Annelies Reul bankbiljetten in circulatie oef 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 14:50:54 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk.htm/, Retrieved Sun, 07 Jun 2009 22:52:41 +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/2009/Jun/07/t1244407957f8kzofmbecprfvk.htm/}, year = {2009}, } @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 = {2009}, 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:

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334053 326018 326894 330958 333913 337042 342103 344795 342060 342535 343083 354261 363049 347562 347577 349715 353818 354073 357040 359177 354845 354481 352747 360446 368285 354819 353017 354551 352682 351146 350760 347555 335363 325165 311274 297987 344276 306152 283323 285869 293660 300831 313351 322765 323613 329199 334038 350683 353929 340715 347752 358474 366179 373163 382739 391636 391693 395453 399368 416075 427623 418000 425316 436397 442533 449148 460852 462789 465097 469728 475434 495992 487101 489496 498649 505533 512839 522584 532603 531520 531623 535608 539804 559182 548414 550774 556397 569125 571988 578807 588234 588724 588550 592764 598593 619494 604560 606210 614823 620033 625236 631307 639704 639223 637312 640124 644649 668209 651667 653170 662102 667617 671420 677156 686086 684954 684331 722145 731098 753123 740228 741472 747315 757533

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.587581147577237 beta 0.113062234272449 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 363049 353087.920959930 9961.07904006977 14 347562 344405.608884013 3156.39111598709 15 347577 347337.391404895 239.608595105237 16 349715 350793.877166463 -1078.87716646300 17 353818 355513.605943885 -1695.60594388511 18 354073 356144.036570634 -2071.03657063353 19 357040 359932.518160865 -2892.51816086471 20 359177 360547.305711935 -1370.30571193516 21 354845 356668.890735919 -1823.89073591860 22 354481 355877.811354502 -1396.81135450187 23 352747 355358.23644073 -2611.23644073005 24 360446 364983.306173255 -4537.30617325479 25 368285 375099.330256504 -6814.3302565043 26 354819 351832.874953392 2986.12504660804 27 353017 351934.072925415 1082.92707458546 28 354551 353915.772399946 635.227600054408 29 352682 358093.648816612 -5411.64881661232 30 351146 354805.161015928 -3659.16101592797 31 350760 355610.127186802 -4850.12718680239 32 347555 353854.734323942 -6299.73432394234 33 335363 344882.718038305 -9519.71803830477 34 325165 337155.456479371 -11990.4564793712 35 311274 326691.810421809 -15417.8104218086 36 297987 322794.807369723 -24807.8073697231 37 344276 312659.944842000 31616.0551579995 38 306152 314480.733949943 -8328.73394994321 39 283323 303717.173372717 -20394.1733727167 40 285869 287563.091179627 -1694.09117962723 41 293660 282341.082760208 11318.9172397919 42 300831 285251.437567236 15579.5624327643 43 313351 293432.039286254 19918.9607137465 44 322765 304111.370968901 18653.6290310990 45 323613 309215.305480487 14397.6945195131 46 329199 316331.178591151 12867.8214088489 47 334038 322299.938532188 11738.0614678123 48 350683 335473.311058166 15209.6889418335 49 353929 385079.064761858 -31150.0647618583 50 340715 335538.365052654 5176.63494734565 51 347752 331339.217858262 16412.7821417376 52 358474 353579.216875421 4894.78312457888 53 366179 366920.185652254 -741.18565225444 54 373163 371988.815886165 1174.18411383481 55 382739 380338.777875581 2400.22212441912 56 391636 385017.921401923 6618.0785980766 57 391693 383811.246172495 7881.75382750528 58 395453 389511.696756687 5941.30324331328 59 399368 393341.967630174 6026.03236982564 60 416075 408270.853033308 7804.14696669194 61 427623 439314.291098872 -11691.2910988723 62 418000 415739.363032042 2260.63696795801 63 425316 416506.304505586 8809.69549441378 64 436397 433328.192245858 3068.80775414233 65 442533 446993.027822810 -4460.02782280958 66 449148 453768.896846519 -4620.89684651862 67 460852 462310.847118031 -1458.84711803065 68 462789 468575.403903413 -5786.40390341281 69 465097 459960.688910753 5136.31108924706 70 469728 463275.226512279 6452.77348772087 71 475434 467450.802087531 7983.19791246857 72 495992 486446.796367037 9545.20363296272 73 487101 513778.002093938 -26677.0020939382 74 489496 484631.682127279 4864.31787272118 75 498649 489366.06686252 9282.93313748017 76 505533 504980.580435954 552.419564045616 77 512839 514630.703435691 -1791.70343569096 78 522584 523794.220730494 -1210.22073049383 79 532603 537359.113234139 -4756.1132341387 80 531520 540205.455461221 -8685.45546122128 81 531623 533628.849129188 -2005.84912918822 82 535608 532292.111027597 3315.8889724029 83 539804 534045.966224957 5758.03377504298 84 559182 552756.344845155 6425.65515484475 85 548414 561998.233876658 -13584.2338766580 86 550774 552690.89639527 -1916.89639527060 87 556397 554464.91820439 1932.08179561037 88 569125 561191.601277878 7933.39872212161 89 571988 573939.989918909 -1951.98991890938 90 578807 583210.341233609 -4403.34123360901 91 588234 593401.584171042 -5167.58417104173 92 588724 593363.118301346 -4639.11830134573 93 588550 590959.540717115 -2409.54071711493 94 592764 590702.05190113 2061.94809887046 95 598593 591621.942751411 6971.05724858865 96 619494 611769.640678385 7724.35932161508 97 604560 612067.245640871 -7507.24564087135 98 606210 610893.931073229 -4683.93107322929 99 614823 612321.103916551 2501.89608344855 100 620033 621911.352555018 -1878.35255501792 101 625236 623794.716763951 1441.28323604865 102 631307 633741.997700565 -2434.99770056549 103 639704 644893.945075553 -5189.9450755528 104 639223 644361.088129804 -5138.08812980389 105 637312 641717.082081744 -4405.0820817441 106 640124 641311.34241897 -1187.34241897031 107 644649 641191.058982215 3457.94101778546 108 668209 659234.839071536 8974.16092846438 109 651667 651742.246322526 -75.2463225261308 110 653170 655481.841083591 -2311.84108359087 111 662102 661048.727640117 1053.27235988271 112 667617 667583.263554396 33.7364456035430 113 671420 671549.249221964 -129.249221963575 114 677156 678682.004715812 -1526.00471581169 115 686086 689283.670760843 -3197.67076084274 116 684954 689495.530469153 -4541.53046915319 117 684331 686988.240550832 -2657.24055083189 118 722145 688775.645191536 33369.3548084638 119 731098 712897.290512316 18200.7094876842 120 753123 746797.90646344 6325.09353656066 121 740228 734364.62341684 5863.37658315944 122 741472 743776.558518572 -2304.55851857178 123 747315 754619.090993971 -7304.09099397098 124 757533 758756.52229664 -1223.52229663951 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 125 764548.96717861 745841.739600701 783256.19475652 126 774210.575115706 751834.732221783 796586.41800963 127 788791.541992229 762542.86547957 815040.218504887 128 792984.302614655 762931.851261701 823036.75396761 129 796807.045928898 762861.553924692 830752.537933104 130 820543.116749691 781888.628161576 859197.605337806 131 818947.29783685 776394.863554706 861499.732118992 132 838663.770140599 791140.21015529 886187.330125908 133 819292.769537547 768666.692545515 869918.84652958 134 820631.911614681 765775.924215194 875487.899014168 135 830459.899339409 770751.927646977 890167.87103184 136 841742.096125143 779695.703355233 903788.488895053

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/1tsxb1244407852.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/1tsxb1244407852.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/2926x1244407852.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/2926x1244407852.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/3lzvq1244407852.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244407957f8kzofmbecprfvk/3lzvq1244407852.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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