Aantal bezoekers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 16 Aug 2010 12:20:14 +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/Aug/16/t12819611841umy7yd4oejoziy.htm/, Retrieved Mon, 16 Aug 2010 14:19:44 +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/Aug/16/t12819611841umy7yd4oejoziy.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 «

556 555 554 552 572 571 556 546 547 547 548 550 555 549 555 550 566 573 543 535 542 541 535 536 548 546 548 548 561 563 527 527 541 534 522 527 539 533 532 519 538 542 503 502 522 511 492 500 509 511 505 493 518 518 474 471 483 461 439 446 461 449 441 424 447 448 404 403 411 386 359 370 385 369 368 352 378 383 334 323 330 303 275 284 301 281 284 272 297 300 240 236 247 218 192 201 223 197 195 175 197 204 142 142 151 127 100 114 139 112 123 108 132 140 76 71 81 57 38 46

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 0.312700997165616 beta 0.158746465680972 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 555 556.096125968013 -1.09612596801264 14 549 550.206838318706 -1.20683831870599 15 555 555.909186031654 -0.909186031654144 16 550 550.436065507093 -0.436065507092508 17 566 566.440247225086 -0.440247225086296 18 573 573.766014542637 -0.766014542637436 19 543 550.225015114608 -7.22501511460837 20 535 537.330053349687 -2.33005334968720 21 542 536.604728002003 5.3952719979975 22 541 537.418402585507 3.58159741449333 23 535 539.109847151401 -4.10984715140148 24 536 539.004461470953 -3.00446147095295 25 548 541.565706931639 6.43429306836106 26 546 537.815268937733 8.18473106226702 27 548 546.775346740264 1.22465325973565 28 548 542.682489447484 5.31751055251561 29 561 560.942550464539 0.0574495354612736 30 563 568.79555489801 -5.79555489801044 31 527 539.90321780154 -12.9032178015398 32 527 528.78717895982 -1.78717895982038 33 541 533.586477691573 7.41352230842665 34 534 534.030031809365 -0.0300318093646865 35 522 529.406827228539 -7.40682722853853 36 527 528.875073865166 -1.8750738651662 37 539 538.046291920791 0.953708079208923 38 533 533.498495593853 -0.498495593853477 39 532 534.147861080172 -2.14786108017165 40 519 530.908081947645 -11.9080819476446 41 538 537.841859469121 0.158140530879336 42 542 539.695301986883 2.30469801311654 43 503 508.300312948131 -5.30031294813119 44 502 506.150266856587 -4.15026685658694 45 522 514.84127872573 7.15872127427008 46 511 509.229119722782 1.77088027721834 47 492 499.454474038915 -7.45447403891473 48 500 501.341235430462 -1.34123543046184 49 509 510.936593504713 -1.9365935047133 50 511 503.555692694639 7.44430730536124 51 505 504.722457199759 0.277542800241463 52 493 495.230095705913 -2.23009570591250 53 518 512.305508189327 5.69449181067341 54 518 517.213528265474 0.786471734525662 55 474 481.725044855555 -7.72504485555481 56 471 479.376457379085 -8.37645737908474 57 483 493.150719195499 -10.150719195499 58 461 477.835306271544 -16.8353062715440 59 439 454.961426817135 -15.9614268171351 60 446 454.966726298304 -8.96672629830408 61 461 457.664975748268 3.33502425173208 62 449 455.441866952845 -6.44186695284452 63 441 444.42357547944 -3.42357547943982 64 424 429.696144133860 -5.69614413385955 65 447 443.917337841272 3.0826621587276 66 448 440.406489689445 7.59351031055508 67 404 403.588119112204 0.411880887795746 68 403 400.068896822909 2.93110317709068 69 411 410.958052253138 0.0419477468622063 70 386 394.209388588765 -8.20938858876485 71 359 375.020366169593 -16.0203661695929 72 370 375.931993643433 -5.9319936434328 73 385 383.427437352347 1.57256264765283 74 369 373.170317363881 -4.17031736388128 75 368 363.747136920517 4.25286307948346 76 352 350.484011589317 1.51598841068346 77 378 367.409369746059 10.5906302539411 78 383 368.167188426949 14.8328115730511 79 334 335.211434335291 -1.21143433529147 80 323 332.266994940328 -9.26699494032829 81 330 334.233761039406 -4.23376103940632 82 303 312.879468444041 -9.8794684440407 83 275 290.078212639396 -15.0782126393955 84 284 293.336608130076 -9.33660813007629 85 301 299.134414442337 1.86558555766288 86 281 285.645488727339 -4.64548872733883 87 284 279.606448339705 4.39355166029526 88 272 265.703218467672 6.29678153232817 89 297 282.207147963618 14.7928520363818 90 300 284.617494792343 15.3825052076568 91 240 250.715508243537 -10.7155082435370 92 236 238.813634439328 -2.8136344393275 93 247 241.618808190292 5.38119180970767 94 218 223.721025347817 -5.72102534781669 95 192 202.998784772789 -10.9987847727890 96 201 206.224278226510 -5.22427822650963 97 223 214.343927679829 8.65607232017149 98 197 202.023412541456 -5.02341254145594 99 195 199.753519815179 -4.75351981517909 100 175 186.183052349202 -11.1830523492015 101 197 192.635037300488 4.36496269951246 102 204 188.571020789394 15.4289792106057 103 142 153.54340498258 -11.5434049825801 104 142 144.302293384114 -2.30229338411394 105 151 145.167174341804 5.83282565819627 106 127 127.096249244895 -0.0962492448953896 107 100 110.522622860485 -10.5226228604849 108 114 109.133999509818 4.86600049018212 109 139 117.041430351892 21.9585696481085 110 112 107.269045840214 4.73095415978588 111 123 105.650453407798 17.3495465922016 112 108 99.995757024145 8.00424297585492 113 132 113.67307143234 18.3269285676599 114 140 120.631786633176 19.3682133668242 115 76 90.8084882621225 -14.8084882621225 116 71 86.612711818103 -15.6127118181030 117 81 84.7881741440841 -3.78817414408411 118 57 68.9266573814876 -11.9266573814876 119 38 50.9446403466986 -12.9446403466986 120 46 49.5255992797587 -3.52559927975867 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 51.0228950707086 34.9303704254978 67.1154197159195 122 35.6830227514078 18.8509671490547 52.5150783537609 123 31.3806633736307 12.9383613663653 49.8229653808961 124 20.8774196972547 1.59373418399446 40.161105210515 125 16.3552363945071 -6.53369141966875 39.244164208683 126 7.4764579354967 -18.2976978723391 33.2506137433325 127 -1.39573003629813 -22.5109808736074 19.7195208010111 128 -7.5376989378109 -30.7840257962577 15.7086279206359 129 -16.8539920080947 -45.6348015673268 11.9268175511373 130 -19.5597083221400 -46.3558488981434 7.23643225386336 131 -20.4147863808383 -45.4306759017807 4.60110314010403 132 -35.6448778254921 -66.1727852380443 -5.11697041293999

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/1vtv61281961209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/1vtv61281961209.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/2o2c91281961209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/2o2c91281961209.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/3o2c91281961209.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t12819611841umy7yd4oejoziy/3o2c91281961209.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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