Double Ex Sm_Gem consumptieprijs roze zalm_Dominique Van Santfoort

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 01 Aug 2008 06:08:39 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi.htm/, Retrieved Fri, 01 Aug 2008 12:09:28 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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11.73 11.74 11.65 11.38 11.53 11.75 11.82 11.83 11.63 11.55 11.4 11.4 11.63 11.46 11.35 11.7 11.52 11.64 11.9 11.73 11.7 11.54 11.97 11.64 11.98 11.79 11.66 11.96 11.83 12.36 12.53 12.55 12.53 12.24 12.34 12.05 12.22 12.23 11.92 12.13 12.1 12.15 12.23 12.08 12.02 11.93 12.16 11.87 11.93 11.79 11.43 11.63 11.93 11.89 11.83 11.59 12.04 11.81 11.9 11.72 11.91 11.94 11.91 11.84 12.01 11.89 11.8 11.7 11.5 11.76 11.61 11.27 11.64 11.39 11.54 11.62 11.59 11.44 11.31 11.56 11.4 11.51 11.5 11.24 11.8 11.87 11.86 12.11 11.92 12.61 13.34 13.31 13.47 13.3 13.18 13.24

Text written by user:

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.776239907184881 beta 0.000989663457731457 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 11.65 11.75 -0.0999999999999996 4 11.38 11.6822991876545 -0.302299187654453 5 11.53 11.4573334415059 0.0726665584940971 6 11.75 11.5234868949778 0.226513105022228 7 11.82 11.7092361885001 0.110763811499872 8 11.83 11.8052213517242 0.0247786482758396 9 11.63 11.8344804351887 -0.204480435188660 10 11.55 11.6856223837861 -0.135622383786060 11 11.4 11.5901105124913 -0.190110512491268 12 11.4 11.4521567352388 -0.052156735238766 13 11.63 11.4212481175839 0.208751882416083 14 11.46 11.5930275476738 -0.133027547673789 15 11.35 11.4994019507464 -0.149401950746443 16 11.7 11.3929511156883 0.307048884311650 17 11.52 11.641051514419 -0.121051514419003 18 11.64 11.5567503056302 0.0832496943697905 19 11.9 11.6310998019591 0.268900198040877 20 11.73 11.8497652015338 -0.119765201533802 21 11.7 11.7666410018402 -0.0666410018401926 22 11.54 11.7247027312841 -0.184702731284119 23 11.97 11.5909783431790 0.379021656820987 24 11.64 11.8951304923781 -0.255130492378139 25 11.98 11.7068324407465 0.273167559253523 26 11.79 11.9288302714429 -0.138830271442945 27 11.66 11.8309122926058 -0.170912292605840 28 11.96 11.7079596710349 0.252040328965073 29 11.83 11.9135133746574 -0.0835133746573735 30 12.36 11.8585327461912 0.501467253808833 31 12.53 12.2580226617741 0.271977338225943 32 12.55 12.4795822840015 0.0704177159985306 33 12.53 12.5447373798140 -0.014737379814024 34 12.24 12.5437803704618 -0.303780370461762 35 12.34 12.3182232878534 0.0217767121466093 36 12.05 12.3453933340569 -0.295393334056911 37 12.22 12.1261364070681 0.0938635929318536 38 12.23 12.2091083484955 0.0208916515044830 39 11.92 12.2354526061888 -0.31545260618881 40 12.13 12.0004706926834 0.129529307316576 41 12.1 12.1110010049378 -0.0110010049378069 42 12.15 12.1124376295002 0.0375623704998027 43 12.23 12.1515999401290 0.0784000598709564 44 12.08 12.2225223231666 -0.142522323166606 45 12.02 12.1218464481325 -0.101846448132452 46 11.93 12.0526665704609 -0.122666570460916 47 12.16 11.9672310485103 0.192768951489729 48 11.87 12.1267972550864 -0.256797255086408 49 11.93 11.9371949553668 -0.00719495536682757 50 11.79 11.9413383943329 -0.151338394332930 51 11.43 11.8334756829978 -0.403475682997785 52 11.63 11.5295839895271 0.100416010472875 53 11.93 11.6169102786404 0.313089721359564 54 11.89 11.8695629099712 0.0204370900288087 55 11.83 11.8950625900254 -0.065062590025434 56 11.59 11.8541440242298 -0.26414402422977 57 12.04 11.6584875846879 0.381512415312088 58 11.81 11.9643085238942 -0.154308523894214 59 11.9 11.8540853246646 0.0459146753354425 60 11.72 11.8993186354218 -0.17931863542184 61 11.91 11.7695791064486 0.140420893551402 62 11.94 11.8881420333840 0.0518579666159624 63 11.91 11.9379987202688 -0.027998720268803 64 11.84 11.9258459508656 -0.0858459508655827 65 12.01 11.8687239042968 0.141276095703203 66 11.89 11.9880115846716 -0.0980115846715677 67 11.8 11.9214793241477 -0.121479324147691 68 11.7 11.8366371453177 -0.136637145317682 69 11.5 11.7399238939114 -0.239923893911355 70 11.76 11.5628510329242 0.197148967075755 71 11.61 11.7252030220270 -0.115203022027035 72 11.27 11.6450064312637 -0.375006431263721 73 11.64 11.3628519801861 0.277148019813861 74 11.39 11.5871387493014 -0.197138749301406 75 11.54 11.4431137555848 0.0968862444151526 76 11.62 11.5273971252902 0.0926028747097813 77 11.59 11.6084267115281 -0.0184267115281074 78 11.44 11.6032565463503 -0.163256546350315 79 11.31 11.4855382672973 -0.175538267297345 80 11.56 11.3581515749633 0.201848425036664 81 11.4 11.5238625569038 -0.123862556903790 82 11.51 11.4366485232222 0.0733514767778374 83 11.5 11.5025762425390 -0.00257624253904609 84 11.24 11.5095638569492 -0.269563856949198 85 11.8 11.3090979469892 0.490902053010766 86 11.87 11.6993131433382 0.170686856661758 87 11.86 11.8410956498146 0.0189043501854336 88 12.11 11.8650730401808 0.244926959819184 89 11.92 12.0646863569465 -0.144686356946488 90 12.61 11.9617551184544 0.648244881545555 91 13.34 12.4748267431988 0.865173256801222 92 13.31 13.1569514699901 0.153048530009924 93 13.47 13.2864141393238 0.183585860676219 94 13.3 13.4397221370248 -0.139722137024782 95 13.18 13.3419582277792 -0.161958227779209 96 13.24 13.2268093585645 0.0131906414354717 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 13.2476281645980 12.8094547422612 13.6858015869348 98 13.2582078683478 12.7033097754527 13.8131059612430 99 13.2687875720977 12.6175908575990 13.9199842865964 100 13.2793672758475 12.5442264885943 14.0145080631007 101 13.2899469795974 12.4793690570989 14.1005249020958 102 13.3005266833472 12.4208272109903 14.1802261557042 103 13.3111063870971 12.3672123340551 14.2550004401391 104 13.3216860908469 12.3175788952916 14.3257932864022 105 13.3322657945968 12.2712487265559 14.3932828626376 106 13.3428454983466 12.227715871125 14.4579751255682 107 13.3534252020965 12.1865909862451 14.5202594179478 108 13.3640049058463 12.1475668882674 14.5804429234253

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/1q3zm1217592511.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/1q3zm1217592511.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/2bdlz1217592511.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/2bdlz1217592511.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/334981217592511.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/01/t12175925683qx747lw6fbw7qi/334981217592511.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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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