Opgave 10 oef 2 willem dierickx

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 13:17:09 -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/Jun/01/t1212347986nbtjqldv37y5ocq.htm/, Retrieved Sun, 01 Jun 2008 19:19:50 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3,35 3,35 3,35 3,4 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 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 0.0267594807601861 gamma 0.189768133478781 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.42 3.37588856275748 0.0441114372425191 14 3.42 3.42125663406065 -0.00125663406064991 15 3.42 3.42122005591351 -0.00122005591351426 16 3.43 3.43118801297687 -0.00118801297686932 17 3.47 3.47116689691699 -0.00116689691698868 18 3.51 3.51114601048734 -0.00114601048734286 19 3.52 3.52111584812909 -0.00111584812909182 20 3.52 3.52108339922625 -0.00108339922625289 21 3.52 3.52105189991888 -0.00105189991887711 22 3.52 3.51893367765305 0.00106632234695114 23 3.52 3.51771756681591 0.00228243318409271 24 3.52 3.51985915877127 0.000140841228727151 25 3.52 3.52725631854992 -0.00725631854992326 26 3.52 3.52066866925353 -0.000668669253534926 27 3.52 3.52064920560608 -0.000649205606076286 28 3.58 3.53092455285644 0.0490754471435606 29 3.6 3.62359185338927 -0.0235918533892709 30 3.61 3.64277357021164 -0.0327735702116403 31 3.61 3.62075858549629 -0.0107585854962853 32 3.61 3.61020987094782 -0.000209870947822655 33 3.63 3.61020376905174 0.0197962309482604 34 3.68 3.62853163971491 0.0514683602850878 35 3.69 3.67845666078794 0.0115433392120616 36 3.69 3.69091057956862 -0.000910579568619063 37 3.69 3.6986360438745 -0.00863604387450012 38 3.69 3.69170027495085 -0.00170027495085101 39 3.69 3.69165078328954 -0.00165078328953872 40 3.69 3.70239690162931 -0.0123969016293137 41 3.69 3.73434575429593 -0.0443457542959322 42 3.69 3.73276847830309 -0.0427684783030871 43 3.78 3.69970235431219 0.0802976456878097 44 3.79 3.78114554027880 0.00885445972120502 45 3.79 3.79135540566411 -0.00135540566411008 46 3.8 3.78906810068412 0.0109318993158816 47 3.8 3.79798584268982 0.00201415731017551 48 3.8 3.80028456439374 -0.000284564393736364 49 3.8 3.80825819241790 -0.00825819241789638 50 3.81 3.80113416193817 0.0088658380618285 51 3.95 3.81134396650686 0.138656033493137 52 3.99 3.96626860334788 0.0237313966521153 53 4 4.0418648555755 -0.041864855575497 54 4.06 4.05045036373338 0.0095496362666152 55 4.16 4.07613213306740 0.0838678669325965 56 4.19 4.16658234981999 0.0234176501800070 57 4.2 4.19712048543048 0.00287951456951863 58 4.2 4.20466226896450 -0.00466226896450372 59 4.2 4.20303330740683 -0.00303330740683005 60 4.2 4.2054193819983 -0.00541938199829772 61 4.2 4.21409271030591 -0.0140927103059125 62 4.23 4.20607422545851 0.0239257745414916 63 4.38 4.23662587007582 0.143374129924178 64 4.43 4.40291268319916 0.0270873168008423 65 4.44 4.4925019439234 -0.0525019439233958 66 4.44 4.50080362897636 -0.0608036289763598 67 4.44 4.46077086208357 -0.0207708620835731 68 4.44 4.44757759426897 -0.00757759426896687 69 4.44 4.44735727938848 -0.00735727938848019 70 4.45 4.44450665996467 0.00549334003532742 71 4.45 4.45303088351653 -0.00303088351652914 72 4.45 4.45556436552752 -0.0055643655275226 73 4.45 4.46475882108412 -0.0147588210841247 74 4.45 4.45626807460502 -0.00626807460502032 75 4.45 4.45608562327545 -0.00608562327544604 76 4.45 4.46893748942416 -0.0189374894241565 77 4.45 4.50739572231754 -0.0573957223175423 78 4.46 4.50542348674352 -0.0454234867435153 79 4.46 4.47571799978883 -0.0157179997888264 80 4.46 4.46261496105226 -0.00261496105225678 81 4.48 4.46253893232714 0.0174610676728584 82 4.58 4.48029360529785 0.0997063947021504 83 4.67 4.58103250063080 0.088967499369196 84 4.68 4.67585918132283 0.00414081867717453 85 4.68 4.69576899697257 -0.0157689969725654 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 4.68683220134191 4.61326257311618 4.76040182956764 87 4.69363142873911 4.58831751033437 4.79894534714385 88 4.71414177389617 4.5833411009018 4.84494244689053 89 4.77594962996827 4.62181187770708 4.93008738222946 90 4.83788189082637 4.66219720044024 5.01356658121249 91 4.85852974054167 4.66387081020305 5.05318867088028 92 4.86536171510408 4.65314750974865 5.07757592045951 93 4.87216118740882 4.64308854197157 5.10123383284608 94 4.87603562921543 4.63078061142329 5.12129064700757 95 4.87815691509444 4.61724439068912 5.13906943949976 96 4.88314036492862 4.60678045330341 5.15950027655383 97 4.89836368675299 0.881671161459107 8.91505621204688

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/17h7d1212347823.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/17h7d1212347823.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/2ahr21212347823.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/2ahr21212347823.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/39us91212347823.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347986nbtjqldv37y5ocq/39us91212347823.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')

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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