gemiddelde temperatuur Nederland

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:40:51 +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/18/t1305729403zi7klyeqjdaiu7g.htm/, Retrieved Wed, 18 May 2011 16:36:46 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

17 16,7 15,4 15,1 16,1 17 16,1 14,3 16,1 14,8 15,9 17,6 15,9 14,8 16,5 15,6 14,6 17,1 15,2 14,8 15,4 16,6 15,1 15,4 15,2 16,6 16,1 15,7 15,8 15,7 16,9 15,9 17,1 17 16,6 17,1 16,6 16,6 16,5 17 15,9 17 16,1 16,1 16,8 16,7 15,7 18,7 16,1 16,3 17,2 16,1 16,5 16,5 15,1 16,7 14,4 16,2 15,9 17,3 15,6 15,6 14,7 15,8 15,8 14,8 16,1 16,3 16,1 17,4 16,7 16,1 15,4 16,9 15,5 17,6 18,4 15,9 15,2 15,5 15,9 15,8 17,6 18,2 15,9 15,7 16,4 15,6 15,8 17 16,8 16,6 17,7 15,7 18 18,2 16,4 18 16,3

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.171048148072183 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 16.7 17 -0.300000000000001 3 15.4 16.9486855555783 -1.54868555557834 4 15.1 16.6837857593505 -1.58378575935053 5 16.1 16.4128821382705 -0.31288213827052 6 17 16.3593642279545 0.640635772045517 7 16.1 16.4689437903517 -0.368943790351661 8 14.3 16.4058366382693 -2.10583663826928 9 16.1 16.0456371811508 0.0543628188492349 10 14.8 16.0549358406389 -1.25493584063891 11 15.9 15.8402813891482 0.0597186108517835 12 17.6 15.8504961469399 1.74950385306014 13 15.9 16.1497455410509 -0.249745541050943 14 14.8 16.1070270287649 -1.3070270287649 15 16.5 15.8834624760144 0.616537523985627 16 15.6 15.9889200777091 -0.388920077709125 17 14.6 15.9223960186689 -1.32239601866889 18 17.1 15.6962026286575 1.40379737134245 19 15.2 15.9363195692943 -0.736319569294274 20 14.8 15.8103734705772 -1.01037347057718 21 15.4 15.6375509595737 -0.237550959573687 22 16.6 15.5969183078658 1.00308169213416 23 15.1 15.7684935736705 -0.668493573670498 24 15.4 15.654148985896 -0.254148985896004 25 15.2 15.6106772725241 -0.410677272524071 26 16.6 15.5404316856035 1.05956831439651 27 16.1 15.721668883537 0.378331116463023 28 15.7 15.7863817203661 -0.0863817203660613 29 15.8 15.7716062870702 0.0283937129298444 30 15.7 15.7764629790837 -0.0764629790837006 31 16.9 15.7633841281154 1.13661587188465 32 15.9 15.9578001680707 -0.0578001680706688 33 17.1 15.9479135563639 1.15208644363608 34 17 16.1449758089669 0.85502419103306 35 16.6 16.2912261134001 0.308773886599941 36 17.1 16.344041314876 0.755958685123971 37 16.6 16.4733466479856 0.126653352014433 38 16.6 16.4950104692948 0.104989530705229 39 16.5 16.5129687340889 -0.0129687340888687 40 17 16.5107504561401 0.489249543859874 41 15.9 16.5944356845625 -0.694435684562519 42 17 16.4756537467629 0.524346253237137 43 16.1 16.5653422023277 -0.465342202327662 44 16.1 16.4857462803997 -0.385746280399683 45 16.8 16.4197650935116 0.380234906488415 46 16.7 16.4848035700988 0.215196429901169 47 15.7 16.5216125209052 -0.821612520905173 48 18.7 16.3810772207714 2.31892277922858 49 16.1 16.7777246676809 -0.67772466768087 50 16.3 16.6618011183712 -0.361801118371222 51 17.2 16.5999157071034 0.600084292896618 52 16.1 16.7025590140906 -0.602559014090552 53 16.5 16.5994924106262 -0.099492410626162 54 16.5 16.5824744180413 -0.0824744180413184 55 15.1 16.568367321572 -1.46836732157202 56 16.7 16.3172058105274 0.382794189472587 57 14.4 16.3826820477295 -1.98268204772949 58 16.2 16.0435479552494 0.156452044750605 59 15.9 16.0703087877661 -0.170308787766091 60 17.3 16.0411777850183 1.25882221498172 61 15.6 16.256496993643 -0.65649699364303 62 15.6 16.1442043986654 -0.544204398665434 63 14.7 16.051119244101 -1.35111924410097 64 15.8 15.8200127995728 -0.0200127995728145 65 15.8 15.8165896472681 -0.0165896472681446 66 14.8 15.8137520188258 -1.01375201882576 67 16.1 15.6403516134012 0.459648386598825 68 16.3 15.7189736186933 0.581026381306728 69 16.1 15.8183571051969 0.281642894803131 70 17.4 15.8665316007706 1.53346839922936 71 16.7 16.128828530586 0.571171469413969 72 16.1 16.226526352661 -0.126526352660957 73 15.4 16.204884254356 -0.804884254355974 74 16.9 16.0672102932359 0.832789706764075 75 15.5 16.2096574303115 -0.709657430311495 76 17.6 16.088271841091 1.51172815890895 77 18.4 16.346850143061 2.053149856939 78 15.9 16.6980376238051 -0.798037623805081 79 15.2 16.5615347661613 -1.3615347661613 80 15.5 16.3286467658735 -0.828646765873515 81 15.9 16.1869082711648 -0.286908271164846 82 15.8 16.1378331427155 -0.337833142715507 83 17.6 16.0800474092966 1.51995259070339 84 18.2 16.3400324850939 1.85996751490605 85 15.9 16.658176483993 -0.758176483993045 86 15.7 16.5284918004942 -0.828491800494156 87 16.4 16.3867798123266 0.0132201876733582 88 15.6 16.3890411009453 -0.789041100945335 89 15.8 16.2540770818758 -0.454077081875798 90 17 16.1764080379389 0.823591962061077 91 16.8 16.3172819178166 0.482718082183393 92 16.6 16.399849951815 0.20015004818497 93 17.7 16.4340852468936 1.26591475310637 94 15.7 16.6506176210297 -0.950617621029732 95 18 16.4880162374278 1.51198376257219 96 18.2 16.746638259931 1.453361740069 97 16.4 16.9952330940488 -0.595233094048766 98 18 16.8934195756404 1.10658042435955 99 16.3 17.0826981079201 -0.78269810792008 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 100 16.9488190460607 15.1389890486533 18.7586490434682 101 16.9488190460607 15.112704395747 18.7849336963745 102 16.9488190460607 15.0867907437308 18.8108473483907 103 16.9488190460607 15.0612328127303 18.8364052793912 104 16.9488190460607 15.0360163437834 18.8616217483381 105 16.9488190460607 15.0111280058223 18.8865100862992 106 16.9488190460607 14.9865553132762 18.9110827788452 107 16.9488190460607 14.96228655285 18.9353515392715 108 16.9488190460607 14.9383107182583 18.9593273738632 109 16.9488190460607 14.9146174518857 18.9830206402358 110 16.9488190460607 14.8911969924938 19.0064410996277 111 16.9488190460607 14.8680401282259 19.0295979638956

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/1404k1305729648.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/1404k1305729648.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/2ovkl1305729648.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/2ovkl1305729648.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/3agd51305729648.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305729403zi7klyeqjdaiu7g/3agd51305729648.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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