Sanne Aertgeerts - opgave 10 - 2

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 12:11:49 -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/25/t1211739244cfavxwp0ydkbqme.htm/, Retrieved Sun, 25 May 2008 20:14:07 +0200

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Dataseries X:

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4,68 4,68 4,67 4,58 4,48 4,46 4,46 4,46 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,44 4,44 4,44 4,44 4,44 4,43 4,38 4,23 4,2 4,2 4,2 4,2 4,2 4,19 4,16 4,06 4 3,99 3,95 3,81 3,8 3,8 3,8 3,8 3,79 3,79 3,78 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,68 3,63 3,61 3,61 3,61 3,6 3,58 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,51 3,47 3,43 3,42 3,42

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.702495359258423 beta 0.000744121041695145 gamma 0.987476481795519 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4.45 4.52479486087743 -0.074794860877434 14 4.45 4.45874328968312 -0.00874328968311566 15 4.45 4.43865964337982 0.0113403566201793 16 4.45 4.43268499432796 0.0173150056720432 17 4.44 4.423443610694 0.0165563893060003 18 4.44 4.43197988864692 0.00802011135307623 19 4.44 4.44206457378818 -0.00206457378817682 20 4.44 4.4463630164589 -0.00636301645889681 21 4.44 4.44767200006759 -0.00767200006758717 22 4.43 4.43806874717169 -0.00806874717168693 23 4.38 4.38770084760291 -0.0077008476029139 24 4.23 4.23737769228695 -0.00737769228695395 25 4.2 4.27301762837097 -0.0730176283709687 26 4.2 4.22649809251183 -0.0264980925118286 27 4.2 4.19940167576739 0.000598324232612413 28 4.2 4.18740248645746 0.0125975135425422 29 4.2 4.17492702948742 0.0250729705125767 30 4.19 4.18635212454012 0.00364787545987788 31 4.16 4.18940474195076 -0.0294047419507564 32 4.06 4.17195639262795 -0.111956392627949 33 4 4.09695432324497 -0.0969543232449706 34 3.99 4.02331385763772 -0.0333138576377161 35 3.95 3.9579761700664 -0.00797617006640339 36 3.81 3.82006252335074 -0.0100625233507445 37 3.8 3.83051487618554 -0.0305148761855389 38 3.8 3.8241995343314 -0.0241995343314003 39 3.8 3.80514360525338 -0.00514360525337754 40 3.8 3.79186362052222 0.00813637947778245 41 3.79 3.77995921271979 0.0100407872802051 42 3.79 3.77408671321380 0.0159132867862044 43 3.78 3.77525803308276 0.00474196691723705 44 3.69 3.75735547532147 -0.0673554753214685 45 3.69 3.71550395482912 -0.0255039548291207 46 3.69 3.70843775579092 -0.0184377557909197 47 3.69 3.66231287706251 0.0276871229374893 48 3.69 3.55678049891460 0.133219501085404 49 3.69 3.66072897782281 0.0292710221771881 50 3.69 3.69727560673611 -0.0072756067361075 51 3.69 3.69522427939798 -0.00522427939797909 52 3.68 3.68556616919589 -0.00556616919588704 53 3.63 3.66469035591541 -0.0346903559154077 54 3.61 3.62896521162893 -0.0189652116289274 55 3.61 3.60226049666730 0.00773950333269635 56 3.61 3.56628619129268 0.0437138087073241 57 3.6 3.61394750604186 -0.013947506041863 58 3.58 3.61646643239148 -0.0364664323914763 59 3.52 3.57135770806769 -0.0513577080676919 60 3.52 3.44365968773492 0.0763403122650814 61 3.52 3.47732015600411 0.0426798439958866 62 3.52 3.51153224511078 0.00846775488922091 63 3.52 3.5202613607948 -0.000261360794798104 64 3.52 3.51357040117549 0.00642959882451111 65 3.52 3.49296524688575 0.0270347531142519 66 3.52 3.50496895216553 0.0150310478344724 67 3.52 3.50979606399883 0.0102039360011665 68 3.51 3.4864813647701 0.0235186352299031 69 3.47 3.50260628389314 -0.0326062838931351 70 3.43 3.48466705053475 -0.0546670505347469 71 3.42 3.42260106780859 -0.00260106780859193 72 3.42 3.36749289077071 0.0525071092292904 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 3.3749473331035 3.29999883966856 3.44989582653844 74 3.36876145535439 3.27694992696200 3.46057298374678 75 3.36833352905565 3.26212483993824 3.47454221817306 76 3.36334661176228 3.24444343887686 3.48224978464769 77 3.34442273382891 3.21433227581699 3.47451319184082 78 3.33366026969917 3.19303235948946 3.47428817990887 79 3.32606661950282 3.17548830015961 3.47664493884604 80 3.30007652922886 3.14079954132471 3.45935351713301 81 3.28320672535708 3.11535392880988 3.45105952190428 82 3.28077316006100 3.10412103970419 3.45742528041781 83 3.27212359849797 3.08730320862586 3.45694398837007 84 3.23583972329864 -1.63634735658003 8.10802680317732

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/1lnwt1211739103.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/1lnwt1211739103.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/2anis1211739103.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/2anis1211739103.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/3ub2t1211739103.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211739244cfavxwp0ydkbqme/3ub2t1211739103.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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