Ann-Sophie Coeman smoothing verkochte ton koffie per maand

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:30:21 +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/18/t1305728791bu0z0h4f62x8b0w.htm/, Retrieved Wed, 18 May 2011 16:26:34 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

600 425 398 582 458 455 621 635 589 220 351 379 683 524 536 598 581 632 645 722 689 645 354 486 423 479 684 601 608 463 602 485 563 645 486 435 479 579 563 202 389 467 466 706 546 689 531 528 579 684 651 637 548 496 582 467 693 615 708 648 899 852 745 689 582 674 684 542 489 472 398 486 549 766 654 628 689 648 578 536 548 496 475 687 642 584 596 609 678 694 485 489 537 706 489 598

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.102723846750587 beta 0.0340175164889182 gamma 0.50686474160226 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 683 610.13817589381 72.8618241061897 14 524 479.466736808435 44.5332631915651 15 536 497.974606674458 38.0253933255424 16 598 549.0546612296 48.9453387704002 17 581 532.196391030527 48.8036089694732 18 632 591.161152259318 40.8388477406818 19 645 729.658622663509 -84.6586226635087 20 722 739.362973822626 -17.3629738226256 21 689 682.8856346614 6.11436533859955 22 645 256.602963515161 388.397036484839 23 354 476.997965622894 -122.997965622894 24 486 498.767626701021 -12.7676267010207 25 423 947.082145169763 -524.082145169763 26 479 683.494731547057 -204.494731547057 27 684 674.225248111374 9.77475188862627 28 601 740.071117509099 -139.071117509099 29 608 695.09744888087 -87.0974488808699 30 463 744.564947816607 -281.564947816607 31 602 801.14831659405 -199.14831659405 32 485 832.454778639389 -347.454778639389 33 563 744.339694678477 -181.339694678477 34 645 430.305762185496 214.694237814504 35 486 398.264203080927 87.7357969190726 36 435 488.602564406121 -53.6025644061212 37 479 678.172154738252 -199.172154738252 38 579 586.773157239927 -7.77315723992717 39 563 694.869138127748 -131.869138127748 40 202 673.648360753349 -471.648360753349 41 389 614.01379803094 -225.013798030941 42 467 554.751022690543 -87.751022690543 43 466 653.405619433389 -187.405619433389 44 706 609.087832538876 96.9121674611237 45 546 636.021533068656 -90.0215330686558 46 689 507.229770687397 181.770229312603 47 531 416.008185786757 114.991814213243 48 528 441.77618643605 86.22381356395 49 579 572.245494247736 6.75450575226432 50 684 587.38581747848 96.61418252152 51 651 648.204110831681 2.79588916831869 52 637 460.891552133065 176.108447866935 53 548 592.48774980799 -44.48774980799 54 496 619.640641855753 -123.640641855753 55 582 679.550607004092 -97.5506070040924 56 467 797.193773178553 -330.193773178553 57 693 684.364719726853 8.63528027314658 58 615 686.968240860749 -71.9682408607486 59 708 520.973475514394 187.026524485606 60 648 540.058158972345 107.941841027655 61 899 647.03632273249 251.963677267511 62 852 737.085895624876 114.914104375124 63 745 758.87680124095 -13.8768012409498 64 689 627.392704591635 61.6072954083651 65 582 648.307551540508 -66.3075515405077 66 674 635.122230456125 38.8777695438753 67 684 736.630252879207 -52.6302528792074 68 542 749.375383720764 -207.375383720764 69 489 818.101760276982 -329.101760276982 70 472 743.94473633468 -271.944736334681 71 398 666.818447517795 -268.818447517795 72 486 599.398719650655 -113.398719650655 73 549 738.342798272456 -189.342798272456 74 766 715.537489541915 50.4625104580851 75 654 672.91159799633 -18.9115979963302 76 628 581.692902135257 46.3070978647434 77 689 544.290750695768 144.709249304232 78 648 594.119116107914 53.8808838920863 79 578 647.527191025146 -69.5271910251463 80 536 587.830021981531 -51.8300219815306 81 548 605.900260290522 -57.900260290522 82 496 579.890039983033 -83.8900399830329 83 475 518.708453726366 -43.7084537263661 84 687 542.978851488934 144.021148511066 85 642 675.867165716623 -33.8671657166227 86 584 784.80647889131 -200.806478891309 87 596 682.126276186204 -86.1262761862039 88 609 611.885449999294 -2.88544999929354 89 678 611.658190420613 66.3418095793871 90 694 610.914198098344 83.085801901656 91 485 609.959056543955 -124.959056543955 92 489 552.216077041558 -63.2160770415579 93 537 564.49793121961 -27.4979312196098 94 706 528.92431163553 177.07568836447 95 489 511.597224588999 -22.5972245889991 96 598 624.972270032514 -26.9722700325143 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 658.508422317156 488.452028936849 828.564815697464 98 691.951977283666 518.538513659586 865.365440907746 99 660.589070868376 484.559585203199 836.618556533552 100 636.24588328311 457.58099258753 814.91077397869 101 668.990136424608 485.716385501104 852.263887348111 102 668.471446579923 481.665443935433 855.277449224413 103 561.065488829984 376.385502518933 745.745475141036 104 543.332928722381 356.151514586947 730.514342857815 105 580.392652666636 386.796854305303 773.988451027968 106 641.736950065045 438.672154444971 844.801745685119 107 512.340330388093 317.766873490839 706.913787285348 108 628.893827061907 485.317236132536 772.470417991277

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/1co3m1305729018.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/1co3m1305729018.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/2c9pe1305729018.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/2c9pe1305729018.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/3k49r1305729018.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728791bu0z0h4f62x8b0w/3k49r1305729018.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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