Wisselkoersen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Jun 2010 15:12:22 +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/05/t1275750768jqlj3hiqgd3j75s.htm/, Retrieved Sat, 05 Jun 2010 17:12:48 +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/05/t1275750768jqlj3hiqgd3j75s.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 «

1,4272 1,4614 1,4914 1,4816 1,4562 1,4268 1,4088 1,4016 1,365 1,319 1,305 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,577 1,5553 1,5557 1,575 1,5527 1,4748 1,4718 1,457 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,265 1,277 1,2271 1,202 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014 1,3119 1,3408 1,2991 1,249 1,2218 1,2176 1,2266 1,2138 1,2007 1,1985 1,2262 1,2646

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 0.356147313163450 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.4914 1.4956 -0.00419999999999998 4 1.4816 1.52410418128471 -0.0425041812847136 5 1.4562 1.49916643132195 -0.0429664313219507 6 1.4268 1.45846405225042 -0.0316640522504159 7 1.4088 1.41778698511756 -0.00898698511756324 8 1.4016 1.39658629451450 0.00501370548549662 9 1.365 1.39117191225216 -0.0261719122521558 10 1.319 1.3452508560232 -0.0262508560232009 11 1.305 1.28990168418230 0.0150983158177027 12 1.2785 1.28127890879407 -0.00277890879406528 13 1.3239 1.25378920789353 0.0701107921064674 14 1.3449 1.32415897812601 0.0207410218739876 15 1.2732 1.35254583733870 -0.0793458373386973 16 1.3322 1.25258703055982 0.0796129694401837 17 1.4369 1.33994097571890 0.0969590242810985 18 1.4975 1.47917267170356 0.0183273282964356 19 1.577 1.54629990043380 0.0307000995661955 20 1.5553 1.63673365840816 -0.0814336584081554 21 1.5557 1.58603127976502 -0.0303312797650204 22 1.575 1.5756288759719 -0.000628875971899756 23 1.5527 1.59470490348419 -0.0420049034841945 24 1.4748 1.55744496996861 -0.0826449699686085 25 1.4718 1.45011118596781 0.0216888140321851 26 1.457 1.45483559881108 0.00216440118892081 27 1.4684 1.44080644447912 0.0275935555208786 28 1.4227 1.46203381513851 -0.0393338151385083 29 1.3896 1.40232518256046 -0.0127251825604611 30 1.3622 1.36469314298204 -0.00249314298203829 31 1.3716 1.33640521680765 0.0351947831923467 32 1.3419 1.35833974427898 -0.0164397442789774 33 1.3511 1.32278477352493 0.0283152264750743 34 1.3516 1.34206916535564 0.0095308346443621 35 1.3242 1.34596354650643 -0.0217635465064323 36 1.3074 1.31081251789326 -0.00341251789325892 37 1.2999 1.29279715881445 0.0071028411855476 38 1.3213 1.28782681661851 0.0334731833814879 39 1.2881 1.32114820094286 -0.0330482009428561 40 1.2611 1.27617817297217 -0.0150781729721723 41 1.2727 1.24380812218072 0.0288918778192804 42 1.2811 1.26569788683830 0.0154021131616973 43 1.2684 1.27958330805788 -0.0111833080578805 44 1.265 1.26290040294079 0.00209959705921259 45 1.277 1.26024816879215 0.0167518312078483 46 1.2271 1.27821428846739 -0.0511142884673943 47 1.202 1.21011007196547 -0.00811007196547076 48 1.1938 1.18212169162541 0.0116783083745942 49 1.2103 1.17808088977531 0.0322191102246880 50 1.1856 1.20605563931435 -0.0204556393143516 51 1.1786 1.17407041833350 0.00452958166649542 52 1.2015 1.16868361667378 0.0328163833262185 53 1.2256 1.20327108342316 0.0223289165768441 54 1.2292 1.23532346706785 -0.00612346706784983 55 1.2037 1.23674261072439 -0.0330426107243904 56 1.2165 1.19947457369499 0.0170254263050071 57 1.2694 1.21833813352898 0.0510618664710167 58 1.2938 1.28942368007775 0.00437631992225307 59 1.3201 1.3153822946596 0.00471770534039906 60 1.3014 1.34336249274088 -0.041962492740881 61 1.3119 1.30971766369758 0.00218233630242470 62 1.3408 1.32099489690810 0.0198051030918969 63 1.2991 1.35694843116121 -0.0578484311612073 64 1.249 1.29464586783242 -0.0456458678324223 65 1.2218 1.22828921464689 -0.00648921464689156 66 1.2176 1.19877809828586 0.01882190171414 67 1.2266 1.20128146800998 0.0253185319900224 68 1.2138 1.21929859515147 -0.00549859515146678 69 1.2007 1.20454028526210 -0.00384028526209823 70 1.1985 1.19007257798422 0.00842742201577895 71 1.2262 1.19087398169203 0.0353260183079651 72 1.2646 1.23115524819718 0.0334447518028205 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.28146650669117 1.21389420383389 1.34903880954846 74 1.29833301338234 1.18447547695615 1.41219054980854 75 1.31519952007352 1.15286997030358 1.47752906984346 76 1.33206602676469 1.11785500052763 1.54627705300175 77 1.34893253345586 1.07925068948818 1.61861437742354 78 1.36579904014704 1.03711226279355 1.69448581750052 79 1.38266554683821 0.991558424746492 1.77377266892992 80 1.39953205352938 0.942721411946858 1.85634269511190 81 1.41639856022055 0.890730550152196 1.94206657028891 82 1.43326506691173 0.835706885765214 2.03082324805824 83 1.45013157360290 0.777761848922768 2.12250129828303 84 1.46699808029407 0.716997431955126 2.21699872863301

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/1u8291275750738.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/1u8291275750738.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/25hkc1275750738.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/25hkc1275750738.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/35hkc1275750738.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s/35hkc1275750738.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=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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