Exponential smoothing (triple) Hotelkamers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 20 Aug 2009 00:45:21 -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/Aug/20/t1250750822anzpnegcepi39di.htm/, Retrieved Thu, 20 Aug 2009 08:47:02 +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/Aug/20/t1250750822anzpnegcepi39di.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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613.20 614.70 618.40 628.20 629.00 629.70 630.40 630.40 639.30 639.40 640.90 640.80 642.10 645.30 647.60 648.40 648.80 648.90 648.90 648.90 650.30 650.30 650.00 650.00 650.50 658.40 666.00 675.50 680.70 690.60 690.60 691.10 692.90 693.80 692.80 697.50 699.00 702.10 704.80 715.50 721.80 726.40 727.70 727.40 731.30 734.40 733.40 733.40 738.10 742.60 747.20 751.10 752.60 758.90 759.10 764.30 765.60 767.60 767.60 765.60 768.20 770.90 775.10 777.60 778.60 778.90 779.40 779.90 781.70 789.10 788.70 788.80 790.80 794.10 795.10 797.30 803.80 805.60 804.60 804.50 805.80 806.80 805.20 814.90 816.60 819.50 823.00 824.00 831.40 831.70 831.10 832.10 833.30 838.80 838.00 837.30 994.20 994.20 994.20 994.20 994.20 1092.60 1100.00 1100.00 1092.60 1000.70 1000.70 1000.50 1000.50 1000.50 1000.50 1000.50 1000.50 1087.70 1113.20 1116.00 1085.20 1031.30 1028.70 1027.50 1027.50 1027.50 1027.50 1027.50 1027.50 etc...

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 0.85113803258568 beta 0.000776052458181784 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 642.1 631.018990384616 11.0810096153845 14 645.3 643.663037746213 1.63696225378703 15 647.6 647.682478475829 -0.0824784758291344 16 648.4 649.055049993036 -0.655049993035732 17 648.8 649.619018103533 -0.819018103532812 18 648.9 649.813719068193 -0.913719068192677 19 648.9 649.26054623663 -0.360546236629602 20 648.9 648.027961689804 0.872038310195649 21 650.3 656.732552734673 -6.43255273467298 22 650.3 650.849012982438 -0.549012982438171 23 650 651.76448170791 -1.76448170790957 24 650 650.085919951226 -0.0859199512262876 25 650.5 652.939696752137 -2.43969675213668 26 658.4 652.66223941392 5.73776058608041 27 666 659.911117117006 6.08888288299408 28 675.5 666.450262111264 9.04973788873633 29 680.7 675.25547318668 5.44452681331995 30 690.6 680.776892838364 9.82310716163613 31 690.6 689.461354289501 1.13864571049919 32 691.1 689.706030978773 1.39396902122724 33 692.9 697.785583048908 -4.8855830489083 34 693.8 694.113686891617 -0.313686891617522 35 692.8 695.067792533913 -2.26779253391271 36 697.5 693.22966434243 4.27033565757051 37 699 699.462652099881 -0.46265209988087 38 702.1 702.10837491168 -0.0083749116799936 39 704.8 704.538101292678 0.261898707322189 40 715.5 706.573922640835 8.92607735916533 41 721.8 714.752606541265 7.04739345873452 42 726.4 722.306553597568 4.09344640243228 43 727.7 724.834174801593 2.86582519840749 44 727.4 726.6007463789 0.799253621100434 45 731.3 733.252753058162 -1.95275305816176 46 734.4 732.773044701903 1.62695529809696 47 733.4 735.104657753112 -1.70465775311197 48 733.4 734.736130627043 -1.33613062704273 49 738.1 735.50599361551 2.5940063844904 50 742.6 740.83631210334 1.76368789665958 51 747.2 744.831045287364 2.36895471263642 52 751.1 749.967923875615 1.13207612438521 53 752.6 751.245919220381 1.35408077961858 54 758.9 753.523327265407 5.37667273459317 55 759.1 756.970239015856 2.12976098414367 56 764.3 757.812032162707 6.48796783729301 57 765.6 768.909356020471 -3.30935602047089 58 767.6 767.820082923837 -0.220082923837026 59 767.6 768.094650210511 -0.49465021051094 60 765.6 768.82265462753 -3.22265462753046 61 768.2 768.582415546898 -0.382415546897619 62 770.9 771.264361604261 -0.364361604260921 63 775.1 773.545102816125 1.55489718387457 64 777.6 777.8116148775 -0.211614877499755 65 778.6 777.984737187726 0.615262812273954 66 778.9 780.237377535784 -1.33737753578441 67 779.4 777.487186682304 1.91281331769596 68 779.9 778.793777970835 1.10622202916500 69 781.7 783.84916889733 -2.14916889733036 70 789.1 784.205141305567 4.89485869443308 71 788.7 788.79362672087 -0.0936267208702475 72 788.8 789.458395673745 -0.658395673745531 73 790.8 791.826726552271 -1.02672655227127 74 794.1 793.965765028985 0.134234971015076 75 795.1 796.95971720046 -1.85971720046018 76 797.3 798.057830996494 -0.757830996494249 77 803.8 797.889654207331 5.91034579266875 78 805.6 804.362480304937 1.23751969506338 79 804.6 804.293426133758 0.306573866241706 80 804.5 804.117468118063 0.38253188193687 81 805.8 808.076469869447 -2.27646986944671 82 806.8 809.376770229757 -2.57677022975668 83 805.2 806.862427975836 -1.66242797583618 84 814.9 806.10597728766 8.79402271233937 85 816.6 816.469153470103 0.130846529896871 86 819.5 819.771397022999 -0.271397022998826 87 823 822.128136386768 0.87186361323154 88 824 825.721895388378 -1.72189538837767 89 831.4 825.731831791799 5.66816820820134 90 831.7 831.308792431808 0.391207568192272 91 831.1 830.38613556318 0.713864436820813 92 832.1 830.573722497607 1.52627750239321 93 833.3 835.116718085362 -1.81671808536248 94 838.8 836.77026372229 2.02973627771064 95 838 838.322484216557 -0.3224842165572 96 837.3 840.273642590616 -2.97364259061635 97 994.2 839.334085104341 154.865914895659 98 994.2 974.38234963584 19.8176503641607 99 994.2 994.126096754754 0.0739032452460151 100 994.2 996.772309653661 -2.57230965366114 101 994.2 997.275704199483 -3.07570419948252 102 1092.6 994.736286828652 97.8637131713479 103 1100 1077.00000433284 22.9999956671645 104 1100 1096.46760955858 3.53239044142470 105 1092.6 1102.41227135412 -9.81227135412018 106 1000.7 1098.01963907956 -97.3196390795565 107 1000.7 1014.78259930551 -14.0825993055078 108 1000.5 1004.73918258754 -4.23918258753804 109 1000.5 1026.32978586146 -25.8297858614569 110 1000.5 987.46916519302 13.0308348069794 111 1000.5 998.484467943944 2.01553205605614 112 1000.5 1002.37780252342 -1.87780252342316 113 1000.5 1003.38628895331 -2.88628895331226 114 1087.7 1016.02316223005 71.6768377699486 115 1113.2 1064.82560855981 48.3743914401898 116 1116 1102.98083626988 13.0191637301211 117 1085.2 1115.00830048850 -29.8083004884954 118 1031.3 1080.55132194164 -49.251321941643 119 1028.7 1050.63118855406 -21.9311885540603 120 1027.5 1035.38096919761 -7.88096919761483 121 1027.5 1050.66360399335 -23.1636039933524 122 1027.5 1019.86461594267 7.63538405732743 123 1027.5 1024.65179725382 2.84820274617641 124 1027.5 1028.67874161845 -1.17874161845452 125 1027.5 1030.13702338420 -2.63702338420171 126 1152.2 1054.09075774105 98.109242258949 127 1155.3 1121.94452808830 33.3554719116967 128 1154 1142.06616028115 11.9338397188540 129 1119.9 1146.80639334363 -26.9063933436250 130 1079.3 1111.93883866952 -32.638838669523 131 1074.3 1100.24995018375 -25.9499501837502 132 1069.8 1083.69289851987 -13.8928985198734 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 1091.60172275452 1043.68974546214 1139.51370004690 134 1085.13643141071 1022.19896939723 1148.07389342419 135 1082.74064876656 1007.71215543054 1157.76914210258 136 1083.77047030927 998.330364773994 1169.21057584455 137 1086.04226951660 991.314572444378 1180.76996658881 138 1127.26683222121 1024.07162064847 1230.46204379395 139 1101.94098774343 990.910546270021 1212.97142921683 140 1090.42587692981 972.066845494074 1208.78490836554 141 1079.16128303771 953.891343066026 1204.43122300939 142 1066.29356380199 934.464683994943 1198.12244360903 143 1083.35423603938 945.268214308324 1221.44025777043 144 1090.66983370732 946.589136170892 1234.75053124375

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/1qy421250750715.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/1qy421250750715.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/23g1z1250750715.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/23g1z1250750715.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/32po01250750715.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/20/t1250750822anzpnegcepi39di/32po01250750715.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=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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