iko Guy Hendrickx opgave 10 oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 15:04:32 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg.htm/, Retrieved Thu, 19 May 2011 17:00:49 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

12,94 12,79 12,82 12,85 12,85 12,72 12,62 12,67 12,6 12,54 12,64 12,67 12,51 12,59 12,52 12,5 12,58 12,51 12,47 12,44 12,51 12,27 12,51 12,41 12,35 12,39 12,31 12,31 12,21 12,1 12,01 11,85 12,12 11,96 11,99 11,93 11,91 11,83 11,92 11,86 11,94 11,87 11,86 11,92 11,82 11,85 11,77 11,82 11,61 11,56 11,45 11,4 11,38 11,33 11,19 11,15 10,98 10,92 10,99 11 10,9 10,99 11,04 11,03 10,99 11 10,87 10,88 10,91 10,92 10,83 10,9 10,82 10,79 10,77 10,72 10,71 10,63 10,61 10,57 10,65 10,57 10,57 10,57 10,52 10,43 10,35 10,2 10,2 10,17 10,14 10,05 10,12 10,12

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 0.629581570005306 beta 0.0178081048922574 gamma 0.529826221021731 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 12.51 12.6435229700855 -0.133522970085474 14 12.59 12.6349101993434 -0.0449101993434446 15 12.52 12.529082878283 -0.00908287828298882 16 12.5 12.4973766108371 0.00262338916289373 17 12.58 12.5747364728286 0.00526352717135481 18 12.51 12.5034008632347 0.00659913676526713 19 12.47 12.3846467827348 0.085353217265153 20 12.44 12.4947651040079 -0.054765104007867 21 12.51 12.3906368384883 0.11936316151165 22 12.27 12.4137247783001 -0.14372477830015 23 12.51 12.4283160073387 0.0816839926612918 24 12.41 12.5099029236739 -0.099902923673886 25 12.35 12.2548411165094 0.095158883490571 26 12.39 12.4080826322851 -0.0180826322850898 27 12.31 12.3269671055889 -0.0169671055889111 28 12.31 12.2932963960858 0.016703603914241 29 12.21 12.3808987914758 -0.170898791475841 30 12.1 12.197801427994 -0.0978014279940229 31 12.01 12.026488915786 -0.0164889157860362 32 11.85 12.0415624001407 -0.191562400140707 33 12.12 11.8805216643384 0.239478335661648 34 11.96 11.9239842657437 0.036015734256301 35 11.99 12.0943754519732 -0.104375451973196 36 11.93 12.0194994657449 -0.0894994657448507 37 11.91 11.8057009166806 0.104299083319377 38 11.83 11.9390060356676 -0.109006035667621 39 11.92 11.7963799254551 0.123620074544874 40 11.86 11.854918839424 0.00508116057597441 41 11.94 11.8953456941662 0.0446543058338378 42 11.87 11.8616792865318 0.0083207134681853 43 11.86 11.7737041056857 0.0862958943142864 44 11.92 11.820848538574 0.0991514614260236 45 11.82 11.9324092011001 -0.112409201100084 46 11.85 11.7154319887301 0.134568011269923 47 11.77 11.9224551321924 -0.152455132192408 48 11.82 11.8218276036797 -0.00182760367968093 49 11.61 11.7038420045317 -0.0938420045317052 50 11.56 11.6708989120675 -0.110898912067508 51 11.45 11.5730749274698 -0.123074927469792 52 11.4 11.4506084677555 -0.050608467755497 53 11.38 11.4606897001496 -0.0806897001496143 54 11.33 11.3365219852837 -0.0065219852836993 55 11.19 11.2498826147686 -0.0598826147685667 56 11.15 11.2012571434799 -0.0512571434799316 57 10.98 11.1686550370624 -0.188655037062434 58 10.92 10.9433431760111 -0.0233431760110587 59 10.99 10.9840447051869 0.00595529481313584 60 11 11.0039140455952 -0.00391404559521291 61 10.9 10.8577357787352 0.0422642212648281 62 10.99 10.8998405137788 0.0901594862211894 63 11.04 10.9211691559302 0.118830844069764 64 11.03 10.9628959521508 0.0671040478491758 65 10.99 11.0401746643781 -0.0501746643781242 66 11 10.949108254159 0.0508917458410192 67 10.87 10.888120433166 -0.018120433165965 68 10.88 10.8679260382209 0.0120739617791248 69 10.91 10.8493862859607 0.0606137140392669 70 10.92 10.8174034376877 0.102596562312346 71 10.83 10.9485066650829 -0.11850666508292 72 10.9 10.8920470122268 0.00795298777321207 73 10.82 10.766502780307 0.0534972196929662 74 10.79 10.8293052876537 -0.039305287653697 75 10.77 10.7775266294246 -0.00752662942463544 76 10.72 10.7309070155251 -0.010907015525083 77 10.71 10.7365376449181 -0.0265376449181165 78 10.63 10.6809357669128 -0.0509357669128097 79 10.61 10.5419014848566 0.0680985151433671 80 10.57 10.5824878960753 -0.0124878960753136 81 10.65 10.5583084291134 0.0916915708866348 82 10.57 10.5547771983643 0.0152228016357085 83 10.57 10.5871448951368 -0.0171448951367736 84 10.57 10.6201223426595 -0.0501223426595274 85 10.52 10.4671051807103 0.0528948192896781 86 10.43 10.5114603307166 -0.081460330716551 87 10.35 10.4390508846258 -0.0890508846258005 88 10.2 10.3392001081631 -0.139200108163061 89 10.2 10.2583121981844 -0.058312198184419 90 10.17 10.1748811437663 -0.00488114376633675 91 10.14 10.0856835191636 0.0543164808364267 92 10.05 10.0991029740418 -0.0491029740417837 93 10.12 10.0692324419545 0.0507675580455391 94 10.12 10.0213849415935 0.09861505840645 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 95 10.0972937278237 9.93145618606037 10.2631312695871 96 10.132176701406 9.93521252354106 10.3291408792709 97 10.0290789611536 9.80438737046983 10.2537705518373 98 10.0113167157982 9.76115022116802 10.2614832104284 99 9.98716919537647 9.7131387339526 10.2611996568003 100 9.93300517147437 9.636321027521 10.2296893154277 101 9.95665471121269 9.63825786515024 10.2750515572751 102 9.92210073437888 9.5827413101585 10.2614601585993 103 9.8493274379848 9.48961477899316 10.2090400969764 104 9.80937770528916 9.42981400790893 10.1889414026694 105 9.83169665765596 9.43270048864053 10.2306928266714 106 9.76238290224417 9.3443061883621 10.1804596161262

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/1ry541305817469.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/1ry541305817469.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/2m6mg1305817469.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/2m6mg1305817469.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/3t6lx1305817469.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13058172465u8jba1bl6ns1hg/3t6lx1305817469.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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