exponential smoothing-us dollar per euro- raf deceulaer

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 12:28:49 -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/t1212345024ji2cxsrwm4x8moq.htm/, Retrieved Sun, 01 Jun 2008 18:30:28 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,0137 0,9834 0,9643 0,947 0,906 0,9492 0,9397 0,9041 0,8721 0,8552 0,8564 0,8973 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.9643 0.9834 -0.0191 4 0.947 0.9643 -0.0173000000000001 5 0.906 0.947 -0.0409999999999999 6 0.9492 0.906 0.0432 7 0.9397 0.9492 -0.00950000000000006 8 0.9041 0.9397 -0.0356 9 0.8721 0.9041 -0.032 10 0.8552 0.8721 -0.0169000000000000 11 0.8564 0.8552 0.00120000000000009 12 0.8973 0.8564 0.0408999999999999 13 0.9383 0.8973 0.041 14 0.9217 0.9383 -0.0166000000000001 15 0.9095 0.9217 -0.0122 16 0.892 0.9095 -0.0175000000000000 17 0.8742 0.892 -0.0178000000000000 18 0.8532 0.8742 -0.021 19 0.8607 0.8532 0.00750000000000006 20 0.9005 0.8607 0.0397999999999999 21 0.9111 0.9005 0.0106000000000001 22 0.9059 0.9111 -0.00519999999999998 23 0.8883 0.9059 -0.0176000000000001 24 0.8924 0.8883 0.00409999999999999 25 0.8833 0.8924 -0.0091 26 0.87 0.8833 -0.0133000000000000 27 0.8758 0.87 0.00580000000000003 28 0.8858 0.8758 0.01 29 0.917 0.8858 0.0312 30 0.9554 0.917 0.0384 31 0.9922 0.9554 0.0367999999999999 32 0.9778 0.9922 -0.0144000000000000 33 0.9808 0.9778 0.003 34 0.9811 0.9808 0.000299999999999967 35 1.0014 0.9811 0.0203000000000001 36 1.0183 1.0014 0.0168999999999999 37 1.0622 1.0183 0.043900 38 1.0773 1.0622 0.0150999999999999 39 1.0807 1.0773 0.00340000000000007 40 1.0848 1.0807 0.00409999999999999 41 1.1582 1.0848 0.0733999999999999 42 1.1663 1.1582 0.0081 43 1.1372 1.1663 -0.0290999999999999 44 1.1139 1.1372 -0.0233000000000001 45 1.1222 1.1139 0.0083000000000002 46 1.1692 1.1222 0.0469999999999999 47 1.1702 1.1692 0.00099999999999989 48 1.2286 1.1702 0.0584 49 1.2613 1.2286 0.0327000000000002 50 1.2646 1.2613 0.00329999999999986 51 1.2262 1.2646 -0.0384 52 1.1985 1.2262 -0.0277000000000001 53 1.2007 1.1985 0.00220000000000020 54 1.2138 1.2007 0.0130999999999999 55 1.2266 1.2138 0.0127999999999999 56 1.2176 1.2266 -0.0089999999999999 57 1.2218 1.2176 0.00419999999999998 58 1.249 1.2218 0.0272000000000001 59 1.2991 1.249 0.0500999999999998 60 1.3408 1.2991 0.0417000000000001 61 1.3119 1.3408 -0.0288999999999999 62 1.3014 1.3119 -0.0105000000000002 63 1.3201 1.3014 0.0187000000000002 64 1.2938 1.3201 -0.0263 65 1.2694 1.2938 -0.0244 66 1.2165 1.2694 -0.0529000000000002 67 1.2037 1.2165 -0.0127999999999999 68 1.2292 1.2037 0.0255000000000001 69 1.2256 1.2292 -0.00360000000000005 70 1.2015 1.2256 -0.0241 71 1.1786 1.2015 -0.0228999999999999 72 1.1856 1.1786 0.0069999999999999 73 1.2103 1.1856 0.0246999999999999 74 1.1938 1.2103 -0.0165000000000000 75 1.202 1.1938 0.00819999999999999 76 1.2271 1.202 0.0251000000000001 77 1.277 1.2271 0.0498999999999998 78 1.265 1.277 -0.012 79 1.2684 1.265 0.00340000000000007 80 1.2811 1.2684 0.0126999999999999 81 1.2727 1.2811 -0.00839999999999996 82 1.2611 1.2727 -0.0115999999999998 83 1.2881 1.2611 0.0269999999999999 84 1.3213 1.2881 0.0331999999999999 85 1.2999 1.3213 -0.0213999999999999 86 1.3074 1.2999 0.00749999999999984 87 1.3242 1.3074 0.0168000000000001 88 1.3516 1.3242 0.0273999999999999 89 1.3511 1.3516 -0.000499999999999945 90 1.3419 1.3511 -0.00919999999999987 91 1.3716 1.3419 0.0296999999999998 92 1.3622 1.3716 -0.00939999999999985 93 1.3896 1.3622 0.0273999999999999 94 1.4227 1.3896 0.0331000000000001 95 1.4684 1.4227 0.0456999999999999 96 1.457 1.4684 -0.0113999999999999 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 1.457 1.40702233492418 1.50697766507582 98 1.457 1.38632090823403 1.52767909176597 99 1.457 1.37043614484501 1.54356385515499 100 1.457 1.35704466984835 1.55695533015165 101 1.457 1.34524654353374 1.56875345646626 102 1.457 1.33458022202852 1.57941977797148 103 1.457 1.32477152710169 1.58922847289831 104 1.457 1.31564181646806 1.59835818353194 105 1.457 1.30706700477253 1.60693299522747 106 1.457 1.29895674622335 1.61504325377665 107 1.457 1.29124283704544 1.62275716295456 108 1.457 1.28387228969003 1.63012771030997

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/1dz6n1212344923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/1dz6n1212344923.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/2m33k1212344923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/2m33k1212344923.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/39kcy1212344923.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212345024ji2cxsrwm4x8moq/39kcy1212344923.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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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