Kelly Janbroers - 2de zit - Stap 32/A

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 08 Jul 2010 13:17:47 +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/Jul/08/t12785950763g99033jsflyk1j.htm/, Retrieved Thu, 08 Jul 2010 15:17:57 +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/Jul/08/t12785950763g99033jsflyk1j.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

33 32 31 29 49 48 33 23 24 24 25 27 24 21 15 21 49 48 35 36 51 50 61 63 61 62 58 65 93 94 86 88 102 107 121 127 125 128 117 127 160 162 153 160 177 178 196 212 212 211 204 216 248 250 240 249 275 277 286 302 290 290 277 285 311 300 291 299 332 337 343 360 353 351 341 348 381 358 353 358 399 409 407 419 418 421 414 424 463 437 430 436 474 489 482 492 502 500 493 504 538 516 502 501 541 571 559 569 576 573 562 570 597 573 562 556 600 630 624 634

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999947806481961 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 32 33 -1 3 31 32.000052193518 -1.00005219351804 4 29 31.0000521962422 -2.0000521962422 5 49 29.0001043897604 19.9998956102396 6 48 48.9989561350877 -0.998956135087695 7 33 48.000052139035 -15.0000521390351 8 23 33.0007829054919 -10.0007829054919 9 24 23.000521976043 0.999478023957021 10 24 23.9999478337257 5.21662742727358e-05 11 25 23.9999999972773 1.00000000272274 12 27 24.9999478064818 2.00005219351818 13 24 26.9998956102398 -2.99989561023976 14 21 24.0001565751056 -3.00015657510565 15 15 21.0001565887263 -6.00015658872632 16 21 15.0003131692811 5.99968683071885 17 49 20.9996868552372 28.0003131447628 18 48 48.9985385651508 -0.998538565150788 19 35 48.0000521172406 -13.0000521172406 20 36 35.0006785184547 0.999321481545316 21 51 35.9999478418962 15.0000521581038 22 50 50.9992170945071 -0.999217094507102 23 61 50.0000521526554 10.9999478473446 24 63 60.9994258740236 2.00057412597639 25 61 62.9998955829983 -1.99989558299827 26 62 61.0001043815862 0.999895618413817 27 58 61.99994781193 -3.99994781193001 28 65 58.0002087713483 6.99979122865172 29 93 64.9996346562702 28.0003653437298 30 94 92.9985385624263 1.00146143757365 31 86 93.9999477302044 -7.9999477302044 32 88 86.0004175454162 1.99958245458383 33 102 87.9998956347571 14.0001043652429 34 107 101.9992692853 5.00073071469973 35 121 106.999738994271 14.0002610057288 36 127 120.999269277125 6.00073072287535 37 125 126.999686800753 -1.99968680075277 38 128 125.000104370689 2.9998956293109 39 117 127.999843424893 -10.9998434248934 40 127 117.000574120526 9.99942587947378 41 160 126.999478094785 33.000521905215 42 162 159.998277586665 2.00172241333536 43 153 161.999895523065 -8.9998955230651 44 160 153.000469736209 6.99953026379066 45 177 159.999634669891 17.0003653301091 46 178 176.999112691125 1.00088730887452 47 196 177.99994776017 18.0000522398298 48 212 195.999060513949 16.0009394860513 49 212 211.999164854676 0.000835145323691222 50 211 211.999999956411 -0.999999956410818 51 204 211.000052193516 -7.00005219351576 52 216 204.00036535735 11.9996346426496 53 248 215.999373696853 32.0006263031472 54 250 247.998329774734 2.0016702252662 55 240 249.999895525789 -9.99989552578899 56 249 240.000521929728 8.99947807027249 57 275 248.999530285579 26.000469714421 58 277 274.998642944015 2.00135705598507 59 286 276.999895542134 9.00010445786558 60 302 285.999530252886 16.0004697471144 61 290 301.999164879194 -11.9991648791936 62 290 290.000626278629 -0.000626278628544696 63 277 290.000000032688 -13.0000000326877 64 285 277.000678515736 7.99932148426382 65 311 284.99958248727 26.0004175127302 66 300 310.99864294674 -10.9986429467396 67 291 300.000574057869 -9.00057405786902 68 299 291.000469771624 7.99953022837553 69 332 298.999582476375 33.0004175236253 70 337 331.998277592113 5.00172240788731 71 343 336.999738942511 6.00026105748873 72 360 342.999686825266 17.0003131747337 73 353 359.999112693848 -6.99911269384768 74 351 353.000365308315 -2.00036530831466 75 341 351.000104406103 -10.0001044061028 76 348 341.00052194063 6.99947805937029 77 381 347.999634672616 33.0003653273844 78 358 380.998277594837 -22.998277594837 79 353 358.001200361017 -5.00120036101652 80 358 353.000261030241 4.99973896975877 81 399 357.999739046034 41.0002609539661 82 409 398.99786005214 10.0021399478597 83 407 408.999477953128 -1.99947795312823 84 419 407.000104359789 11.9998956402114 85 418 418.99937368323 -0.99937368323043 86 421 418.000052160828 2.99994783917163 87 414 420.999843422168 -6.99984342216834 88 424 414.000365346454 9.99963465354608 89 463 423.999478083888 39.0005219161117 90 437 462.997964425556 -25.9979644255558 91 430 437.001356925225 -7.0013569252252 92 436 430.000365425449 5.99963457455101 93 474 435.999686857965 38.0003131420354 94 489 473.998016629971 15.0019833700294 95 482 488.99921699371 -6.99921699371038 96 492 482.000365313758 9.99963468624156 97 502 491.999478083887 10.0005219161134 98 500 501.999478037579 -1.99947803757897 99 493 500.000104359793 -7.000104359793 100 504 493.000365360073 10.9996346399268 101 538 503.999425890371 34.000574109629 102 516 537.998225390422 -21.9982253904219 103 502 516.001148164774 -14.0011481647738 104 501 502.00073076918 -1.00073076917931 105 541 501.00005223166 39.9999477683405 106 571 540.997912262005 30.0020877379953 107 559 570.998434085492 -11.9984340854925 108 569 559.000626240486 9.99937375951413 109 576 568.999478097505 7.00052190249471 110 573 575.999634618134 -2.99963461813377 111 562 573.000156561484 -11.0001565614835 112 570 562.00057413687 7.99942586313011 113 597 569.999582481822 27.0004175181781 114 573 596.998590753221 -23.9985907532213 115 562 573.001252570879 -11.0012525708794 116 556 562.000574194074 -6.00057419407449 117 600 556.000313191077 43.9996868089225 118 630 599.997703501553 30.0022964984472 119 624 629.998434074597 -5.9984340745965 120 634 624.000313079377 9.99968692062293 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 633.99947808116 605.147847133371 662.85110902895 122 633.99947808116 593.198175093878 674.800781068442 123 633.99947808116 584.028726209965 683.970229952355 124 633.99947808116 576.298474973024 691.700481189296 125 633.99947808116 569.487963784892 698.510992377429 126 633.99947808116 563.330777839043 704.668178323278 127 633.99947808116 557.668652649866 710.330303512455 128 633.99947808116 552.398469336566 715.600486825754 129 633.99947808116 547.448600874468 720.550355287852 130 633.99947808116 542.766895840163 725.232060322158 131 633.99947808116 538.313983989982 729.684972172339 132 633.99947808116 534.05927847867 733.93967768365

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/1msau1278595063.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/1msau1278595063.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/2msau1278595063.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/2msau1278595063.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/3ejrf1278595063.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t12785950763g99033jsflyk1j/3ejrf1278595063.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

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