opdracht 10 axel vermeyen eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 15:27:04 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo.htm/, Retrieved Wed, 18 May 2011 17:23:11 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

8 8 8.2 8.5 8.7 8.7 8 8 8.3 8.5 8.7 8.6 8.3 7.9 7.9 8.1 8.3 8.1 7.4 7.3 7.7 8 8 7.7 6.9 6.6 6.9 7.5 7.9 7.7 6.5 6.1 6.4 6.8 7.1 7.3 7.2 7 7 7 7.3 7.5 7.2 7.7 8 7.9 8 8 7.9 7.9 8 8.1 8.1 8.2 8 8.3 8.5 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 7.9 8.1 8.2 8.5 8.6 8.5

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.807498366458812 gamma 0.100845034414204 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.3 8.49863782051282 -0.198637820512822 14 7.9 7.75196916553784 0.148030834462162 15 7.9 7.87150382255157 0.0284961774484316 16 8.1 8.08618110595816 0.0138188940418367 17 8.3 8.30150650698988 -0.00150650698988208 18 8.1 8.11695667172316 -0.0169566717231593 19 7.4 7.50326418700613 -0.103264187006131 20 7.3 7.24487852468498 0.0551214753150164 21 7.7 7.51438902595866 0.185610974041342 22 8 7.97676958429387 0.0232304157061298 23 8 8.2996947736954 -0.299694773695396 24 7.7 7.76602506683345 -0.0660250668334541 25 6.9 7.22104326655344 -0.321043266553441 26 6.6 6.0659680199156 0.534031980084398 27 6.9 6.59719797147052 0.302802028529483 28 7.5 7.33337678153516 0.166623218464845 29 7.9 8.0720914249263 -0.172091424926295 30 7.7 7.9497945470834 -0.249794547083408 31 6.5 7.14808585836324 -0.648085858363239 32 6.1 5.94975758640987 0.150242413590134 33 6.4 5.99607808995673 0.403921910043273 34 6.8 6.5347443724936 0.265255627506406 35 7.1 7.15310452506569 -0.0531045250656899 36 7.3 7.11855604115691 0.181443958843093 37 7.2 7.27340507485986 -0.0734050748598598 38 7 7.0182972634874 -0.0182972634874012 39 7 7.20352225311066 -0.203522253110658 40 7 7.23084503285245 -0.230845032852449 41 7.3 7.04860471258564 0.251395287414365 42 7.5 7.16827266317484 0.331727336825158 43 7.2 7.23614194577089 -0.0361419457708916 44 7.7 7.43195738360025 0.268042616399747 45 8 8.4734013584844 -0.473401358484393 46 7.9 8.30363053482886 -0.403630534828864 47 8 7.88186620396833 0.118133796031674 48 8 7.78559238462081 0.214407615379185 49 7.9 7.76705951712917 0.132940482870829 50 7.9 7.67857540655028 0.221424593449724 51 8 8.25737540405474 -0.257375404054736 52 8.1 8.34121185238052 -0.241211852380525 53 8.1 8.25060034227942 -0.150600342279416 54 8.2 7.74565747856731 0.454342521432686 55 8 7.81253832243699 0.187461677563014 56 8.3 8.28891332084275 0.0110866791572519 57 8.5 8.92286579615168 -0.422865796151683 58 8.6 8.6939023565279 -0.0939023565278934 59 8.7 8.72224302369165 -0.0222430236916527 60 8.7 8.51261515172887 0.187384848271128 61 8.5 8.47226144394027 0.0277385560597256 62 8.4 8.1988269493131 0.201173050686906 63 8.5 8.66127385911831 -0.161273859118307 64 8.7 8.82271214799443 -0.122712147994431 65 8.7 8.92778895561094 -0.227788955610945 66 8.6 8.36051641272441 0.239483587275588 67 7.9 8.05389901824315 -0.153899018243147 68 8.1 7.75462581241219 0.345374187587808 69 8.2 8.55851490470639 -0.358514904706386 70 8.5 8.28151470480484 0.218485295195158 71 8.6 8.76210789043687 -0.16210789043687 72 8.5 8.43953936705235 0.0604606329476542 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 8.19669456272598 7.71725899230308 8.67613013314888 74 7.79755579211862 6.80719341026737 8.78791817396987 75 7.79841702151126 6.20071941877999 9.39611462424254 76 7.99094491757057 5.70073128135157 10.2811585537896 77 8.18763948029655 5.12857093859765 11.2467080219955 78 8.00100070968919 4.10345491190648 11.8985465074719 79 7.41436193908184 2.61397369491823 12.2147501832454 80 7.35272316847448 1.58936888683793 13.116077450111 81 7.61608439786712 0.833149990484747 14.3990188052495 82 7.79194562725976 -0.0642192881718868 15.6481105426914 83 7.97197352331907 -1.00852739103176 16.9524744376699 84 7.86033475271172 -2.29339203815762 18.014061543581

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/1qotk1305732419.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/1qotk1305732419.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/2vcn01305732419.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/2vcn01305732419.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/3jdky1305732419.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305732190t5z5al47sewovvo/3jdky1305732419.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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