exponential smoothing eigen reeks - opgave 10 - Vanovermeire Bart

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 08:43:51 -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/t1212331487ymq737xbl7v7w1h.htm/, Retrieved Sun, 01 Jun 2008 14:44:51 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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42.3 50.8 54.1 38.2 48.4 61.1 54.1 61.4 64.3 57.4 71.7 55.3 55.1 66.8 59.4 64.9 59.2 77.4 75.8 38.3 54 61.8 61.3 104.3 39.7 62.6 50.2 90.9 56.2 50.2 52.8 45.6 69 81.9 73.9 54.9 55.4 64.6 49.6 55.8 44.6 61.5 40.5 48.3 50.9 65.3 56.5 53.2 56.9 79.5 94 68.4 65.9 85.5 77.5 114.8 87.4 107.5 151.7 94.4 67.5 95.2 96.2 70.6 80.1 83.4 115.4 61.5 80.6 94.3 82.6 107.7 79.1 102.8 125.2 106.4 62.3 107.4 67.9 88 76.5 130.5 100.9 85.6

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.176253502446095 beta 0 gamma 0.418332059342259 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 55.1 49.8291168600151 5.27088313998491 14 66.8 61.593061668187 5.20693833181301 15 59.4 56.8396307629743 2.56036923702569 16 64.9 62.8460006896219 2.05399931037810 17 59.2 57.8921204207593 1.30787957924071 18 77.4 74.04576836115 3.35423163885002 19 75.8 71.5005422509939 4.29945774900614 20 38.3 36.9807768193409 1.31922318065913 21 54 52.9339946550697 1.06600534493033 22 61.8 60.125300431647 1.67469956835297 23 61.3 59.0411762408223 2.25882375917774 24 104.3 103.146368300788 1.15363169921187 25 39.7 56.6300743549653 -16.9300743549653 26 62.6 64.652505069366 -2.05250506936604 27 50.2 57.7020879009876 -7.50208790098762 28 90.9 61.59061520845 29.3093847915500 29 56.2 60.9339263879327 -4.73392638793268 30 50.2 77.1517397456751 -26.9517397456751 31 52.8 69.7016294630241 -16.9016294630241 32 45.6 33.8703690083966 11.7296309916035 33 69 50.8518929037716 18.1481070962284 34 81.9 61.3365832404395 20.5634167595605 35 73.9 63.7008558230243 10.1991441769757 36 54.9 112.623356679300 -57.7233566792996 37 55.4 49.840091276851 5.55990872314898 38 64.6 67.9640419486506 -3.36404194865058 39 49.6 58.3359411989728 -8.73594119897277 40 55.8 74.8655780331879 -19.0655780331879 41 44.6 55.1524772585909 -10.5524772585909 42 61.5 61.3013367902296 0.19866320977043 43 40.5 61.8256271891787 -21.3256271891787 44 48.3 35.9279540333495 12.3720459666505 45 50.9 54.0801733459901 -3.18017334599011 46 65.3 60.3737382365941 4.92626176340593 47 56.5 57.0530012679981 -0.553001267998113 48 53.2 74.9000841626525 -21.7000841626525 49 56.9 44.525723173122 12.3742768268779 50 79.5 59.1580314999023 20.3419685000977 51 94 52.3499857097922 41.6500142902078 52 68.4 75.4511122681335 -7.0511122681335 53 65.9 58.7278553793876 7.17214462061242 54 85.5 74.1436847384617 11.3563152615383 55 77.5 66.9643134136831 10.5356865863169 56 114.8 54.2060932429432 60.5939067570568 57 87.4 81.1194894424056 6.2805105575944 58 107.5 97.3208492953723 10.1791507046277 59 151.7 89.5443595691264 62.1556404308736 60 94.4 118.655250946366 -24.2552509463664 61 67.5 87.3905255427864 -19.8905255427864 62 95.2 108.235746459935 -13.0357464599350 63 96.2 98.6241737833614 -2.42417378336138 64 70.6 96.7872624601969 -26.1872624601969 65 80.1 78.519982375964 1.58001762403606 66 83.4 98.340186507812 -14.9401865078121 67 115.4 84.2762821251624 31.1237178748376 68 61.5 88.7683680484569 -27.2683680484569 69 80.6 81.5030701162586 -0.903070116258633 70 94.3 97.1270994408894 -2.82709944088941 71 82.6 102.283715607434 -19.6837156074336 72 107.7 89.1420738267124 18.5579261732876 73 79.1 69.949016417805 9.15098358219494 74 102.8 96.2881208677823 6.51187913221773 75 125.2 93.9197088299157 31.2802911700843 76 106.4 89.1688579796499 17.2311420203501 77 62.3 87.6758576226446 -25.3758576226446 78 107.4 97.5773954718848 9.8226045281152 79 67.9 103.462129093953 -35.5621290939532 80 88 76.2504165400699 11.7495834599301 81 76.5 85.2807586458286 -8.78075864582861 82 130.5 99.3519870964662 31.1480129035338 83 100.9 104.412252298965 -3.51225229896471 84 85.6 107.491704678564 -21.8917046785639 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 76.5977799453311 56.2451429734555 96.9504169172067 86 100.987519666047 79.4013045443748 122.573734787718 87 105.466879518987 83.3812703818284 127.552488656145 88 90.8246549539113 68.6537323092663 112.995577598556 89 72.6100164422124 47.2459989803746 97.9740339040501 90 98.3979097573256 73.3259679701948 123.469851544456 91 86.6350381965648 61.1872628011026 112.082813592027 92 81.7930500026288 55.4518909698628 108.134209035395 93 81.6230129905803 49.7398467184914 113.506179262669 94 110.766225800591 80.233922491469 141.298529109713 95 98.9006007839252 68.1115197089342 129.689681858916 96 96.089343064161 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/1nxgf1212331422.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/1nxgf1212331422.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/2je8b1212331422.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/2je8b1212331422.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/3hg321212331422.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212331487ymq737xbl7v7w1h/3hg321212331422.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; 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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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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