Tijdreeks 1 - Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 29 Jul 2010 12:07:54 +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/Jul/29/t1280405277bgorhoc3v4w8szg.htm/, Retrieved Thu, 29 Jul 2010 14:07:57 +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/Jul/29/t1280405277bgorhoc3v4w8szg.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:

Habimana Christelle

Dataseries X:

» Textbox « » Textfile « » CSV «

900 899 898 896 916 915 900 890 891 891 892 894 896 889 878 883 901 897 881 866 867 866 862 871 865 856 847 859 870 872 856 839 829 825 822 827 822 812 810 816 820 823 810 793 777 772 765 765 753 742 736 740 742 742 728 707 699 696 689 692 673 653 642 648 654 653 630 609 598 601 592 591 568 538 523 530 529 534 513 491 480 478 462 461 437 411 400 405 395 407 385 366 349 343 332 327 306 276 269 268 260 274 247 226 212 199 188 179 155 124 117 116 105 112 86 64 53 42 32 24

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.768991824691135 beta 0.729803955352783 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 896 903.770032051282 -7.77003205128221 14 889 886.612471780298 2.38752821970195 15 878 874.814238181876 3.18576181812375 16 883 881.459398185756 1.54060181424438 17 901 900.954049786438 0.0459502135618095 18 897 897.241781061954 -0.241781061954157 19 881 880.339225263874 0.660774736125859 20 866 869.70989638307 -3.70989638307083 21 867 865.304180709716 1.69581929028436 22 866 865.132132493982 0.867867506018456 23 862 865.602121557149 -3.60212155714862 24 871 861.821500470522 9.17849952947813 25 865 871.391894037613 -6.3918940376135 26 856 860.792986846258 -4.7929868462578 27 847 842.779990723652 4.22000927634758 28 859 849.54346293209 9.45653706791052 29 870 878.925685014414 -8.92568501441428 30 872 867.358390803323 4.64160919667722 31 856 856.270800335272 -0.270800335272043 32 839 845.243805159692 -6.24380515969244 33 829 840.044603702055 -11.0446037020552 34 825 822.640221050535 2.35977894946518 35 822 816.818364626724 5.18163537327587 36 827 821.267860589491 5.73213941050903 37 822 821.180051966459 0.819948033541323 38 812 817.13264328428 -5.13264328428022 39 810 801.386200506656 8.61379949334412 40 816 815.649666180763 0.350333819237335 41 820 831.583850658154 -11.5838506581536 42 823 817.41580865937 5.58419134062945 43 810 802.75644298545 7.24355701454988 44 793 797.183464927787 -4.1834649277871 45 777 794.671265536733 -17.6712655367334 46 772 773.760226477783 -1.76022647778268 47 765 761.602460117091 3.3975398829092 48 765 759.986382743761 5.01361725623906 49 753 752.987246497228 0.0127535027721706 50 742 741.266972680605 0.733027319395319 51 736 730.821573637208 5.17842636279181 52 740 736.221210656225 3.77878934377543 53 742 749.645923301676 -7.64592330167602 54 742 742.293058489909 -0.293058489908503 55 728 720.020057341917 7.97994265808313 56 707 709.309482295501 -2.30948229550097 57 699 703.110135911258 -4.11013591125823 58 696 701.901328632517 -5.90132863251654 59 689 691.024787126059 -2.02478712605864 60 692 685.843442157568 6.15655784243177 61 673 679.440541357478 -6.44054135747831 62 653 660.175014836356 -7.17501483635579 63 642 637.488110453274 4.51188954672614 64 648 634.49058011224 13.5094198877603 65 654 650.65854670793 3.34145329207013 66 653 657.519398794553 -4.51939879455335 67 630 635.601571358116 -5.6015713581163 68 609 606.141919772997 2.85808022700292 69 598 600.472463694726 -2.47246369472634 70 601 598.00035886708 2.99964113292026 71 592 597.750571584554 -5.75057158455377 72 591 592.389595163245 -1.38959516324496 73 568 573.834239012965 -5.83423901296533 74 538 551.766057103879 -13.7660571038787 75 523 519.912257582851 3.08774241714946 76 530 510.300614558721 19.6993854412788 77 529 524.756163242897 4.2438367571026 78 534 526.877881912528 7.12211808747224 79 513 516.578531067405 -3.57853106740504 80 491 494.680422662202 -3.68042266220232 81 480 483.133610528595 -3.1336105285954 82 478 481.428244198975 -3.42824419897539 83 462 470.617734449276 -8.61773444927587 84 461 458.853904045013 2.14609595498695 85 437 438.769542800978 -1.76954280097806 86 411 417.054752106214 -6.05475210621438 87 400 398.411923176506 1.58807682349357 88 405 394.030517291353 10.9694827086469 89 395 395.849189114665 -0.849189114664853 90 407 389.507750384278 17.4922496157224 91 385 385.319295289814 -0.31929528981442 92 366 368.341387966974 -2.34138796697374 93 349 361.139497893285 -12.1394978932851 94 343 350.575288727777 -7.57528872777664 95 332 331.184218230723 0.815781769276782 96 327 330.262729297620 -3.26272929761961 97 306 303.180488353435 2.81951164656454 98 276 284.646170170953 -8.6461701709535 99 269 264.963225222065 4.03677477793508 100 268 265.193378621304 2.80662137869615 101 260 253.984909981498 6.01509001850235 102 274 256.991635633593 17.0083643664070 103 247 247.877468977656 -0.87746897765615 104 226 229.250960956314 -3.25096095631363 105 212 217.823459001706 -5.823459001706 106 199 215.452532419926 -16.4525324199259 107 188 188.473243654802 -0.473243654801763 108 179 182.194820801609 -3.19482080160881 109 155 153.184444959842 1.81555504015776 110 124 127.280588985871 -3.28058898587113 111 117 113.715994330466 3.28400566953428 112 116 111.723033187744 4.27696681225648 113 105 101.851542268803 3.14845773119688 114 112 103.049706897292 8.9502931027082 115 86 76.9411985476 9.05880145239999 116 64 64.3176950315437 -0.317695031543721 117 53 55.1081601179772 -2.10816011797725 118 42 55.7805178084333 -13.7805178084333 119 32 38.6885555070466 -6.68855550704657 120 24 27.6550092910357 -3.65500929103571 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 -0.156966635392177 -13.2660857899975 12.9521525192132 122 -29.2582907949413 -51.0740298877948 -7.4425517020878 123 -37.5666244872557 -70.5925235666712 -4.54072540784015 124 -42.4815647584413 -88.5733304084701 3.61020089158754 125 -58.9289813252306 -119.636478939499 1.77851628903826 126 -63.6049181363643 -140.297873939165 13.0880376664360 127 -106.387320288330 -200.31244851559 -12.4621920610693 128 -143.043192933233 -255.355312657759 -30.7310732087067 129 -167.143917895076 -298.925207483226 -35.3626283069263 130 -181.085567773435 -333.358576216247 -28.8125593306231 131 -191.747069148066 -365.484071319053 -18.0100669770792 132 -198.98763661954 -395.117670008475 -2.85760323060447

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/1fa7a1280405270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/1fa7a1280405270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/2c5w11280405270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/2c5w11280405270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/3c5w11280405270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280405277bgorhoc3v4w8szg/3c5w11280405270.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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