Katleen van den Akker - Opgave 10 - Oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 09:13:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec.htm/, Retrieved Wed, 02 Jun 2010 11:16:59 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

285708 905858 225733 405481 845758 805651 395747 695853 175625 405534 965639 575634 576023 566089 336141 26271 586226 376484 176583 287042 997142 207694 418003 838258 848182 658215 208304 398599 438399 578393 988390 958304 318251 78307 408520 748640 258520 518618 388588 238842 328957 499266 109011 168896 798921 878732 897576 518317 228370 758167 658491 518170 398212 498286 78136 647990 357927 698061 407932 637934 397784 217980 47737 467672 67651 167524 687406 367345 157553 887453 227566 817279 697059 997185 847075 547122 996977 346998 967154 547097 586853 46728 236883 36784 277085 446998 586725 496845 86765 146966 197113 657096 337200 17273 457284 507696 547628 157435 67793 267631 518397 918560 918895 429509 289569 9010172 1810617 7111400 1611919 9712714 2913310 1013816 6714518 2414721 9114534 8214993 6215159 515612 9415340 3715267

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.173659852690062 beta 0.000673607157187447 gamma 0.0799120898660841 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 576023 739236.348343582 -163213.348343582 14 566089 722597.22335502 -156508.223355020 15 336141 387184.554260695 -51043.5542606952 16 26271 27219.7972199181 -948.79721991812 17 586226 627443.268855386 -41217.2688553861 18 376484 397321.350841869 -20837.3508418691 19 176583 309024.876298841 -132441.876298841 20 287042 487831.212121884 -200789.212121884 21 997142 111930.940482397 885211.059517603 22 207694 615987.623242758 -408293.623242758 23 418003 1339190.23642928 -921187.236429283 24 838258 728062.325250325 110195.674749675 25 848182 762595.511260388 85586.4887396124 26 658215 792626.93376749 -134411.933767490 27 208304 432249.652555293 -223945.652555293 28 398599 28533.8767881063 370065.123211894 29 438399 2192383.68639341 -1753984.68639341 30 578393 1235199.51962694 -656806.519626942 31 988390 873787.559488568 114602.440511432 32 958304 1563666.53137693 -605362.53137693 33 318251 465543.10628409 -147292.10628409 34 78307 798431.473768609 -720124.473768609 35 408520 1658292.15935405 -1249772.15935405 36 748640 952307.363652946 -203667.363652946 37 258520 937394.005680403 -678874.005680403 38 518618 820844.364617842 -302226.364617842 39 388588 420527.621090478 -31939.6210904782 40 238842 39614.7499949613 199227.250005039 41 328957 1296548.27519747 -967591.275197469 42 499266 752144.103420064 -252878.103420064 43 109011 575868.96336755 -466857.963367551 44 168896 827763.85529732 -658867.85529732 45 798921 226363.709418321 572557.290581679 46 878732 559760.11243461 318971.88756539 47 897576 1536469.43460782 -638893.434607823 48 518317 985389.101518985 -467072.101518985 49 228370 887028.133628562 -658658.133628562 50 758167 797520.147968473 -39353.1479684729 51 658491 442654.497684608 215836.502315392 52 518170 54427.5431997364 463742.456800264 53 398212 1898231.69665058 -1500019.69665058 54 498286 1135850.29550629 -637564.295506293 55 78136 804813.882360483 -726677.882360483 56 647990 1143970.69913980 -495980.699139798 57 357927 402378.270111733 -44451.2701117332 58 698061 629247.639937292 68813.3600627081 59 407932 1503017.21771447 -1095085.21771447 60 637934 902609.559980435 -264675.559980435 61 397784 820829.792641808 -423045.792641808 62 217980 815303.86657468 -597323.86657468 63 47737 410651.930193338 -362914.930193338 64 467672 46558.0856360961 421113.914363904 65 67651 1285103.20654577 -1217452.20654577 66 167524 756911.43381467 -589387.43381467 67 687406 495339.173641111 192066.826358889 68 367345 927128.056999731 -559783.056999731 69 157553 322300.243151604 -164747.243151604 70 887453 472840.802374417 414612.197625583 71 227566 1195209.45119596 -967643.451195957 72 817279 729633.967985096 87645.0320149038 73 697059 699827.566442166 -2768.56644216599 74 997185 748295.097241629 248889.902758371 75 847075 451961.163959089 395113.836040911 76 547122 93313.8912772429 453808.108722757 77 996977 1389751.15843093 -392774.158430927 78 346998 950519.584159758 -603521.584159758 79 967154 699936.111890899 267217.888109101 80 547097 1226515.11523930 -679418.115239301 81 586853 436094.680233765 150758.319766235 82 46728 818005.68409107 -771277.68409107 83 236883 1343887.29824682 -1107004.29824682 84 36784 882171.265927443 -845387.265927443 85 277085 685219.690924196 -408134.690924196 86 446998 669347.168823079 -222349.168823079 87 586725 368482.338266265 218242.661733735 88 496845 80959.0361636194 415885.963836381 89 86765 1029634.82821167 -942869.828211673 90 146966 602295.422765024 -455329.422765024 91 197113 462310.402054415 -265197.402054415 92 657096 635365.158905275 21730.8410947252 93 337200 265518.250985887 71681.7490141131 94 17273 442027.094132448 -424754.094132448 95 457284 724639.179859548 -267355.179859548 96 507696 507573.661244126 122.338755873789 97 547628 486041.84298517 61586.1570148298 98 157435 550592.895460722 -393157.895460722 99 67793 296661.622649114 -228868.622649114 100 267631 57419.8798939864 210211.120106014 101 518397 491087.368034462 27309.6319655378 102 918560 346967.885466356 571592.114533644 103 918895 400023.419307796 518871.580692204 104 429509 785818.286904767 -356309.286904767 105 289569 305955.351629511 -16386.3516295106 106 9010172 438500.679990297 8571671.3200097 107 1810617 4079254.52753124 -2268637.52753124 108 7111400 2894967.20906553 4216432.79093447 109 1611919 3585486.10766381 -1973567.10766381 110 9712714 3453102.02765783 6259611.97234217 111 2913310 2860115.64356294 53194.3564370624 112 1013816 810355.40686907 203460.593130930 113 6714518 3949731.22325645 2764786.77674355 114 2414721 3424420.25408295 -1009699.25408295 115 9114534 2921745.61264709 6192788.38735291 116 8214993 5877982.54477447 2337010.45522553 117 6215159 2779197.89647447 3435961.10352553 118 515612 6448467.49319585 -5932855.49319585 119 9415340 8524589.71609453 890750.283905465 120 3715267 7673911.81918202 -3958644.81918202 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 6166347.07528942 5401927.3974007 6930766.75317815 122 7479700.45746127 6461110.62297475 8498290.29194779 123 4328727.01841742 3412254.21228529 5245199.82454954 124 1241755.33515733 447523.10083525 2035987.56947942 125 5949794.52131328 2995648.53709142 8903940.50553514 126 4329376.40357058 2076173.48229449 6582579.32484667 127 4384821.06495008 2033626.90187425 6736015.2280259 128 5993230.63581933 2762968.99530699 9223492.27633166 129 2760643.42206654 1102778.63907367 4418508.2050594 130 4581658.65588738 1857889.68893316 7305427.6228416 131 7821611.38370955 3186432.93890474 12456789.8285144 132 6610628.31328764 2710255.76798363 10511000.8585916

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/1i4hy1275470025.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/1i4hy1275470025.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/2i4hy1275470025.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/2i4hy1275470025.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/3bez11275470025.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275470219l9rfujrunn35wec/3bez11275470025.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

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