exponential smoothing gemiddelde consumptieprijzen mineraalwater - Rebecca De Cauwer

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 12:54:41 -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/27/t1211914613bqb3hvov8t0ncv2.htm/, Retrieved Tue, 27 May 2008 20:56:53 +0200

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Dataseries X:

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1,12 1,12 1,12 1,13 1,13 1,13 1,14 1,14 1,14 1,14 1,14 1,15 1,15 1,17 1,17 1,18 1,18 1,18 1,18 1,18 1,18 1,19 1,19 1,19 1,19 1,19 1,2 1,21 1,21 1,21 1,21 1,21 1,23 1,24 1,24 1,24 1,27 1,28 1,29 1,29 1,3 1,31 1,31 1,31 1,32 1,32 1,33 1,33 1,34 1,35 1,36 1,37 1,37 1,37 1,37 1,37 1,38 1,38 1,39 1,39 1,39 1,41 1,42 1,42 1,42 1,43 1,43 1,44 1,46 1,46 1,47 1,47 1,47 1,48 1,49 1,49 1,5 1,5 1,51 1,52 1,53 1,53 1,53 1,54

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.759655664815453 beta 0.044937528401639 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.15 1.12774841291029 0.0222515870897062 14 1.17 1.16526984716494 0.00473015283505496 15 1.17 1.16972069619852 0.000279303801478337 16 1.18 1.18038026833481 -0.000380268334809974 17 1.18 1.18010511594078 -0.000105115940782996 18 1.18 1.18045345413021 -0.000453454130213471 19 1.18 1.18093696889368 -0.000936968893684664 20 1.18 1.1818509133503 -0.0018509133502993 21 1.18 1.18241938937945 -0.00241938937945396 22 1.19 1.19207223355274 -0.00207223355274166 23 1.19 1.19191034063664 -0.00191034063663831 24 1.19 1.19180347375300 -0.00180347375299506 25 1.19 1.19324618402795 -0.00324618402795362 26 1.19 1.20726961663339 -0.0172696166333872 27 1.2 1.19274871305413 0.00725128694587274 28 1.21 1.20782720314550 0.00217279685449712 29 1.21 1.20867934663052 0.00132065336947784 30 1.21 1.20920615390046 0.000793846099539364 31 1.21 1.20975410275259 0.000245897247410198 32 1.21 1.21063980567670 -0.000639805676704075 33 1.23 1.21133893225502 0.0186610677449845 34 1.24 1.23750595458373 0.00249404541626941 35 1.24 1.24102933090185 -0.00102933090184676 36 1.24 1.24182235135665 -0.00182235135665354 37 1.27 1.24315558254281 0.0268444174571874 38 1.28 1.27854766646240 0.00145233353760288 39 1.29 1.28622381241383 0.00377618758617393 40 1.29 1.29968527029284 -0.00968527029284272 41 1.3 1.29248682282913 0.00751317717087008 42 1.31 1.29896462704650 0.0110353729535040 43 1.31 1.30887930689162 0.0011206931083807 44 1.31 1.31200807273773 -0.00200807273772763 45 1.32 1.31844168784066 0.00155831215933699 46 1.32 1.32943417942494 -0.00943417942494151 47 1.33 1.32382677178720 0.00617322821280308 48 1.33 1.33094975351980 -0.000949753519796648 49 1.34 1.34140676183843 -0.00140676183843169 50 1.35 1.34976220245625 0.000237797543754859 51 1.36 1.35745628536314 0.00254371463686032 52 1.37 1.36707754873906 0.0029224512609376 53 1.37 1.37420497360625 -0.00420497360625105 54 1.37 1.37267651700804 -0.00267651700803784 55 1.37 1.36928972036853 0.000710279631471744 56 1.37 1.37095027998639 -0.000950279986389413 57 1.38 1.37901250042340 0.000987499576595052 58 1.38 1.38678527581468 -0.00678527581468247 59 1.39 1.38682504115994 0.00317495884005803 60 1.39 1.38953252870718 0.0004674712928181 61 1.39 1.40104198283157 -0.0110419828315653 62 1.41 1.40214809861978 0.00785190138022474 63 1.42 1.41605444334184 0.00394555665815766 64 1.42 1.42673714751333 -0.00673714751333354 65 1.42 1.42419946559852 -0.00419946559851736 66 1.43 1.42239492672203 0.00760507327797422 67 1.43 1.42721553475342 0.00278446524658116 68 1.44 1.42975609075328 0.0102439092467184 69 1.46 1.44726801429782 0.0127319857021790 70 1.46 1.46276466598419 -0.00276466598418956 71 1.47 1.46922115442562 0.000778845574378684 72 1.47 1.46987909612269 0.000120903877314893 73 1.47 1.47925419800945 -0.00925419800945382 74 1.48 1.48758814296854 -0.00758814296853738 75 1.49 1.48918684753247 0.000813152467529221 76 1.49 1.49506919389382 -0.00506919389381655 77 1.5 1.49453036414859 0.00546963585141191 78 1.5 1.50340991621185 -0.00340991621184950 79 1.51 1.49851406704948 0.0114859329505226 80 1.52 1.50974736498271 0.0102526350172862 81 1.53 1.52856490062989 0.00143509937010777 82 1.53 1.53164817768346 -0.00164817768345782 83 1.53 1.54009091682670 -0.0100909168267043 84 1.54 1.53182630437490 0.00817369562509818 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 1.54512845793083 1.53107300035020 1.55918391551147 86 1.56174308446 1.5437498820082 1.5797362869118 87 1.57194603783913 1.55048132462939 1.59341075104888 88 1.57627958784398 1.55164303891961 1.60091613676834 89 1.58290070388133 1.55521862696688 1.61058278079577 90 1.58589045558745 1.55531678403221 1.61646412714270 91 1.58759009383502 1.55421930783424 1.62096087983580 92 1.58988904036232 1.55376216838224 1.62601591234241 93 1.59885870738419 1.55987046154572 1.63784695322266 94 1.59977312282775 1.55812200628954 1.64142423936596 95 1.60743681985243 1.56297387726326 1.65189976244161 96 1.61140351917486 -0.738231184452612 3.96103822280233

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/1fwbe1211914475.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/1fwbe1211914475.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/2h7x71211914475.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/2h7x71211914475.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/3ehk71211914475.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211914613bqb3hvov8t0ncv2/3ehk71211914475.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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Software written by Ed van Stee & Patrick Wessa

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