Alexander De Raeymaeker - Opdracht 10.1

*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 19:33:00 +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/t1305055746xhts7t0dq5c7ecf.htm/, Retrieved Tue, 10 May 2011 21:29:10 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W101

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 0.122697358324306 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 1379 2435 -1056 3 1511 2305.43158960953 -794.431589609533 4 2021 2207.95693219506 -186.956932195064 5 1614 2185.01781049431 -571.017810494313 6 1680 2114.95543359053 -434.955433590532 7 1630 2061.58755090017 -431.587550900171 8 870 2008.63289851906 -1138.63289851906 9 1877 1868.92564976963 8.07435023037397 10 2428 1869.91635121308 558.083648786922 11 1711 1938.39174064322 -227.391740643224 12 127 1910.49137476153 -1783.49137476153 13 3192 1691.66169448411 1500.33830551589 14 1934 1875.74924116367 58.2507588363251 15 2075 1882.89645539328 192.103544606721 16 1700 1906.46705284126 -206.467052841259 17 1198 1881.13409087663 -683.134090876632 18 1582 1797.31534254479 -215.315342544793 19 1705 1770.89671880785 -65.8967188078536 20 911 1762.81136548789 -851.81136548789 21 1817 1658.29636115191 158.703638848094 22 1168 1677.76887839502 -509.768878395022 23 920 1615.22158366001 -695.221583660008 24 84 1529.91973189488 -1445.91973189488 25 2254 1352.50920044239 901.490799557607 26 1485 1463.11974010178 21.8802598982215 27 1886 1465.80439019074 420.19560980926 28 1358 1517.36128149381 -159.361281493807 29 1167 1497.80807323534 -330.808073235341 30 1781 1457.21879653701 323.781203462989 31 1218 1496.94589487698 -278.945894876984 32 779 1462.71997046017 -683.719970460169 33 1418 1378.82933625113 39.1706637488664 34 1641 1383.63547321693 257.364526783071 35 1196 1415.2134207796 -219.213420779597 36 132 1388.31651314071 -1256.31651314071 37 2926 1234.16979575914 1691.83020424086 38 1777 1441.75289255276 335.247107447236 39 2094 1482.8868270224 611.113172977596 40 1648 1557.86879898394 90.1312010160595 41 1646 1568.92765925121 77.072340748792 42 1537 1578.38423186096 -41.3842318609559 43 1917 1573.30649593534 343.693504064664 44 977 1615.47678095729 -638.476780957295 45 1475 1537.13736658243 -62.1373665824278 46 2124 1529.51327584953 594.486724150465 47 1209 1602.45522646167 -393.455226461668 48 135 1554.17930955593 -1419.17930955593 49 2917 1380.0497572849 1536.9502427151 50 1981 1568.62949194195 412.370508058052 51 1398 1619.22626393152 -221.226263931523 52 1171 1592.08238575517 -421.082385755169 53 903 1540.41668938611 -637.416689386113 54 1390 1462.20734544661 -72.2073454466124 55 1280 1453.3476949087 -173.347694908703 56 781 1432.0783906718 -651.078390671797 57 1828 1352.19279207433 475.807207925673 58 1631 1410.57307955847 220.426920441529 59 1063 1437.61888040021 -374.618880400209 60 186 1391.65413339669 -1205.65413339669 61 2275 1243.72355617614 1031.27644382386 62 1342 1370.25845153541 -28.2584515354115 63 1070 1366.79121418168 -296.791214181681 64 950 1330.37571622773 -380.375716227725 65 1121 1283.70462067587 -162.704620675868 66 1305 1263.74119353178 41.2588064682195 67 1586 1268.80354009304 317.196459906955 68 548 1307.72270779345 -759.72270779345 69 1225 1214.5067384882 10.493261511795 70 1419 1215.79423395591 203.205766044091 71 880 1240.72704464579 -360.727044645786 72 124 1196.46678919161 -1072.46678919161 73 2044 1064.87794726725 979.122052732748 74 1143 1185.01363661463 -42.0136366146328 75 897 1179.85867438842 -282.85867438842 76 1264 1145.15266226185 118.847337738154 77 1326 1159.73491664619 166.265083353806 78 1529 1180.13520315528 348.864796844723 79 1373 1222.93999214047 150.06000785953 80 587 1241.35195869496 -654.351958694959 81 1137 1161.06470194875 -24.0647019487521 82 1426 1158.11202659078 267.887973409221 83 1016 1190.98117325494 -174.981173254942 84 176 1169.51144554007 -993.511445540073 85 2614 1047.61021570734 1566.38978429266 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 1239.80210434623 -60.472931154512 2540.07713984698 87 1239.80210434623 -70.2239561135891 2549.82816480605 88 1239.80210434623 -79.9029347520116 2559.50714344448 89 1239.80210434623 -89.5114408186075 2569.11564951107 90 1239.80210434623 -99.0509915892897 2578.65520028175 91 1239.80210434623 -108.523050664068 2588.12725935653 92 1239.80210434623 -117.92903058843 2597.5332392809 93 1239.80210434623 -127.27029531239 2606.87450400485 94 1239.80210434623 -136.548162499313 2616.15237119178 95 1239.80210434623 -145.763905695592 2625.36811438806 96 1239.80210434623 -154.918756371294 2634.52296506376 97 1239.80210434623 -164.01390584102 2643.61811453348

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/1do141305055978.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/1do141305055978.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/20o5w1305055978.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/20o5w1305055978.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/333jy1305055978.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/10/t1305055746xhts7t0dq5c7ecf/333jy1305055978.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=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