Wisselkoers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 26 May 2010 15:18:21 +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/May/26/t1274887242tjp1wwicwa4107q.htm/, Retrieved Wed, 26 May 2010 17:20:42 +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/May/26/t1274887242tjp1wwicwa4107q.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:

KDG2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

0,8833 0,87 0,8758 0,8858 0,917 0,9554 0,9922 0,9778 0,9808 0,9811 1,0014 1,0183 1,0622 1,0773 1,0807 1,0848 1,1582 1,1663 1,1372 1,1139 1,1222 1,1692 1,1702 1,2286 1,2613 1,2646 1,2262 1,1985 1,2007 1,2138 1,2266 1,2176 1,2218 1,249 1,2991 1,3408 1,3119 1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,202 1,2271 1,277 1,265 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,457 1,4718 1,4748 1,5527 1,575 1,5557 1,5553 1,577 1,4975 1,4369 1,3322 1,2732 1,3449 1,3239 1,2785 1,305 1,319 1,365 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614 1,4272

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 gamma 0.0784959467629734 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.0622 0.941115751262627 0.121084248737373 14 1.0773 1.0655875 0.0117125000000002 15 1.0807 1.0691375 0.0115624999999997 16 1.0848 1.07107083333333 0.0137291666666668 17 1.1582 1.14332916666667 0.0148708333333334 18 1.1663 1.15050416666667 0.0157958333333332 19 1.1372 1.161975 -0.024775 20 1.1139 1.10670833333333 0.00719166666666649 21 1.1222 1.099725 0.0224750000000002 22 1.1692 1.10567083333333 0.0635291666666669 23 1.1702 1.17115833333333 -0.000958333333333838 24 1.2286 1.1682625 0.0603375000000002 25 1.2613 1.25767083333333 0.00362916666666679 26 1.2646 1.2646875 -8.7499999999796e-05 27 1.2262 1.2564375 -0.0302375000000004 28 1.1985 1.21657083333333 -0.0180708333333333 29 1.2007 1.25702916666667 -0.0563291666666663 30 1.2138 1.19300416666667 0.0207958333333331 31 1.2266 1.209475 0.0171249999999998 32 1.2176 1.19610833333333 0.0214916666666667 33 1.2218 1.203425 0.0183750000000000 34 1.249 1.20527083333333 0.043729166666667 35 1.2991 1.25095833333333 0.0481416666666661 36 1.3408 1.2971625 0.0436375000000002 37 1.3119 1.36987083333333 -0.0579708333333333 38 1.3014 1.3152875 -0.0138874999999998 39 1.3201 1.2932375 0.0268624999999998 40 1.2938 1.31047083333333 -0.0166708333333332 41 1.2694 1.35232916666667 -0.0829291666666665 42 1.2165 1.26170416666667 -0.0452041666666669 43 1.2037 1.212175 -0.00847500000000001 44 1.2292 1.17320833333333 0.0559916666666667 45 1.2256 1.215025 0.010575 46 1.2015 1.20907083333333 -0.00757083333333308 47 1.1786 1.20345833333333 -0.0248583333333336 48 1.1856 1.1766625 0.00893750000000004 49 1.2103 1.21467083333333 -0.00437083333333343 50 1.1938 1.2136875 -0.0198874999999996 51 1.202 1.1856375 0.0163624999999996 52 1.2271 1.19237083333333 0.0347291666666669 53 1.277 1.28562916666667 -0.00862916666666669 54 1.265 1.26930416666667 -0.00430416666666678 55 1.2684 1.260675 0.00772499999999998 56 1.2811 1.23790833333333 0.0431916666666665 57 1.2727 1.266925 0.00577500000000009 58 1.2611 1.25617083333333 0.0049291666666671 59 1.2881 1.26305833333333 0.0250416666666662 60 1.3213 1.2861625 0.0351375000000000 61 1.2999 1.35037083333333 -0.0504708333333332 62 1.3074 1.3032875 0.00411250000000019 63 1.3242 1.2992375 0.0249624999999998 64 1.3516 1.31457083333333 0.0370291666666667 65 1.3511 1.41012916666667 -0.0590291666666665 66 1.3419 1.34340416666667 -0.00150416666666664 67 1.3716 1.337575 0.0340249999999997 68 1.3622 1.34110833333333 0.0210916666666667 69 1.3896 1.348025 0.0415749999999999 70 1.4227 1.37307083333333 0.0496291666666671 71 1.4684 1.42465833333333 0.0437416666666661 72 1.457 1.4664625 -0.0094624999999997 73 1.4718 1.48607083333333 -0.0142708333333335 74 1.4748 1.4751875 -0.000387499999999541 75 1.5527 1.4666375 0.0860624999999995 76 1.575 1.54307083333333 0.0319291666666668 77 1.5557 1.63352916666667 -0.0778291666666664 78 1.5553 1.54800416666667 0.00729583333333306 79 1.577 1.550975 0.0260250000000000 80 1.4975 1.54650833333333 -0.0490083333333333 81 1.4369 1.483325 -0.0464249999999999 82 1.3322 1.42037083333333 -0.088170833333333 83 1.2732 1.33415833333333 -0.0609583333333337 84 1.3449 1.2712625 0.0736375 85 1.3239 1.37397083333333 -0.0500708333333333 86 1.2785 1.3272875 -0.0487874999999998 87 1.305 1.2703375 0.0346624999999996 88 1.319 1.29537083333333 0.0236291666666668 89 1.365 1.37752916666667 -0.0125291666666665 90 1.4016 1.35730416666667 0.0442958333333332 91 1.4088 1.397275 0.011525 92 1.4268 1.37830833333333 0.0484916666666666 93 1.4562 1.412625 0.0435749999999999 94 1.4816 1.43967083333333 0.041929166666667 95 1.4914 1.48355833333333 0.0078416666666663 96 1.4614 1.4894625 -0.0280624999999999 97 1.4272 1.49047083333333 -0.0632708333333334 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 98 1.4305875 1.35359898482770 1.50757601517230 99 1.422425 1.31354679769637 1.53130320230363 100 1.41279583333333 1.27944781345563 1.54614385321104 101 1.471325 1.31734796965541 1.62530203034459 102 1.46362916666667 1.29147761325464 1.63578072007869 103 1.45930416666667 1.27072158844002 1.64788674489331 104 1.4288125 1.22512003504598 1.63250496495402 105 1.4146375 1.19688109539275 1.63239390460725 106 1.39810833333333 1.16714278781645 1.62907387885022 107 1.40006666666667 1.15660760504778 1.64352572828555 108 1.39812916666667 1.14278714867358 1.65347118465976 109 1.4272 1.16050396024459 1.69389603975541

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/1dmg81274887097.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/1dmg81274887097.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/2dmg81274887097.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/2dmg81274887097.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/36vft1274887097.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t1274887242tjp1wwicwa4107q/36vft1274887097.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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