Opgave 10 - Sofie Loopmans - 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: Sun, 31 May 2009 02:52:16 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/May/31/t12437599749irha7s02v18yeg.htm/, Retrieved Sun, 31 May 2009 10:52:54 +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/2009/May/31/t12437599749irha7s02v18yeg.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

30,06 30,46 30,46 30,49 30,49 30,5 30,5 30,5 30,51 30,51 30,61 30,88 30,95 31,09 31,28 31,31 31,32 31,34 31,34 31,34 31,34 31,36 31,36 31,36 31,72 32,07 32,13 32,19 32,26 32,27 32,28 32,28 32,28 32,29 32,61 32,68 32,69 32,74 32,86 32,86 32,9 32,95 32,95 32,96 32,99 33 33,06 33,42 33,48 33,5 33,51 33,52 33,55 33,56 33,56 33,56 33,6 33,61 33,62 33,72 33,83 33,96 34,06 34,11 34,11 34,21 34,19 34,17 34,12 34,15 34,15 34,15

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.601307369123789 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 30.46 30.86 -0.400000000000002 4 30.49 30.6194770523505 -0.129477052350488 5 30.49 30.5716215466397 -0.0816215466397097 6 30.5 30.522541909166 -0.0225419091659695 7 30.5 30.5189872930704 -0.0189872930703530 8 30.5 30.5075700938274 -0.0075700938274359 9 30.51 30.5030181406240 0.00698185937596207 10 30.51 30.517216384117 -0.00721638411699033 11 30.61 30.512877119169 0.0971228808309803 12 30.88 30.6712778231232 0.208722176876783 13 30.95 31.0667840061788 -0.116784006178786 14 31.09 31.0665609226677 0.0234390773323163 15 31.28 31.2206550125931 0.0593449874069343 16 31.31 31.4463395908414 -0.136339590841416 17 31.32 31.3943575901651 -0.0743575901651461 18 31.34 31.3596458232486 -0.0196458232485597 19 31.34 31.3678326449567 -0.0278326449566961 20 31.34 31.351096670442 -0.0110966704420292 21 31.34 31.3444241607325 -0.00442416073249774 22 31.36 31.3417638802819 0.0182361197181393 23 31.36 31.3727293934526 -0.0127293934526023 24 31.36 31.3650751153651 -0.00507511536507721 25 31.72 31.3620234110969 0.357976588903096 26 32.07 31.9372773719781 0.132722628021870 27 32.13 32.3670844662572 -0.237084466257159 28 32.19 32.2845238295920 -0.0945238295919566 29 32.26 32.2876859543005 -0.0276859543005088 30 32.27 32.3410381859584 -0.0710381859583791 31 32.28 32.3083224012524 -0.0283224012524315 32 32.28 32.3012919326681 -0.0212919326680634 33 32.28 32.2884889366519 -0.00848893665186523 34 32.29 32.2833844764871 0.00661552351292016 35 32.61 32.297362439526 0.312637560473995 36 32.68 32.8053537085039 -0.125353708503901 37 32.69 32.7999775998335 -0.109977599833513 38 32.74 32.7438472586151 -0.00384725861506752 39 32.86 32.7915338736589 0.068466126341093 40 32.86 32.9527030599632 -0.0927030599631635 41 32.9 32.896960026867 0.00303997313300641 42 32.95 32.9387879851138 0.0112120148861976 43 32.95 32.9955298522876 -0.0455298522876006 44 32.96 32.9681524165920 -0.00815241659195465 45 32.99 32.9732503084190 0.0167496915809622 46 33 33.0133220213972 -0.0133220213972223 47 33.06 33.0153113917594 0.0446886082405555 48 33.42 33.1021829812104 0.317817018789619 49 33.48 33.6532886966415 -0.173288696641535 50 33.5 33.6090889263651 -0.109088926365118 51 33.51 33.563492951052 -0.0534929510519717 52 33.52 33.5413272453882 -0.0213272453882354 53 33.55 33.5385030155732 0.0114969844268131 54 33.56 33.5754162370317 -0.0154162370317223 55 33.56 33.5761463401004 -0.0161463401003914 56 33.56 33.5664374268136 -0.00643742681364756 57 33.6 33.5625665546324 0.03743344536759 58 33.61 33.6250755611836 -0.0150755611836360 59 33.62 33.6260105151502 -0.00601051515023698 60 33.72 33.6323963480982 0.08760365190183 61 33.83 33.7850730695489 0.0449269304511049 62 33.96 33.9220879639013 0.0379120360987457 63 34.06 34.0748847505859 -0.0148847505859209 64 34.11 34.1659344403710 -0.0559344403710398 65 34.11 34.1823006491881 -0.0723006491881151 66 34.21 34.1388257360389 0.071174263961133 67 34.19 34.2816233454507 -0.0916233454506639 68 34.17 34.2065295526474 -0.0365295526473943 69 34.12 34.1645640634497 -0.0445640634497266 70 34.15 34.0877673636993 0.0622326363006991 71 34.15 34.1551883065069 -0.00518830650691626 72 34.15 34.152068539571 -0.00206853957103448 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 34.1508247114836 33.9364514527894 34.3651979701779 74 34.1516494229673 33.7469330759336 34.556365770001 75 34.1524741344509 33.5305811545034 34.7743671143985 76 34.1532988459346 33.2883970244155 35.0182006674537 77 34.1541235574182 33.0223370207418 35.2859100940946 78 34.1549482689019 32.7341596548986 35.5757368829052 79 34.1557729803855 32.4253434614297 35.8862024993414 80 34.1565976918692 32.0971289584944 36.2160664252439 81 34.1574224033528 31.7505679597537 36.5642768469519 82 34.1582471148365 31.3865636078652 36.9299306218077 83 34.1590718263201 31.0059008017565 37.3122428508838 84 34.1598965378038 30.6092691213271 37.7105239542804

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/1rea41243759931.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/1rea41243759931.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/207ml1243759931.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/207ml1243759931.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/30qkd1243759931.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/31/t12437599749irha7s02v18yeg/30qkd1243759931.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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