opgave 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 11:46:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go.htm/, Retrieved Sun, 06 Jun 2010 13:47:04 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

103,6 104,7 105,5 106,6 107,2 107,5 108,3 108,7 108,8 109,8 109,5 109,2 110,6 110,1 109,9 109,7 109,4 109,4 109,4 109,5 109,5 109,9 110 110,8 112,4 112,8 113,7 114,5 114,8 115,6 115,8 115,8 116,3 116,3 116,8 116,7 116,8 117 117,2 117,1 117,3 117,4 117,7 117,9 118,8 119,9 122,4 123,5 125,6 127,4 128,9 129,5 130,8 132,7 134 132,9 133,1 131,7 128,8 125,1 123,9 121,8 119,2 118,9 119,6 120,2 119,6 121 120,4 120,4 121,4 121,7

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.696623499130001 beta 1 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 105.5 105.8 -0.300000000000011 4 106.6 106.482025900522 0.117974099477991 5 107.2 107.537405910753 -0.337405910753148 6 107.5 108.040512618647 -0.540512618647227 7 108.3 108.025596629265 0.274403370734589 8 108.7 108.769526104198 -0.0695261041979336 9 108.8 109.225432706862 -0.42543270686177 10 109.8 109.137039985716 0.66296001428394 11 109.5 110.268680735336 -0.768680735336247 12 109.2 109.867525832895 -0.667525832895151 13 110.6 109.071823631076 1.52817636892435 14 110.1 110.870262749543 -0.770262749542965 15 109.9 110.53097203493 -0.630972034930153 16 109.7 109.849164558501 -0.149164558501042 17 109.4 109.39908395552 0.000916044480220535 18 109.4 109.05419116545 0.345808834549956 19 109.4 109.190457357978 0.209542642022356 20 109.5 109.377769647156 0.122230352843872 21 109.5 109.589406680028 -0.08940668002802 22 109.9 109.591329588228 0.308670411771516 23 110 110.085589415368 -0.0855894153680197 24 110.8 110.245574984137 0.554425015862932 25 112.4 111.23763514004 1.16236485996045 26 112.8 113.462931153409 -0.662931153409204 27 113.7 113.954869651227 -0.254869651227025 28 114.5 114.553525192295 -0.053525192295453 29 114.8 115.255155108127 -0.45515510812676 30 115.6 115.359928442566 0.240071557433794 31 115.8 116.116252497838 -0.316252497838036 32 115.8 116.264719221424 -0.464719221423692 33 116.3 115.98602620638 0.31397379362042 34 116.3 116.468510566971 -0.168510566970568 35 116.8 116.497496563208 0.302503436792264 36 116.7 117.065332985522 -0.365332985522471 37 116.8 116.913439319756 -0.113439319755599 38 117 116.857996204977 0.142003795023157 39 117.2 117.079423947223 0.120576052777309 40 117.1 117.369920732484 -0.269920732483826 41 117.3 117.200355155647 0.0996448443532927 42 117.4 117.357652584248 0.0423474157524879 43 117.7 117.504535482586 0.195464517414123 44 117.9 117.894248528137 0.00575147186279423 45 118.8 118.15580961852 0.644190381479817 46 119.9 119.310880413754 0.589119586246341 47 122.4 120.837982146489 1.56201785351134 48 123.5 124.13096601728 -0.630966017279945 49 125.6 125.456720035675 0.143279964324734 50 127.4 127.421644189066 -0.0216441890664925 51 128.9 129.256600450908 -0.356600450907933 52 129.5 130.609802055667 -1.1098020556671 53 130.8 130.665191531608 0.134808468391924 54 132.7 131.681516692837 1.01848330716336 55 134 134.022929917585 -0.0229299175849178 56 132.9 135.622896698246 -2.72289669824602 57 133.1 133.445169346927 -0.345169346926582 58 131.7 132.683369664812 -0.983369664811988 59 128.8 130.791946227267 -1.99194622726651 60 125.1 126.810288104726 -1.71028810472632 61 123.9 121.833412765034 2.06658723496645 62 121.8 120.927230771135 0.872769228864883 63 119.2 119.797398654647 -0.597398654646639 64 118.9 117.227251101662 1.67274889833769 65 119.6 117.403817871305 2.19618212869477 66 120.2 119.474932608659 0.725067391341497 67 119.6 121.026333233316 -1.42633323331643 68 121 120.085400378876 0.914599621123628 69 120.4 121.412347949095 -1.01234794909483 70 120.4 120.691713189672 -0.291713189672151 71 121.4 120.269875275021 1.1301247249786 72 121.7 121.625794504038 0.0742054959616922 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 122.29782887719 120.639835353955 123.955822400425 74 122.918169958091 120.074753507716 125.761586408466 75 123.538511038991 119.056191892455 128.020830185528 76 124.158852119892 117.721812172827 130.595892066956 77 124.779193200792 116.131306207431 133.427080194153 78 125.399534281693 114.317538940848 136.481529622538 79 126.019875362593 112.302093675039 139.737657050148 80 126.640216443494 110.100726493009 143.179706393979 81 127.260557524394 107.725710757335 146.795404291453 82 127.880898605295 105.187020512473 150.574776698116 83 128.501239686195 102.493003314733 154.509476057657 84 129.121580767096 99.650797874676 158.592363659515

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/16ntr1275824806.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/16ntr1275824806.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/2yxau1275824806.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/2yxau1275824806.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/3yxau1275824806.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275824823gil0gazcezj36go/3yxau1275824806.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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