Kim Van Assche Werkloosheid Opdracht 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 14:03:06 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/05/t12442322445syst3tbeactafj.htm/, Retrieved Fri, 05 Jun 2009 22:04:08 +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/2009/Jun/05/t12442322445syst3tbeactafj.htm/}, year = {2009}, } @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 = {2009}, 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 «

519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.941500704926866 beta 0.113828330159863 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 562 543.086271367522 18.9137286324783 14 561 562.640959569084 -1.64095956908352 15 555 557.250866933101 -2.25086693310107 16 544 545.420321905766 -1.42032190576595 17 537 537.719520485293 -0.71952048529306 18 543 543.851413479316 -0.85141347931608 19 594 608.517883609563 -14.5178836095628 20 611 605.011488831915 5.98851116808487 21 613 608.370331326282 4.6296686737179 22 611 600.32098171405 10.6790182859496 23 594 594.486563575286 -0.486563575286027 24 595 604.045930824328 -9.04593082432825 25 591 605.141973441108 -14.1419734411083 26 589 589.8239595535 -0.823959553499662 27 584 582.706650787304 1.29334921269560 28 573 572.180662694284 0.819337305715635 29 567 564.788610078104 2.21138992189606 30 569 572.145457393583 -3.14545739358323 31 621 632.079969015195 -11.0799690151947 32 629 631.60578663998 -2.60578663998001 33 628 624.46835791529 3.53164208470992 34 612 613.296180828051 -1.29618082805086 35 595 591.807632718812 3.19236728118801 36 597 600.997975125051 -3.99797512505097 37 593 603.757519454681 -10.7575194546810 38 590 589.976738652291 0.0232613477088535 39 580 581.443419079719 -1.44341907971852 40 574 565.682203434264 8.31779656573565 41 573 563.604166458405 9.3958335415955 42 573 576.354530472415 -3.35453047241469 43 620 634.548359816644 -14.5483598166444 44 626 629.853036717227 -3.85303671722693 45 620 620.315307275957 -0.315307275957252 46 588 603.241475814077 -15.2414758140771 47 566 565.394165305976 0.605834694024111 48 557 567.959623973831 -10.9596239738306 49 561 559.254234804727 1.74576519527318 50 549 554.700835947309 -5.70083594730852 51 532 536.903889144647 -4.90388914464666 52 526 514.296220223063 11.7037797769375 53 511 511.672584694536 -0.672584694536113 54 499 509.322043123141 -10.3220431231413 55 555 554.678823337326 0.321176662673793 56 565 560.580108337159 4.41989166284134 57 542 555.89616684606 -13.8961668460602 58 527 520.565188265278 6.43481173472162 59 510 501.778622217126 8.22137778287362 60 514 509.379150439082 4.62084956091815 61 517 516.297396770418 0.702603229581769 62 508 510.425796546431 -2.42579654643055 63 493 496.209463932967 -3.20946393296674 64 490 476.800766549019 13.1992334509815 65 469 475.653492145676 -6.6534921456763 66 478 467.258863930558 10.7411360694421 67 528 535.478020905203 -7.47802090520258 68 534 535.849049945234 -1.8490499452339 69 518 525.092502066135 -7.09250206613456 70 506 498.986754686744 7.01324531325594 71 502 482.541515625095 19.4584843749053 72 516 503.407652339791 12.5923476602094 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 521.352649272085 505.681790835391 537.023507708779 74 518.312034996166 495.604376579365 541.019693412966 75 510.269215406278 481.222382864873 539.316047947682 76 499.121552156867 463.972455250068 534.270649063665 77 487.25068942133 446.062094297472 528.439284545188 78 489.715823073684 442.466658373058 536.96498777431 79 549.183184182753 495.806694763435 602.559673602072 80 560.152280575576 500.554968880954 619.749592270199 81 554.256252507838 488.328303958905 620.18420105677 82 539.839752906322 467.461198360502 612.218307452143 83 520.9544462907 441.998997742049 599.909894839352 84 524.448257103744 438.78578859228 610.110725615209

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/1wdrk1244232177.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/1wdrk1244232177.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/2ove51244232177.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/2ove51244232177.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/3835r1244232177.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12442322445syst3tbeactafj/3835r1244232177.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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