Prijzen van sigaretten: Luk Glorie

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 23 May 2008 08:30:52 -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/May/23/t1211553173oq5b925wnti9vn6.htm/, Retrieved Fri, 23 May 2008 16:32:56 +0200

User-defined keywords:

Dataseries X:

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3.42 3.42 3.43 3.47 3.51 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.58 3.6 3.61 3.61 3.61 3.63 3.68 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.78 3.79 3.79 3.8 3.8 3.8 3.8 3.81 3.95 3.99 4 4.06 4.16 4.19 4.2 4.2 4.2 4.2 4.2 4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0663859853102358 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 3.43 3.42 0.0100000000000002 4 3.47 3.4306638598531 0.0393361401468977 5 3.51 3.47327522827506 0.0367247717249439 6 3.52 3.51571323843131 0.00428676156869079 7 3.52 3.52599781932184 -0.0059978193218373 8 3.52 3.52559964817644 -0.00559964817644421 9 3.52 3.52522791001486 -0.00522791001486045 10 3.52 3.52488085005741 -0.00488085005741068 11 3.52 3.5245568300172 -0.00455683001719764 12 3.52 3.52425432036662 -0.00425432036661499 13 3.52 3.52397189311725 -0.00397189311725166 14 3.52 3.52370821507912 -0.00370821507911590 15 3.58 3.52346204156735 0.0565379584326533 16 3.6 3.58721536964533 0.0127846303546724 17 3.61 3.60806408992825 0.00193591007174998 18 3.61 3.61819260722583 -0.0081926072258347 19 3.61 3.61764873292289 -0.00764873292288781 20 3.63 3.61714096425143 0.0128590357485727 21 3.68 3.63799462400974 0.0420053759902643 22 3.69 3.69078319228318 -0.000783192283176692 23 3.69 3.70073119929177 -0.0107311992917705 24 3.69 3.70001879805323 -0.0100187980532258 25 3.69 3.69935369027284 -0.00935369027283794 26 3.69 3.69873273632779 -0.0087327363277887 27 3.69 3.69815300502221 -0.00815300502221428 28 3.69 3.69761175975058 -0.00761175975057515 29 3.69 3.69710644557959 -0.00710644557958862 30 3.78 3.69663467718773 0.083365322812266 31 3.79 3.79216896628333 -0.00216896628333174 32 3.79 3.80202497731951 -0.0120249773195082 33 3.8 3.80122668735182 -0.00122668735181986 34 3.8 3.8111452525033 -0.0111452525033013 35 3.8 3.81040536393434 -0.0104053639343382 36 3.8 3.80971459359705 -0.00971459359704552 37 3.81 3.80906968072922 0.00093031927078302 38 3.95 3.81913144089066 0.130868559109339 39 3.99 3.96781927913327 0.0221807208667344 40 4 4.00929176814290 -0.00929176814289523 41 4.06 4.01867492495945 0.0413250750405449 42 4.16 4.08141833078404 0.0785816692159598 43 4.19 4.18663505232227 0.00336494767773488 44 4.2 4.21685843768937 -0.0168584376893692 45 4.2 4.22573927369257 -0.0257392736925688 46 4.2 4.22403054664732 -0.0240305466473183 47 4.2 4.22243525513059 -0.0224352551305920 48 4.2 4.22094586861306 -0.0209458686130617 49 4.23 4.21955535648700 0.0104446435129955 50 4.38 4.25024873443783 0.129751265562170 51 4.43 4.40886240004742 0.0211375999525760 52 4.44 4.46026564044737 -0.0202656404473682 53 4.44 4.46892028593833 -0.0289202859383275 54 4.44 4.46700038426086 -0.0270003842608579 55 4.44 4.46520793714795 -0.0252079371479459 56 4.44 4.46353448340274 -0.0235344834027407 57 4.45 4.46197212353328 -0.0119721235332833 58 4.45 4.47117734231627 -0.0211773423162702 59 4.45 4.46977146358035 -0.0197714635803523 60 4.45 4.46845891548955 -0.0184589154895454 61 4.45 4.46723350219701 -0.0172335021970129 62 4.45 4.46608943917332 -0.0160894391733182 63 4.45 4.46502132590071 -0.0150213259007081 64 4.45 4.46402412038012 -0.0140241203801237 65 4.46 4.46309311533058 -0.00309311533058043 66 4.46 4.47288777582168 -0.0128877758216808 67 4.46 4.4720322081253 -0.0120322081253015 68 4.48 4.47123343813345 0.00876656186655467 69 4.58 4.49181541498074 0.0881845850192597 70 4.67 4.59766963554642 0.072330364453582 71 4.68 4.69247135805852 -0.0124713580585176 72 4.68 4.70164343466565 -0.0216434346656458 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4.70020661392987 4.63337214938476 4.76704107847498 74 4.72041322785974 4.62270729644914 4.81811915927034 75 4.74061984178961 4.61701489930042 4.8642247842788 76 4.76082645571948 4.61351245218189 4.90814045925706 77 4.78103306964935 4.61116393711853 4.95090220218016 78 4.80123968357921 4.60945888914018 4.99302047801824 79 4.82144629750908 4.60810656823353 5.03478602678464 80 4.84165291143895 4.60692584703375 5.07637997584415 81 4.86185952536882 4.60579682053107 5.11792223020658 82 4.88206613929869 4.60463659169532 5.15949568690206 83 4.90227275322856 4.60338598261058 5.20115952384655 84 4.92247936715843 4.60200171774689 5.24295701656997

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/168me1211553047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/168me1211553047.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/2oph61211553047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/2oph61211553047.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/3bm6i1211553047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211553173oq5b925wnti9vn6/3bm6i1211553047.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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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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