*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 17:32:32 +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/Jun/02/t1275499992ay55j5k2caom6i5.htm/, Retrieved Wed, 02 Jun 2010 19:33:19 +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/Jun/02/t1275499992ay55j5k2caom6i5.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

562674 599000 668516 597798 579889 668233 499232 215187 555813 586935 546136 571111 634712 639283 712182 621557 621000 675989 501322 220286 560727 602530 626379 605508 646783 658442 712906 687714 723916 707183 629000 237530 613296 730444 734925 651812 676155 748183 810681 729363 701108 790079 594621 230716 617189 691389 701067 705777 747636 773392 813788 766713 728875 749197 680954 241424 680234 708326 694238 772071 795337 788421 889968 797393 751000 821255 691605 290655 727147 868355 812390 799556 843038 847000 941952 804309 840307 871528 656330 370508 742000 847152 731675 898527 778139 856075 938833 813023 783417 828110 657311 310032 780000 860000 780000 807993 895217 856075 893268 875000 835088 934595 832500 300000 791443 900000 781729 880000 875024 992968 976804 968697 871675 1006852 832037 345587 849528 913871 868746 993733

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.175227912761956 beta 0 gamma 0.28039163452554 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 634712 619554.406762921 15157.5932370792 14 639283 628499.919733411 10783.0802665888 15 712182 704141.440656674 8040.55934332637 16 621557 616925.923311347 4631.07668865321 17 621000 614982.406241976 6017.59375802369 18 675989 667318.110855819 8670.88914418127 19 501322 519139.232379148 -17817.2323791476 20 220286 221303.387136167 -1017.38713616732 21 560727 569501.226683812 -8774.22668381152 22 602530 598780.316898144 3749.68310185627 23 626379 556961.898796497 69417.1012035034 24 605508 594947.333797703 10560.6662022970 25 646783 668652.31125539 -21869.3112553904 26 658442 670285.927135215 -11843.9271352155 27 712906 745272.76983353 -32366.7698335300 28 687714 646023.54288252 41690.4571174798 29 723916 650641.248704137 73274.7512958628 30 707183 719075.658912477 -11892.6589124774 31 629000 550304.498029574 78695.5019704263 32 237530 243535.140489665 -6005.14048966489 33 613296 622755.681361663 -9459.68136166257 34 730444 657902.742809847 72541.2571901528 35 734925 639524.447399176 95400.5526008242 36 651812 669693.193506365 -17881.1935063653 37 676155 737874.078085287 -61719.0780852865 38 748183 735410.171252373 12772.8287476272 39 810681 817488.285284563 -6807.28528456332 40 729363 730691.404920605 -1328.40492060478 41 701108 734968.695528562 -33860.6955285618 42 790079 767331.821670047 22747.1783299531 43 594621 613312.747193763 -18691.7471937635 44 230716 253642.775494520 -22926.7754945197 45 617189 642454.913711632 -25265.9137116324 46 691389 695127.772412943 -3738.77241294342 47 701067 667815.762934695 33251.2370653052 48 705777 660978.1501507 44798.8498492998 49 747636 730361.356309192 17274.6436908082 50 773392 759634.404212902 13757.5957870976 51 813788 839466.974308982 -25678.9743089821 52 766713 748482.069205271 18230.9307947287 53 728875 748447.241538165 -19572.2415381655 54 749197 798000.115042067 -48803.1150420669 55 680954 619030.343110814 61923.6568891864 56 241424 258131.639720939 -16707.6397209391 57 680234 664837.821991449 15396.1780085505 58 708326 732971.165874855 -24645.165874855 59 694238 709465.977862678 -15227.9778626784 60 772071 696231.924334372 75839.0756656277 61 795337 767042.402600392 28294.5973996082 62 788421 798515.457734531 -10094.4577345313 63 889968 867732.1450247 22235.8549752998 64 797393 791247.944867612 6145.05513238837 65 751000 779654.019083943 -28654.0190839426 66 821255 822757.408468614 -1502.40846861433 67 691605 669070.250518267 22534.7494817328 68 290655 265564.42091586 25090.5790841401 69 727147 717763.781765935 9383.21823406534 70 868355 779446.427363071 88908.5726369286 71 812390 776111.09212828 36278.9078717206 72 799556 793555.445755648 6000.55424435192 73 843038 845214.216072039 -2176.21607203863 74 847000 863783.437214284 -16783.4372142840 75 941952 945644.270329026 -3692.27032902581 76 804309 854184.040582017 -49875.040582017 77 840307 823196.87157843 17110.1284215699 78 871528 884553.590219084 -13025.5902190842 79 656330 723428.13446402 -67098.1344640201 80 370508 284612.116935953 85895.8830640467 81 742000 782162.077508625 -40162.0775086255 82 847152 858787.930539864 -11635.930539864 83 731675 823922.787155937 -92247.7871559366 84 898527 811886.486890023 86640.5131099772 85 778139 877604.094570184 -99465.094570184 86 856075 875986.169298653 -19911.1692986527 87 938833 961875.459262197 -23042.4592621974 88 813023 854720.928859736 -41697.9288597363 89 783417 840500.032015401 -57083.0320154008 90 828110 881899.559526141 -53789.5595261412 91 657311 702207.740221743 -44896.7402217428 92 310032 302690.227103269 7341.7728967308 93 780000 735269.148354947 44730.8516450532 94 860000 830743.591591135 29256.4084088654 95 780000 785121.037605322 -5121.03760532173 96 807993 829232.905936562 -21239.9059365618 97 895217 832415.100724539 62801.8992754614 98 856075 877849.309781133 -21774.3097811330 99 893268 963276.153969898 -70008.1539698981 100 875000 843667.124162504 31332.8758374964 101 835088 838354.149920531 -3266.1499205312 102 934595 891061.092074049 43533.9079259512 103 832500 722718.484718449 109781.515281551 104 3e+05 330126.176007452 -30126.1760074521 105 791443 792146.906842533 -703.906842533033 106 9e+05 880234.625848807 19765.3741511930 107 781729 822043.126160688 -40314.1261606885 108 880000 857838.818329303 22161.1816706973 109 875024 889078.137458024 -14054.1374580237 110 992968 901889.620794426 91078.3792055736 111 976804 999976.874470696 -23172.8744706957 112 968697 906340.62620922 62356.37379078 113 871675 896980.881478231 -25305.8814782314 114 1006852 960664.618673954 46187.3813260460 115 832037 796680.263005263 35356.7369947374 116 345587 337970.054733646 7616.94526635355 117 849528 845236.042694702 4291.95730529772 118 913871 945124.313741886 -31253.3137418862 119 868746 859533.465010763 9212.5349892372 120 993733 922237.972678414 71495.0273215859 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 955061.71633301 922437.751567954 987685.681098066 122 997290.304336678 961526.527776444 1033054.08089691 123 1056294.78469796 1017242.44198319 1095347.12741273 124 981542.757045696 941163.23923355 1021922.27485784 125 938674.58725364 896722.14997822 980627.02452906 126 1028064.58716711 981896.856511124 1074232.3178231 127 844658.726667276 800903.499963127 888413.953371425 128 353769.924801058 318451.748058775 389088.101543340 129 877677.315879882 819381.982782185 935972.648977579 130 971769.667736124 907311.441741026 1036227.89373122 131 897942.62113054 835813.258045257 960071.984215824 132 976153.976366589 916801.596285473 1035506.35644770

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/11xpy1275499947.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/11xpy1275499947.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/2c7pk1275499947.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/2c7pk1275499947.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/3c7pk1275499947.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275499992ay55j5k2caom6i5/3c7pk1275499947.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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