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: Sat, 10 Jul 2010 07:31:40 +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/10/t1278747263zum1hf3yu1chdrk.htm/, Retrieved Sat, 10 Jul 2010 09:34:23 +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/10/t1278747263zum1hf3yu1chdrk.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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.312591008980173 beta 0.140711984725360 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 24 26.3878205128205 -2.38782051282053 14 21 22.4469280703411 -1.44692807034106 15 15 14.6948399120256 0.305160087974350 16 21 18.9621946506821 2.03780534931794 17 49 45.4857922020282 3.51420779797183 18 48 43.2088067065506 4.79119329344939 19 35 37.4167374760649 -2.41673747606485 20 36 28.2235663010092 7.77643369899084 21 51 33.8504042340795 17.1495957659205 22 50 42.0365384915958 7.96346150840424 23 61 48.0347783599471 12.9652216400529 24 63 56.8334693212053 6.16653067879469 25 61 57.0534447021164 3.94655529788356 26 62 58.4995867099273 3.50041329007271 27 58 56.4761920324154 1.52380796758464 28 65 65.3469215664832 -0.346921566483189 29 93 95.066474805018 -2.06647480501803 30 94 94.6038689715942 -0.603868971594153 31 86 84.614291484125 1.38570851587494 32 88 86.2275961011497 1.77240389885026 33 102 98.7677229706117 3.23227702938829 34 107 98.0235385734672 8.97646142653278 35 121 109.555986433162 11.4440135668382 36 127 114.918067778019 12.0819322219815 37 125 117.433691822238 7.56630817776154 38 128 121.836448291654 6.16355170834557 39 117 121.535723698735 -4.5357236987348 40 127 129.208744717578 -2.20874471757821 41 160 159.064782473613 0.935217526386936 42 162 162.578427468024 -0.578427468023733 43 153 155.998115664341 -2.99811566434119 44 160 158.347729758693 1.65227024130724 45 177 173.689385345459 3.31061465454076 46 178 178.757289793167 -0.757289793167416 47 196 190.354127291890 5.64587270810952 48 212 195.498095208953 16.5019047910471 49 212 197.641518449603 14.3584815503967 50 211 204.852171709063 6.14782829093696 51 204 198.840054277366 5.15994572263395 52 216 213.218207869913 2.78179213008718 53 248 249.089707968217 -1.08970796821694 54 250 253.135096802614 -3.13509680261444 55 240 246.185032381257 -6.18503238125749 56 249 252.687739205703 -3.68773920570348 57 275 269.217811945876 5.78218805412376 58 277 274.08840205953 2.91159794047019 59 286 293.221477618580 -7.22147761857957 60 302 303.227572561421 -1.22757256142074 61 290 298.997486764376 -8.9974867643757 62 290 292.877852730668 -2.87785273066805 63 277 282.582967183926 -5.58296718392558 64 285 290.713346351007 -5.71334635100698 65 311 319.639505059182 -8.63950505918217 66 300 317.958262924178 -17.9582629241781 67 291 301.665441877772 -10.6654418777717 68 299 305.674587565542 -6.67458756554169 69 332 324.839646887358 7.16035311264159 70 337 325.287323940258 11.7126760597415 71 343 337.712642602145 5.28735739785526 72 360 353.806028467815 6.19397153218483 73 353 344.938057933809 8.06194206619085 74 351 347.49141973338 3.50858026662013 75 341 336.747945209618 4.25205479038237 76 348 347.710225897421 0.289774102578519 77 381 376.612673231963 4.38732676803681 78 358 373.281927734667 -15.2819277346667 79 353 363.640799246914 -10.6407992469138 80 358 371.204024533344 -13.2040245333438 81 399 398.354131323248 0.645868676752343 82 409 400.124033422123 8.87596657787685 83 407 407.350313450249 -0.350313450248791 84 419 422.161167217467 -3.16116721746681 85 418 411.097973979096 6.90202602090386 86 421 409.552765171137 11.4472348288627 87 414 401.545128431635 12.4548715683648 88 424 412.451846562614 11.5481534373855 89 463 448.289477843102 14.7105221568984 90 437 435.718138122637 1.28186187736293 91 430 436.226908175786 -6.22690817578598 92 436 445.383891728934 -9.3838917289342 93 474 485.392708207393 -11.3927082073935 94 489 490.671411677834 -1.6714116778345 95 482 489.40902761187 -7.40902761187016 96 492 500.921284338081 -8.92128433808057 97 502 495.5617989935 6.43820100650044 98 500 497.562357779892 2.43764222010827 99 493 487.60111002836 5.39888997163956 100 504 495.53859415838 8.46140584162049 101 538 532.309093662436 5.690906337564 102 516 507.014507877921 8.985492122079 103 502 504.435800492344 -2.43580049234362 104 501 512.440497412423 -11.4404974124232 105 541 550.167884585948 -9.1678845859476 106 571 562.664739742437 8.33526025756282 107 559 560.866594239744 -1.86659423974424 108 569 573.595944203855 -4.59594420385486 109 576 580.861138276491 -4.86113827649149 110 573 576.796968931272 -3.79696893127243 111 562 566.865558683047 -4.86555868304686 112 570 573.191317093755 -3.19131709375461 113 597 603.393913078432 -6.39391307843232 114 573 575.033994035413 -2.03399403541266 115 562 559.122444448725 2.87755555127546 116 556 560.794697965195 -4.79469796519504 117 600 600.65059316829 -0.650593168289788 118 630 626.705208193313 3.29479180668727 119 624 614.960416555852 9.03958344414764 120 634 628.344276903117 5.65572309688298 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 638.204192887778 624.201608526867 652.206777248689 122 636.177349545383 621.311202883193 651.043496207573 123 626.651548574078 610.762494145502 642.540603002654 124 635.816407799673 618.751524090595 652.881291508752 125 665.122740779326 646.737811686329 683.507669872324 126 642.347440459369 622.507913727433 662.186967191304 127 631.126299738903 609.707323324408 652.545276153399 128 627.176866338428 604.062769083514 650.29096359334 129 672.142919272718 647.22641209767 697.059426447765 130 701.904296873383 675.085576743761 728.723017003005 131 693.724981849439 664.910845809426 722.539117889452 132 702.20582234445 671.308847186826 733.102797502074

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/1t2nk1278747095.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/1t2nk1278747095.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/24t451278747095.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/24t451278747095.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/3e23q1278747095.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/10/t1278747263zum1hf3yu1chdrk/3e23q1278747095.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

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