sven van roy - opgave 10 - oefening 2- eigen reeks

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 31 May 2008 10:28:22 -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/31/t12122513941o3im1928g1bnym.htm/, Retrieved Sat, 31 May 2008 16:29:54 +0000

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Dataseries X:

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7,1 7,1 7,3 7,1 7,4 7,3 7,4 7,6 7,8 7,7 8 8,1 7,7 7,9 8,1 8,1 8,2 8,1 8,3 8,3 8,3 8,5 8,7 8,7 8,4 8,4 8,6 8,7 8,7 8,6 8 8,1 8,1 8,5 8,6 8,6 8,3 8,3 8,5 9,2 9,2 9 7,4 7,3 7,4 8,6 8,7 8,7 8,5 8,4 8,6 8,4 8,4 8,2 7,7 7,6 7,7 8,1 8,2 8,3 8,1 8 8,2 7,6 7,7 7,6 6,9 6,9 7 7,4 7,4 7,5

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 0.759346220500825 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7.7 7.37274716299798 0.327252837002016 14 7.9 7.75400583960488 0.145994160395121 15 8.1 8.01386373524959 0.0861362647504098 16 8.1 8.0252429356433 0.074757064356703 17 8.2 8.11913964169434 0.080860358305662 18 8.1 8.02750710970904 0.0724928902909596 19 8.3 8.22788294657541 0.0721170534245879 20 8.3 8.23287423418936 0.0671257658106406 21 8.3 8.24257116279 0.057428837210006 22 8.5 8.4395906568518 0.0604093431481942 23 8.7 8.63803477639236 0.061965223607638 24 8.7 8.64249299494366 0.0575070050563422 25 8.4 8.32228438272953 0.0777156172704654 26 8.4 8.47778538836818 -0.0777853883681825 27 8.6 8.56197071735786 0.0380292826421424 28 8.7 8.53050762919589 0.169492370804109 29 8.7 8.70031868514656 -0.000318685146565301 30 8.6 8.53544788077916 0.0645521192208385 31 8 8.73826863996108 -0.738268639961078 32 8.1 8.12734877532027 -0.0273487753202684 33 8.1 8.06391840080886 0.0360815991911441 34 8.5 8.24149342570072 0.258506574299279 35 8.6 8.58953675722952 0.0104632427704807 36 8.6 8.55426006664101 0.0457399333589894 37 8.3 8.23443026712994 0.0655697328700562 38 8.3 8.34234278710195 -0.0423427871019530 39 8.5 8.47945253846481 0.0205474615351875 40 9.2 8.46610319297355 0.733896807026447 41 9.2 9.02363594479763 0.176364055202370 42 9 9.00060930513061 -0.000609305130609528 43 7.4 8.94616870431184 -1.54616870431184 44 7.3 7.8894016654441 -0.589401665444092 45 7.4 7.41664253361104 -0.0166425336110434 46 8.6 7.58888286558445 1.01111713441555 47 8.7 8.44717107745916 0.252828922540841 48 8.7 8.60422046692174 0.0957795330782574 49 8.5 8.32393465665722 0.176065343342783 50 8.4 8.49035250013043 -0.0903525001304306 51 8.6 8.60883654246001 -0.00883654246001164 52 8.4 8.73552077333166 -0.335520773331657 53 8.4 8.35672076964868 0.0432792303513203 54 8.2 8.2076243241798 -0.00762432417980641 55 7.7 7.76246074038417 -0.0624607403841715 56 7.6 8.06849393088288 -0.468493930882877 57 7.7 7.83174362246814 -0.131743622468142 58 8.1 8.1599319666047 -0.0599319666046956 59 8.2 8.02635607461968 0.173643925380317 60 8.3 8.08983014938727 0.210169850612727 61 8.1 7.93237442633346 0.167625573666543 62 8 8.02972734991236 -0.0297273499123598 63 8.2 8.2041951279071 -0.00419512790709753 64 7.6 8.25093153080812 -0.650931530808116 65 7.7 7.7262645662722 -0.0262645662721974 66 7.6 7.5281470531668 0.0718529468331965 67 6.9 7.16412147444243 -0.264121474442434 68 6.9 7.19014777554868 -0.290147775548684 69 7 7.15290119137087 -0.152901191370868 70 7.4 7.44385958051969 -0.0438595805196851 71 7.4 7.38079267391257 0.0192073260874306 72 7.5 7.34075095423805 0.159249045761952 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 7.16687434547354 6.52223420163409 7.811514489313 74 7.0983494555209 6.28134134869522 7.91535756234659 75 7.27863436635374 6.33346568336328 8.2238030493442 76 7.17593473059832 6.10086325624796 8.25100620494868 77 7.28917054753561 6.12451545701084 8.45382563806038 78 7.14273803532654 5.94046872807326 8.3450073425798 79 6.67162651148807 5.34249305529731 8.00075996767882 80 6.88252279331681 5.43093074680084 8.33411483983279 81 7.09747476790229 5.48713679370552 8.70781274209906 82 7.53676503004288 5.85650358553808 9.21702647454767 83 7.52190117838208 5.77619217391868 9.26761018284548 84 7.5 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/1t9dh1212251296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/1t9dh1212251296.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/2umuh1212251296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/2umuh1212251296.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/319g81212251296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t12122513941o3im1928g1bnym/319g81212251296.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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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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