Opgave 10

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 17 Aug 2008 11:01:50 -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/Aug/17/t121899257118cf8xghfeybnhx.htm/, Retrieved Sun, 17 Aug 2008 17:02:52 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Alain Piscaer 2MAR04

Dataseries X:

» Textbox « » Textfile « » CSV «

2005/12 2005/11 2005/10 2005/09 2005/08 2005/07 2005/06 2005/05 2005/04 2005/03 2005/02 2005/01 2004/12 2004/11 2004/10 2004/09 2004/08 2004/07 2004/06 2004/05 2004/04 2004/03 2004/02 2004/01 2003/12 2003/11 2003/10 2003/09 2003/08 2003/07 2003/06 2003/05 2003/04 2003/03 2003/02 2003/01 2002/12 2002/11 2002/10 2002/09 2002/08 2002/07 2002/06 2002/05 2002/04 2002/03 2002/02 2002/01 2001/12 2001/11 2001/10 2001/09 2001/08 2001/07 2001/06 2001/05 2001/04 2001/03 2001/02 2001/01 2000/12 2000/11 2000/10 2000/09 2000/08 2000/07 2000/06 2000/05 2000/04 2000/03 2000/02 2000/01 1999/12 1999/11 1999/10 1999/09 1999/08 1999/07 1999/06 1999/05 1999/04 1999/03 1999/02 1999/01 1998/12 1998/11 1998/10 1998/09 1998/08 1998/07 1998/06 1998/05 1998/04 1998/03 1998/02 1998/01

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0587893134639656 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 182.272727272727 167.083333333333 15.1893939393939 3 200.5 167.976307374964 32.523692625036 4 222.777777777778 169.888352935703 52.8894248420748 5 250.625 172.997685911673 77.6273140883275 6 286.428571428571 177.561342412977 108.867229015595 7 334.166666666667 183.961572065528 150.205094601139 8 401 192.792026455919 208.207973544081 9 501.25 205.032430278299 296.217569721701 10 668.333333333333 222.446857838202 445.886475495131 11 1002.5 248.660217615428 753.839782384572 12 2005 292.977940883642 1712.02205911636 13 167 393.626542374258 -226.626542374258 14 182.181818181818 380.303323535363 -198.121505353545 15 200.4 368.655896253181 -168.255896253181 16 222.666666666667 358.764247626192 -136.097580959525 17 250.5 350.763164277475 -100.263164277475 18 286.285714285714 344.868761683877 -58.5830473981632 19 334 341.424704546712 -7.42470454671246 20 400.8 340.988211263738 59.8117887362616 21 501 344.504505260595 156.495494739405 22 668 353.704767956528 314.295232043472 23 1002 372.181968873362 629.818031126638 24 2004 409.208538530523 1594.79146146948 25 166.916666666667 502.965233668508 -336.048567001842 26 182.090909090909 483.20916912392 -301.118260033011 27 200.3 465.506633345116 -265.206633345116 28 222.555555555556 449.915317444667 -227.359761889111 29 250.375 436.548993133875 -186.173993133875 30 286.142857142857 425.60395189269 -139.461094749833 31 333.833333333333 417.405129877414 -83.5717965440808 32 400.6 412.492001333637 -11.8920013336373 33 500.75 411.79287873952 88.9571212604798 34 667.666666666667 417.022606826155 250.644059840512 35 1001.5 431.757799027999 569.742200972 36 2003 465.252551874592 1537.74744812541 37 166.833333333333 555.65566863085 -388.822335297516 38 182 532.797070479253 -350.797070479253 39 200.2 512.173951540607 -311.973951540607 40 222.444444444444 493.833217110895 -271.38877266645 41 250.25 477.878457484006 -227.628457484006 42 286 464.496336743659 -178.496336743659 43 333.666666666667 454.002659650667 -120.335992984000 44 400.4 446.928189238133 -46.5281892381329 45 500.5 444.192828936102 56.3071710638984 46 667.333333333333 447.503088866046 219.830244467287 47 1001 460.426758016894 540.573241983106 48 2002 492.206687790071 1509.79331220993 49 166.75 580.966400087379 -414.216400087379 50 181.909090909091 556.614902300727 -374.705811391636 51 200.1 534.586204898054 -334.486204898054 52 222.333333333333 514.92199054893 -292.588657215597 53 250.125 497.720904263882 -247.595904263882 54 285.857142857143 483.164911035718 -197.307768178576 55 333.5 471.565322803393 -138.065322803393 56 400.2 463.448557262601 -63.2485572626005 57 500.25 459.730218003546 40.5197819964541 58 667 462.112348168827 204.887651831173 59 1000.5 474.157552557226 526.342447442774 60 2001 505.10086368933 1495.89913631067 61 166.666666666667 593.043746924373 -426.377080257707 62 181.818181818182 567.977331099252 -386.159149281071 63 200 545.275299825189 -345.275299825189 64 222.222222222222 524.976801992401 -302.754579770179 65 250 507.178068099641 -257.178068099641 66 285.714285714286 492.058746038074 -206.344460323789 67 333.333333333333 479.927896878546 -146.594563545213 68 400 471.309703130174 -71.3097031301735 69 500 467.117454639831 32.8825453601685 70 666.666666666667 469.050596906503 197.616069760163 71 1000 480.668309977151 519.331690022849 72 2000 511.199463493675 1488.80053650632 73 166.583333333333 598.725024919665 -432.141691586332 74 181.727272727273 573.319711552148 -391.592438824875 75 199.9 550.298260915954 -350.398260915954 76 222.111111111111 529.698587717737 -307.587476606626 77 249.875 511.61573113792 -261.74073113792 78 285.571428571429 496.228173248766 -210.656744677337 79 333.166666666667 483.843807852631 -150.677141185964 80 399.8 474.985602167595 -75.1856021675952 81 499.75 470.565492233787 29.1845077662126 82 666.333333333333 472.281229409147 194.052103924186 83 999.5 483.689419375088 515.810580624912 84 1999 514.013569287476 1484.98643071252 85 166.5 601.31490205237 -434.81490205237 86 181.636363636364 575.75243247681 -394.116068840446 87 199.8 552.582619364563 -352.782619364563 88 222 531.842771370101 -309.842771370101 89 249.75 513.62732755948 -263.87732755948 90 285.428571428571 498.114160633552 -212.685589204981 91 333 485.610520860512 -152.610520860512 92 399.6 476.638653111745 -77.0386531117446 93 499.5 472.109603585117 27.3903964148834 94 666 473.719866185853 192.280133814147 95 999 485.023883245547 513.976116754453 96 1998 515.240186286416 1482.75981371358 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 602.410617766595 -421.269546571162 1626.09078210435 98 602.410617766595 -423.037033882345 1627.85826941554 99 602.410617766595 -424.801479945497 1629.62271547869 100 602.410617766595 -426.562900405679 1631.38413593887 101 602.410617766595 -428.321310774273 1633.14254630746 102 602.410617766595 -430.076726430576 1634.89796196377 103 602.410617766595 -431.829162623368 1636.65039815656 104 602.410617766595 -433.578634472456 1638.39987000565 105 602.410617766595 -435.325156970201 1640.14639250339 106 602.410617766595 -437.068744983012 1641.88998051620 107 602.410617766595 -438.809413252824 1643.63064878601 108 602.410617766595 -440.547176398553 1645.36841193174

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/1r9ip1218992501.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/1r9ip1218992501.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/2gc3k1218992501.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/2gc3k1218992501.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/3mf3b1218992501.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t121899257118cf8xghfeybnhx/3mf3b1218992501.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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