huishoudbroodprijzen - exponential smoothing - Joris Hoefnagels

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 14:09:25 -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/Jun/07/t1244405469ww49rupy9dg9gdg.htm/, Retrieved Sun, 07 Jun 2009 22:11:13 +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/Jun/07/t1244405469ww49rupy9dg9gdg.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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40.04 40.04 40.03 40.03 41.63 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.03 42.38 42.06 42.06 42.05 42.05 42.05 42.05 44.36 44.48 44.49 44.49 44.49 44.49 44.49 44.48 44.48 44.48 44.48 44.48 44.48 44.49 44.49 44.49 44.49 44.49 44.49 44.49 44.49 45.5 45.94 45.95 45.96 45.96 45.96 45.96 45.96 45.96 45.96 45.96 45.97 46.06 47.9 47.93 47.94 47.94 47.94 47.94 47.94 47.94 47.94 47.94

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.894925705383375 beta 0.00194398841394829 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 42.03 41.5236000239299 0.5063999760701 14 42.03 42.0270791765929 0.0029208234071163 15 42.03 42.0799869748432 -0.0499869748432147 16 42.03 42.0708617495105 -0.0408617495104835 17 42.03 42.0685695653491 -0.0385695653491140 18 42.03 42.0815838565958 -0.0515838565958262 19 42.03 42.7441940129195 -0.714194012919492 20 42.03 41.9863994382988 0.0436005617012256 21 42.03 41.9072195914854 0.122780408514600 22 42.38 41.8991978959644 0.480802104035611 23 42.06 42.2786232324901 -0.218623232490089 24 42.06 42.1157796963423 -0.0557796963422987 25 42.05 42.1686448008874 -0.118644800887367 26 42.05 42.0587154064800 -0.00871540647995772 27 42.05 42.0945256342213 -0.0445256342213227 28 42.05 42.090128442476 -0.0401284424760178 29 44.36 42.0876161813483 2.27238381865168 30 44.48 44.1701115943261 0.309888405673917 31 44.49 45.1228281182427 -0.632828118242664 32 44.49 44.5158871038238 -0.0258871038238340 33 44.49 44.3770758734333 0.112924126566696 34 44.49 44.3933271654744 0.096672834525613 35 44.49 44.3496307034071 0.140369296592922 36 44.48 44.5286923503892 -0.048692350389203 37 44.48 44.5874775530088 -0.107477553008820 38 44.48 44.5002271325712 -0.0202271325712289 39 44.48 44.5249456558405 -0.044945655840543 40 44.48 44.5233837679123 -0.0433837679122959 41 44.48 44.7659788994564 -0.285978899456438 42 44.49 44.350866323073 0.139133676927010 43 44.49 45.0495630977604 -0.55956309776036 44 44.49 44.5707960839758 -0.0807960839757627 45 44.49 44.3961574695561 0.0938425304439363 46 44.49 44.3923892528813 0.0976107471187504 47 44.49 44.3528831570848 0.137116842915226 48 44.49 44.5079248156548 -0.0179248156548297 49 44.49 44.5868623097427 -0.09686230974269 50 45.5 44.5170896004101 0.982910399589876 51 45.94 45.4372550501044 0.502744949895551 52 45.95 45.9270843736982 0.0229156263017884 53 45.96 46.2116943006226 -0.251694300622589 54 45.96 45.8679484243749 0.092051575625149 55 45.96 46.4667498236828 -0.506749823682789 56 45.96 46.0879636217293 -0.127963621729272 57 45.96 45.8865627572664 0.0734372427336112 58 45.96 45.8619399052531 0.0980600947468773 59 45.96 45.8228210615924 0.137178938407622 60 45.96 45.9620497300195 -0.00204973001952879 61 45.97 46.0496538079115 -0.0796538079114981 62 46.06 46.1109550520416 -0.0509550520416227 63 47.9 46.0539749865253 1.8460250134747 64 47.93 47.6952204938199 0.234779506180089 65 47.94 48.1507024651347 -0.210702465134716 66 47.94 47.8764362660807 0.0635637339193451 67 47.94 48.4060110834942 -0.466011083494195 68 47.94 48.1088100038075 -0.168810003807515 69 47.94 47.8894284546906 0.05057154530936 70 47.94 47.8433992573208 0.0966007426791649 71 47.94 47.8020381669398 0.137961833060182 72 47.94 47.9276676359048 0.0123323640952293 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 48.02373549978 47.1234789161183 48.9239920834416 74 48.1657088151805 46.9555785894038 49.3758390409573 75 48.35557953096 46.8975514424516 49.8136076194685 76 48.1726870245262 46.510417642363 49.8349564066894 77 48.3710444264978 46.5169190690239 50.2251697839718 78 48.3126650805351 46.2917624012649 50.3335677598053 79 48.7314979926908 46.5388638548014 50.9241321305802 80 48.8843068606402 46.5405544158451 51.2280593054353 81 48.8375728550328 46.3596041620671 51.3155415479985 82 48.7488720812766 46.1456141108932 51.35213005166 83 48.6226070484274 45.9019438895835 51.3432702072713 84 48.6106390534819 32.3763247194075 64.8449533875563

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/1j9h91244405363.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/1j9h91244405363.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/2m3zt1244405363.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/2m3zt1244405363.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/3c78u1244405363.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244405469ww49rupy9dg9gdg/3c78u1244405363.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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