Exponential smoothing Koers EUR in USD SVEN VAN LAERE 2MAR04B

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 06:20:41 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp.htm/, Retrieved Sun, 01 Jun 2008 12:23:29 +0000

User-defined keywords:

Dataseries X:

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1,1591 1,1203 1,0886 1,0701 1,0630 1,0377 1,0370 1,0606 1,0497 1,0706 1,0328 1,0110 1,0131 0,9834 0,9643 0,9449 0,9059 0,9505 0,9386 0,9045 0,8695 0,8525 0,8552 0,8983 0,9376 0,9205 0,9083 0,8925 0,8753 0,8530 0,8615 0,9014 0,9114 0,9050 0,8883 0,8912 0,8832 0,8706 0,8766 0,8860 0,9170 0,9561 0,9935 0,9781 0,9806 0,9812 1,0013 1,0194 1,0622 1,0785 1,0805 1,0862 1,1556 1,1674 1,1365 1,1155 1,1266 1,1714 1,1710 1,2298 1,2638 1,2640 1,2261 1,1989 1,2000 1,2146 1,2266 1,2191 1,2224 1,2507 1,2997 1,3406

Text written by user:

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.926470202526935 beta 0.0777052499017337 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.0131 1.06825441666667 -0.0551544166666673 14 0.9834 0.986105876504275 -0.00270587650427467 15 0.9643 0.966362878926515 -0.00206287892651502 16 0.9449 0.949350422826513 -0.0044504228265132 17 0.9059 0.910097252058817 -0.0041972520588166 18 0.9505 0.949984802911376 0.000515197088624464 19 0.9386 0.933521220675307 0.00507877932469325 20 0.9045 0.897376290840329 0.00712370915967131 21 0.8695 0.861926274774181 0.00757372522581912 22 0.8525 0.845000929770446 0.00749907022955365 23 0.8552 0.847187955857812 0.00801204414218792 24 0.8983 0.892706203522535 0.00559379647746538 25 0.9376 0.897022896713716 0.0405771032862837 26 0.9205 0.91235881540497 0.00814118459503088 27 0.9083 0.9084290011099 -0.000129001109899551 28 0.8925 0.898888317425963 -0.00638831742596302 29 0.8753 0.863574496384422 0.0117255036155782 30 0.853 0.925422951711084 -0.0724229517110838 31 0.8615 0.843331413698399 0.0181685863016013 32 0.9014 0.822018025827002 0.0793819741729983 33 0.9114 0.861302079349607 0.050097920650393 34 0.905 0.894585880312208 0.0104141196877923 35 0.8883 0.910538426185757 -0.022238426185757 36 0.8912 0.936702015956785 -0.0455020159567849 37 0.8832 0.901423122437301 -0.0182231224373013 38 0.8706 0.86083510083186 0.0097648991681405 39 0.8766 0.858856121704333 0.0177438782956674 40 0.886 0.867755196200307 0.0182448037996932 41 0.917 0.860709825576437 0.0562901744235625 42 0.9561 0.964981675521665 -0.00888167552166552 43 0.9935 0.960317825930085 0.0331821740699146 44 0.9781 0.970393351914477 0.00770664808552346 45 0.9806 0.948937343872319 0.0316626561276810 46 0.9812 0.968714538403716 0.0124854615962839 47 1.0013 0.990825363637466 0.0104746363625339 48 1.0194 1.05458130760473 -0.0351813076047325 49 1.0622 1.04060830220747 0.0215916977925279 50 1.0785 1.05157005913042 0.0269299408695782 51 1.0805 1.07992099158223 0.000579008417773919 52 1.0862 1.08555875133296 0.000641248667040628 53 1.1556 1.07633896451764 0.0792610354823593 54 1.1674 1.21009155354270 -0.0426915535427048 55 1.1365 1.18775377229719 -0.0512537722971858 56 1.1155 1.12220698746692 -0.00670698746691989 57 1.1266 1.09259928311246 0.0340007168875387 58 1.1714 1.11674147388885 0.0546585261111547 59 1.171 1.18442158535483 -0.0134215853548254 60 1.2298 1.22760604661451 0.00219395338549022 61 1.2638 1.26005004619234 0.00374995380766419 62 1.264 1.26120545498016 0.00279454501983722 63 1.2261 1.26985151398983 -0.0437515139898315 64 1.1989 1.23582494737013 -0.0369249473701265 65 1.2 1.19627965098917 0.00372034901082663 66 1.2146 1.24433815565131 -0.0297381556513099 67 1.2266 1.22756352908810 -0.00096352908809516 68 1.2191 1.20969694286422 0.00940305713577927 69 1.2224 1.1969800026457 0.0254199973542999 70 1.2507 1.21304569586367 0.037654304136328 71 1.2997 1.25709614329856 0.0426038567014435 72 1.3406 1.35449823349823 -0.0138982334982334 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.37215273046220 1.31307068034652 1.43123478057789 74 1.36949871923386 1.28600831975989 1.45298911870783 75 1.37166706095966 1.26692679228447 1.47640732963486 76 1.38136053356065 1.25675514485829 1.505965922263 77 1.38435563618171 1.24056840846948 1.52814286389393 78 1.43158121252066 1.26894204511328 1.59422037992804 79 1.45168885212512 1.270324904017 1.63305280023323 80 1.44276152449059 1.24267379732406 1.64284925165712 81 1.42911803789289 1.21022461072526 1.64801146506051 82 1.42730980436677 1.18947211523566 1.66514749349787 83 1.43890516432376 1.18194488856292 1.69586544008459 84 1.49168090748019 1.21539126541036 1.76797054955001

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/1e3cr1212322835.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/1e3cr1212322835.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/2ekit1212322835.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/2ekit1212322835.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/3y1dt1212322835.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212323009lw3pul3su478icp/3y1dt1212322835.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=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')

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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