733.71063114617 -33.7106311461653 17 1198 1297.17337321995 -99.1733732199496 18 1582 1680.13038134319 -98.1303813431896 19 1705 1579.7557498446 125.244250155402 20 911 783.452318029758 127.547681970242 21 1817 1762.74641464387 54.2535853561258 22 1168 2304.85325633389 -1136.85325633389 23 920 1332.35677105251 -412.356771052509 24 84 -341.596644965116 425.596644965116 25 2254 2807.88668600327 -553.886686003271 26 1485 1407.51579205898 77.4842079410155 27 1886 1560.10851918255 325.891480817446 28 1358 1289.70047834944 68.2995216505603 29 1167 853.388716470799 313.611283529201 30 1781 1336.34710717206 444.652892827941 31 1218 1450.18599529009 -232.18599529009 32 779 568.486130720039 210.513869279961 33 1418 1540.4920824362 -122.492082436203 34 1641 1596.1391629753 44.8608370247025 35 1196 1178.76085376048 17.2391462395196 36 132 -79.3005861876447 211.300586187645 37 2926 2653.51250850884 272.487491491158 38 1777 1687.8108381098 89.1891618901986 39 2094 1935.78500761612 158.214992383879 40 1648 1528.93441251148 119.065587488523 41 1646 1196.27688907951 449.723110920492 42 1537 1760.90788749864 -223.907887498643 43 1917 1461.2194932455 455.780506754497 44 977 910.489429391354 66.5105706086464 45 1475 1723.66628214382 -248.666282143823 46 2124 1811.22101293278 312.778987067223 47 1209 1448.20456067661 -239.204560676608 48 135 200.565892665725 -65.5658926657254 49 2917 2889.36416379953 27.6358362004694 50 1981 1796.2779940856 184.722005914396 51 1398 2093.02514798195 -695.025147981953 52 1171 1465.68442236021 -294.684422360208 53 903 1156.38452452118 -253.384524521181 54 1390 1300.34669266396 89.6533073360408 55 1280 1329.57918022557 -49.5791802255671 56 781 511.853850125609 269.146149874391 57 1828 1256.49527758593 571.504722414073 58 1631 1751.16792626116 -120.16792626116 59 1063 1078.00351732836 -15.0035173283613 60 186 -50.8332357183974 236.833235718397 61 2275 2745.66674126203 -470.666741262032 62 1342 1590.86118801742 -248.86118801742 63 1070 1455.18176904721 -385.181769047214 64 950 1051.77950618361 -101.779506183611 65 1121 804.419607482853 316.580392517147 66 1305 1213.74137716196 91.258622838041 67 1586 1191.48308425614 394.516915743859 68 548 599.683959002229 -51.6839590022289 69 1225 1379.56212629246 -154.562126292462 70 1419 1441.30311315137 -22.3031131513717 71 880 830.939709868298 49.0602901317023 72 124 -188.602588921406 312.602588921406 73 2044 2362.56672247207 -318.56672247207 74 1143 1327.11077303898 -184.110773038982 75 897 1156.26366260798 -259.263662607975 76 1264 888.843811557384 375.156188442616 77 1326 912.458882032014 413.541117967986 78 1529 1261.22398084633 267.776019153669 79 1373 1394.55704558892 -21.5570455889231 80 587 536.096463736991 50.9035362630091 81 1137 1302.39842337136 -165.39842337136 82 1426 1410.80425583969 15.1957441603083 83 1016 836.08011793973 179.919882060269 84 176 -53.6871387335377 229.687138733538 85 2614 2242.2987433802 371.701256619805 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 1423.51597279861 849.423550164685 1997.60839543254 87 1269.09623512974 678.524249025653 1859.66822123382 88 1300.62713453557 694.02311887448 1907.23115019666 89 1248.01217075773 625.789065383624 1870.23527613183 90 1442.6697269915 805.210117363863 2080.12933661914 91 1403.57755331851 751.237216567927 2055.91789006908 92 577.317985383771 -89.5711178388643 1244.20708860641 93 1250.74161564305 569.61443438956 1931.86879689654 94 1466.35080272204 771.277138937 2161.42446650708 95 949.336033359659 240.590268552001 1658.08179816732 96 34.694031440516 -687.465037032646 756.853099913678 97 2328.16666483583 1592.83892754908 3063.49440212259

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/1vq6o1305056197.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/1vq6o1305056197.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/2u5gp1305056197.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/2u5gp1305056197.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/310r81305056197.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t13050559735ztx5f7z43bvgz8/310r81305056197.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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