Exponential Smoothing: Werkloosheid Belgie 2000 - 2010

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 28 Dec 2010 09:47:16 +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/Dec/28/t129352971909e74hoq751cuj9.htm/, Retrieved Tue, 28 Dec 2010 10:48:43 +0100

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/Dec/28/t129352971909e74hoq751cuj9.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:

Data Paper Statistiek

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601 604 586 564 549

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.536611617913518 beta 0.166578889966966 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 471 463.071581196581 7.92841880341877 14 471 467.751552884205 3.24844711579470 15 476 474.627236794817 1.37276320518305 16 475 475.035782381664 -0.0357823816636937 17 470 471.64362085405 -1.64362085404969 18 461 463.200087599295 -2.20008759929476 19 455 455.052952691543 -0.052952691543112 20 456 451.594928643116 4.40507135688415 21 517 508.839560015662 8.16043998433759 22 525 541.662145934044 -16.6621459340436 23 523 536.133578501047 -13.1335785010471 24 519 518.199494830221 0.800505169779285 25 509 489.613095194284 19.3869048057157 26 512 498.599085098242 13.4009149017578 27 519 511.286947545559 7.71305245444125 28 517 516.245225687211 0.754774312789436 29 510 514.403062155734 -4.40306215573378 30 509 505.84508877072 3.15491122927972 31 501 503.669307708342 -2.66930770834210 32 507 502.742084420553 4.25791557944746 33 569 563.503761208528 5.49623879147248 34 580 585.011876546371 -5.01187654637124 35 578 590.029141065672 -12.0291410656716 36 565 581.902392373837 -16.9023923738370 37 547 553.604492859586 -6.604492859586 38 555 544.721394179860 10.2786058201395 39 562 551.67103798072 10.3289620192795 40 561 553.61542775731 7.38457224268984 41 555 552.340204233303 2.65979576669702 42 544 551.105250362051 -7.10525036205081 43 537 539.838465791353 -2.83846579135343 44 543 541.128938165233 1.87106183476715 45 594 600.06874267317 -6.06874267317039 46 611 608.352960108755 2.64703989124450 47 613 612.764329901227 0.235670098773085 48 611 608.593102913576 2.40689708642446 49 594 596.787031036753 -2.78703103675298 50 595 599.475406005942 -4.47540600594198 51 591 598.911923547078 -7.91192354707778 52 589 588.453840275072 0.54615972492843 53 584 579.458559536532 4.54144046346835 54 573 573.015426832889 -0.0154268328886928 55 567 566.471166359232 0.528833640767857 56 569 570.992771866034 -1.99277186603410 57 621 623.076464890373 -2.07646489037290 58 629 636.795119478016 -7.79511947801586 59 628 632.805641128437 -4.80564112843717 60 612 624.804612392861 -12.8046123928613 61 595 598.938635959318 -3.93863595931759 62 597 596.633307254131 0.366692745869045 63 593 593.915169523852 -0.915169523852 64 590 588.595890879709 1.40410912029097 65 580 579.453940564458 0.546059435542247 66 574 565.939678962967 8.06032103703274 67 573 561.887477248082 11.1125227519179 68 573 569.772301821045 3.22769817895528 69 620 623.937596823766 -3.93759682376572 70 626 633.160244599522 -7.16024459952166 71 620 630.106143626558 -10.1061436265580 72 588 614.289777716373 -26.2897777163729 73 566 582.826085556346 -16.8260855563458 74 557 571.978445650377 -14.9784456503767 75 561 555.43845916651 5.56154083349043 76 549 550.254857467324 -1.25485746732409 77 532 534.636256526055 -2.63625652605481 78 526 517.959679332787 8.0403206672131 79 511 510.372642804143 0.627357195856575 80 499 503.101562688043 -4.10156268804326 81 555 543.482720567128 11.5172794328715 82 565 554.355923893489 10.6440761065107 83 542 555.932855417494 -13.9328554174937 84 527 526.663783270571 0.336216729428997 85 510 512.353382708619 -2.35338270861905 86 514 509.901935189993 4.09806481000726 87 517 514.595628298504 2.40437170149607 88 508 505.756010964664 2.24398903533626 89 493 492.88436069052 0.115639309479718 90 490 484.387424791358 5.61257520864183 91 469 473.601079162435 -4.60107916243538 92 478 462.404200940752 15.5957990592484 93 528 523.424661152204 4.57533884779582 94 534 532.379458080291 1.62054191970924 95 518 519.130346449903 -1.13034644990262 96 506 505.892519087918 0.107480912082281 97 502 492.741748299746 9.2582517002544 98 516 503.07740846181 12.9225915381903 99 528 516.077059626759 11.9229403732409 100 533 517.477196976979 15.5228030230213 101 536 517.138128488837 18.8618715111627 102 537 529.316814624977 7.68318537502341 103 524 523.162741553029 0.837258446970736 104 536 532.983308090758 3.01669190924167 105 587 589.76266759015 -2.76266759015039 106 597 600.370403048525 -3.37040304852474 107 581 589.682047832455 -8.68204783245471 108 564 578.804137022419 -14.8041370224188 109 558 566.397709905406 -8.39770990540592 110 575 571.884484623554 3.11551537644561 111 580 581.209177648417 -1.20917764841727 112 575 578.107606064073 -3.10760606407325 113 563 568.530194661399 -5.53019466139949 114 552 559.471044825142 -7.47104482514192 115 537 537.68940729755 -0.689407297549792 116 545 543.240900085893 1.75909991410708 117 601 592.095147897925 8.90485210207453 118 604 605.152945466706 -1.15294546670555 119 586 589.862116780835 -3.86211678083487 120 564 575.833544283051 -11.8335442830514 121 549 565.35518379774 -16.3551837977404 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 122 568.561024560532 552.643901893686 584.478147227378 123 570.58543727255 551.806768810062 589.364105735038 124 563.736654902548 541.77531873324 585.697991071856 125 551.465644931159 526.041459224428 576.88983063789 126 541.730451673823 512.593637842211 570.867265505435 127 525.023975938094 491.947653227259 558.10029864893 128 530.065227641141 492.840161304098 567.290293978185 129 579.114742983349 537.545644208624 620.683841758075 130 579.76540093894 533.668274292965 625.862527584915 131 560.972891379286 510.173091837153 611.772690921419 132 542.803169970987 487.133947307406 598.472392634567 133 535.117591698618 474.418975784733 595.816207612502

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/1ar2m1293529633.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/1ar2m1293529633.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/230jp1293529633.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/230jp1293529633.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/330jp1293529633.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t129352971909e74hoq751cuj9/330jp1293529633.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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