Pieter De Bock Oef 10.2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 09:19:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8.htm/, Retrieved Fri, 20 May 2011 11:15:09 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

193.230 199.068 195.076 191.563 191.067 186.665 185.508 184.371 183.046 175.714 175.768 171.029 170.465 170.102 156.389 124.291 99.360 86.675 85.056 128.236 164.257 162.401 152.779 156.005 153.387 153.190 148.840 144.211 145.953 145.542 150.271 147.489 143.824 134.754 131.736 126.304 125.511 125.495 130.133 126.257 110.323 98.417 105.749 120.665 124.075 127.245 146.731 144.979 148.210 144.670 142.970 142.524 146.142 146.522 148.128 148.798 150.181 152.388 155.694 160.662 155.520 158.262 154.338 158.196 160.371 154.856 150.636 145.899 141.242 140.834 141.119 139.104 134.437 129.425 123.155 119.273 120.472 121.523 121.983 123.658 124.794 124.827 120.382 117.395 115.790 114.283 117.271 117.448 118.764 120.550 123.554 125.412 124.182 119.828 115.361 114.226 115.214 115.864 114.276 113.469

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 0.55298969290894 beta 0.0295901195827954 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 170.465 207.245518963675 -36.7805189636753 14 170.102 187.558447053807 -17.4564470538071 15 156.389 161.519122348371 -5.13012234837052 16 124.291 122.042933804745 2.24806619525545 17 99.36 94.025592655243 5.33440734475697 18 86.675 80.1195450903855 6.55545490961448 19 85.056 130.497241356277 -45.4412413562767 20 128.236 99.9960774077378 28.2399225922622 21 164.257 111.177345083744 53.0796549162556 22 162.401 132.55235608923 29.8486439107699 23 152.779 151.16443840933 1.61456159066989 24 156.005 150.76003333926 5.24496666074015 25 153.387 140.547132329906 12.8398676700938 26 153.19 158.197271180858 -5.00727118085806 27 148.84 146.015501938255 2.82449806174472 28 144.211 115.829719848576 28.3812801514235 29 145.953 105.66447858772 40.28852141228 30 145.542 114.22654755418 31.3154524458197 31 150.271 158.051387579523 -7.78038757952336 32 147.489 184.926952533313 -37.4379525333133 33 143.824 173.432384685125 -29.6083846851251 34 134.754 139.883969831799 -5.12996983179946 35 131.736 127.146666456923 4.5893335430769 36 126.304 130.673137371871 -4.36913737187055 37 125.511 119.044448346111 6.46655165388938 38 125.495 125.593780731207 -0.0987807312074693 39 130.133 120.108982090508 10.024017909492 40 126.257 105.928155649466 20.3288443505337 41 110.323 97.1004480715298 13.2225519284702 42 98.417 86.7091673800778 11.7078326199222 43 105.749 101.919018999164 3.82998100083643 44 120.665 121.851808429494 -1.18680842949372 45 124.075 134.390873293253 -10.3158732932535 46 127.245 123.256032233516 3.98896776648361 47 146.731 120.858159709848 25.8728402901515 48 144.979 133.450047896589 11.5289521034105 49 148.21 137.017030346183 11.1929696538173 50 144.67 144.883117628552 -0.213117628551714 51 142.97 145.49608199744 -2.5260819974396 52 142.524 130.412180425553 12.1118195744474 53 146.142 115.160138580633 30.9818614193666 54 146.522 115.499255680238 31.0227443197616 55 148.128 139.771401851633 8.35659814836694 56 148.798 161.941704836096 -13.1437048360956 57 150.181 165.569189583034 -15.3881895830336 58 152.388 159.722069264881 -7.33406926488053 59 155.694 162.357959314036 -6.66395931403557 60 160.662 151.52603491747 9.13596508252957 61 155.52 154.560944171426 0.959055828573582 62 158.262 152.443097741044 5.81890225895626 63 154.338 156.230443881107 -1.89244388110743 64 158.196 148.923254632423 9.2727453675765 65 160.371 141.372905452979 18.9980945470205 66 154.856 135.743875556652 19.1121244433477 67 150.636 143.743154384477 6.89284561552287 68 145.899 155.914792482284 -10.0157924822835 69 141.242 160.741487049076 -19.4994870490761 70 140.834 156.626677459881 -15.792677459881 71 141.119 155.151723001848 -14.0327230018476 72 139.104 147.454234569359 -8.35023456935872 73 134.437 137.024722977954 -2.58772297795429 74 129.425 134.920339864681 -5.4953398646806 75 123.155 128.621234219819 -5.46623421981917 76 119.273 123.887511080067 -4.6145110800671 77 120.472 112.336526591918 8.13547340808204 78 121.523 99.90534934514 21.6176506548601 79 121.983 103.022810403793 18.9601895962067 80 123.658 113.701483802267 9.95651619773327 81 124.794 125.052411468092 -0.258411468092035 82 124.827 133.268604243427 -8.44160424342707 83 120.382 136.799624923596 -16.4176249235956 84 117.395 130.438606619547 -13.0436066195474 85 115.79 120.027978352994 -4.23797835299443 86 114.283 115.722650746628 -1.43965074662773 87 117.271 111.757037709688 5.51396229031165 88 117.448 113.733376190591 3.71462380940913 89 118.764 112.88137892438 5.88262107561951 90 120.55 105.587893252327 14.9621067476732 91 123.554 104.08491327636 19.4690867236396 92 125.412 111.276512460468 14.1354875395316 93 124.182 120.696816620873 3.48518337912689 94 119.828 127.711090173141 -7.88309017314117 95 115.361 128.380621834522 -13.0196218345223 96 114.226 125.857508714399 -11.631508714399 97 115.214 120.637692373301 -5.42369237330057 98 115.864 117.381886285159 -1.51788628515904 99 114.276 116.934394197803 -2.65839419780274 100 113.469 113.906504100355 -0.43750410035463 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 101 111.97892179512 79.9180345773316 144.039809012908 102 105.646155242574 68.7529674352973 142.539343049851 103 97.7942497985216 56.3968842244173 139.191615372626 104 91.427196457038 45.7505652645845 137.103827649492 105 87.6303521197976 37.8358139991389 137.424890240456 106 86.9390177189653 33.1457422714561 140.732293166474 107 89.1041236341693 31.401728142495 146.806519125844 108 94.0466577788788 32.5032068585061 155.590108699252 109 97.8696602108024 32.5369988634763 163.202321558128 110 99.2835401806874 30.2009971882181 168.366083173157 111 99.1149464914984 26.311992484433 171.917900498564 112 98.5427228563814 22.0409308872353 175.044514825528

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/1gyu21305883136.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/1gyu21305883136.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/2h12m1305883136.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/2h12m1305883136.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/3dyhv1305883136.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058829096iu06y1ut1hv4u8/3dyhv1305883136.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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