Wisselkoersen - Referentiewisselkoersen voor de euro in nationale munteenheden - Dollar van de Verenigde Staten

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 31 May 2008 13:30:47 -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/May/31/t1212262327mivzrtt9secimgr.htm/, Retrieved Sat, 31 May 2008 19:32:07 +0000

User-defined keywords:

Dataseries X:

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0,9383 0,9217 0,9095 0,892 0,8742 0,8532 0,8607 0,9005 0,9111 0,9059 0,8883 0,8924 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

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta -2.88939878967387e-17 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.9095 0.9217 -0.0122 4 0.892 0.9095 -0.0175000000000000 5 0.8742 0.892 -0.0178000000000000 6 0.8532 0.8742 -0.021 7 0.8607 0.8532 0.00750000000000006 8 0.9005 0.8607 0.0397999999999999 9 0.9111 0.9005 0.0106000000000001 10 0.9059 0.9111 -0.00519999999999998 11 0.8883 0.9059 -0.0176000000000001 12 0.8924 0.8883 0.00409999999999999 13 0.8833 0.8924 -0.0091 14 0.87 0.8833 -0.0133000000000000 15 0.8758 0.87 0.00580000000000003 16 0.8858 0.8758 0.01 17 0.917 0.8858 0.0312 18 0.9554 0.917 0.0384 19 0.9922 0.9554 0.0367999999999999 20 0.9778 0.9922 -0.0144000000000000 21 0.9808 0.9778 0.003 22 0.9811 0.9808 0.000299999999999967 23 1.0014 0.9811 0.0203000000000001 24 1.0183 1.0014 0.0168999999999999 25 1.0622 1.0183 0.0439000000000001 26 1.0773 1.0622 0.0150999999999999 27 1.0807 1.0773 0.00340000000000007 28 1.0848 1.0807 0.00409999999999999 29 1.1582 1.0848 0.0733999999999999 30 1.1663 1.1582 0.0081 31 1.1372 1.1663 -0.0290999999999999 32 1.1139 1.1372 -0.0233000000000001 33 1.1222 1.1139 0.0083000000000002 34 1.1692 1.1222 0.0469999999999999 35 1.1702 1.1692 0.00099999999999989 36 1.2286 1.1702 0.0584 37 1.2613 1.2286 0.0327000000000002 38 1.2646 1.2613 0.00329999999999986 39 1.2262 1.2646 -0.0384 40 1.1985 1.2262 -0.0277000000000001 41 1.2007 1.1985 0.0022000000000002 42 1.2138 1.2007 0.0130999999999999 43 1.2266 1.2138 0.0127999999999999 44 1.2176 1.2266 -0.0089999999999999 45 1.2218 1.2176 0.00419999999999998 46 1.249 1.2218 0.0272000000000001 47 1.2991 1.249 0.0500999999999998 48 1.3408 1.2991 0.0417000000000001 49 1.3119 1.3408 -0.0288999999999999 50 1.3014 1.3119 -0.0105000000000002 51 1.3201 1.3014 0.0187000000000002 52 1.2938 1.3201 -0.0263 53 1.2694 1.2938 -0.0244 54 1.2165 1.2694 -0.0529000000000002 55 1.2037 1.2165 -0.0127999999999999 56 1.2292 1.2037 0.0255000000000001 57 1.2256 1.2292 -0.00360000000000005 58 1.2015 1.2256 -0.0241 59 1.1786 1.2015 -0.0228999999999999 60 1.1856 1.1786 0.0069999999999999 61 1.2103 1.1856 0.0246999999999999 62 1.1938 1.2103 -0.0165000000000000 63 1.202 1.1938 0.00819999999999999 64 1.2271 1.202 0.0251000000000001 65 1.277 1.2271 0.0498999999999998 66 1.265 1.277 -0.012 67 1.2684 1.265 0.00340000000000007 68 1.2811 1.2684 0.0126999999999999 69 1.2727 1.2811 -0.00839999999999996 70 1.2611 1.2727 -0.0115999999999998 71 1.2881 1.2611 0.0269999999999999 72 1.3213 1.2881 0.0331999999999999 73 1.2999 1.3213 -0.0213999999999999 74 1.3074 1.2999 0.00749999999999984 75 1.3242 1.3074 0.0168000000000001 76 1.3516 1.3242 0.0273999999999999 77 1.3511 1.3516 -0.000499999999999945 78 1.3419 1.3511 -0.00919999999999987 79 1.3716 1.3419 0.0296999999999998 80 1.3622 1.3716 -0.00939999999999985 81 1.3896 1.3622 0.0273999999999999 82 1.4227 1.3896 0.0331000000000001 83 1.4684 1.4227 0.0456999999999999 84 1.457 1.4684 -0.0113999999999999 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 1.457 1.40886651426556 1.50513348573444 86 1.457 1.38892897167006 1.52507102832994 87 1.457 1.37363035716255 1.54036964283745 88 1.457 1.36073302853111 1.55326697146889 89 1.457 1.34937025390377 1.56462974609623 90 1.457 1.33909752040908 1.57490247959092 91 1.457 1.32965076701199 1.58434923298801 92 1.457 1.32085794334011 1.59314205665989 93 1.457 1.31259954279667 1.60140045720333 94 1.457 1.30478855335593 1.60921144664407 95 1.457 1.29735928796692 1.61664071203308 96 1.457 1.29026071432510 1.6237392856749

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/1x6jr1212262238.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/1x6jr1212262238.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/26ojl1212262238.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/26ojl1212262238.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/3qnl71212262238.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212262327mivzrtt9secimgr/3qnl71212262238.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')

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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