Exponential smoothing Eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 29 May 2011 13:56:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3.htm/, Retrieved Sun, 29 May 2011 15:52:51 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 577 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601 604 586 564 549 551 556

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 0.896019100477419 beta 0.149965314457529 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 519 495.152617126487 23.8473828735126 14 517 517.285341877365 -0.285341877364772 15 510 512.543885898163 -2.54388589816313 16 509 511.77398259048 -2.77398259047987 17 501 504.039839483569 -3.03983948356949 18 507 509.798531759515 -2.79853175951524 19 569 568.25967113385 0.74032886614998 20 580 579.627228729263 0.372771270736848 21 578 579.810609693414 -1.81060969341377 22 565 575.267047567444 -10.2670475674438 23 547 555.059916434488 -8.05991643448772 24 555 549.807403639914 5.19259636008599 25 562 563.870693221883 -1.87069322188279 26 561 556.062514240995 4.93748575900509 27 555 551.903892114055 3.09610788594466 28 544 553.618642200399 -9.61864220039945 29 537 535.969238799313 1.03076120068749 30 543 543.183176255541 -0.183176255541412 31 594 606.001986407741 -12.0019864077411 32 611 602.089278051318 8.91072194868218 33 613 606.504469851434 6.49553014856622 34 611 606.22826727301 4.77173272698951 35 594 598.804345495192 -4.80434549519202 36 595 598.594921159887 -3.59492115988689 37 591 603.94776852926 -12.9477685292593 38 589 584.523110792841 4.47688920715916 39 584 577.198186207734 6.80181379226588 40 573 579.132619056229 -6.13261905622869 41 567 564.185069114877 2.81493088512309 42 569 572.34002679714 -3.34002679713979 43 621 632.664381004718 -11.6643810047181 44 629 630.341379251068 -1.34137925106791 45 628 622.547424939059 5.45257506094106 46 612 618.258537483585 -6.25853748358486 47 595 595.884560743539 -0.884560743539168 48 597 595.814635810382 1.18536418961776 49 593 601.58976680362 -8.58976680362014 50 590 585.577187886504 4.42281211349575 51 580 576.205294108798 3.7947058912016 52 574 571.571038970495 2.42896102950533 53 573 563.798811603177 9.20118839682266 54 573 576.500238726862 -3.50023872686211 55 620 635.617675603752 -15.6176756037519 56 626 629.6454873794 -3.64548737939992 57 620 619.03325840312 0.966741596879956 58 588 607.604795019858 -19.6047950198581 59 566 570.691464189829 -4.69146418982916 60 577 563.14318215259 13.8568178474098 61 561 576.565347258292 -15.5653472582917 62 549 552.509894888093 -3.50989488809262 63 532 532.45165269515 -0.451652695150301 64 526 519.65593034402 6.34406965597975 65 511 512.607365407336 -1.60736540733615 66 499 508.389266012661 -9.38926601266144 67 555 546.117985666576 8.88201433342363 68 565 558.274471318732 6.72552868126752 69 542 555.404035729895 -13.4040357298946 70 527 526.148836956353 0.85116304364658 71 510 508.95177478121 1.04822521878958 72 514 507.296656213074 6.7033437869265 73 517 509.3459771847 7.6540228153002 74 508 508.962377934173 -0.962377934172878 75 493 493.950882115909 -0.950882115908826 76 490 483.391228790408 6.60877120959174 77 469 477.913011507385 -8.91301150738468 78 478 466.790646709776 11.2093532902241 79 528 526.07737427003 1.92262572996981 80 534 534.053007923467 -0.0530079234665664 81 518 525.160939996395 -7.1609399963952 82 506 505.982412837625 0.0175871623750368 83 502 490.951338984673 11.0486610153267 84 516 502.525559431693 13.4744405683071 85 528 515.379209738477 12.6207902615226 86 533 523.712064885863 9.2879351141371 87 536 523.847723464494 12.1522765355063 88 537 533.461265846623 3.53873415337728 89 524 530.12959350431 -6.12959350430958 90 536 531.81186884958 4.18813115042008 91 587 597.663629278294 -10.6636292782937 92 597 601.212283981931 -4.21228398193148 93 581 592.438111859684 -11.4381118596835 94 564 573.873529788956 -9.87352978895626 95 558 553.234302823314 4.76569717668644 96 575 562.350248676714 12.6497513232858 97 580 576.847250405073 3.1527495949274 98 575 576.989648381008 -1.98964838100778 99 563 566.087652129082 -3.08765212908213 100 552 558.459977641041 -6.45997764104072 101 537 541.206802761931 -4.20680276193082 102 545 542.436351880473 2.56364811952699 103 601 602.243509146296 -1.24350914629565 104 604 612.4278443106 -8.42784431060045 105 586 595.76513711945 -9.76513711945017 106 564 575.800839572587 -11.8008395725869 107 549 551.792750259015 -2.79275025901529 108 551 550.682609940456 0.317390059544437 109 556 547.350519139623 8.64948086037668 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 547.139995750804 532.051174650631 562.228816850977 111 533.845816089555 512.421395963215 555.270236215894 112 524.853108568665 497.47066666358 552.23555047375 113 511.02146025158 478.087713288261 543.955207214899 114 513.811713301297 474.370722208903 553.252704393691 115 564.409407826634 514.420059079258 614.398756574011 116 571.17868902913 513.591608022507 628.765770035754 117 560.379162514143 496.73682117116 624.021503857127 118 548.654016850196 479.086521267024 618.221512433369 119 537.255806517171 461.765465835619 612.746147198723 120 540.084730482562 456.593869518811 623.575591446313 121 538.488961909698 448.073347236991 628.904576582405

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/1qxsa1306677356.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/1qxsa1306677356.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/236tz1306677356.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/236tz1306677356.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/3kzs11306677356.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306677170mmvscje9jnycfb3/3kzs11306677356.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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