Verbetering opgave 10.2.1

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 02 Jun 2008 02:08:19 -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/02/t1212394134e8brzgr32lt597f.htm/, Retrieved Mon, 02 Jun 2008 08:08:54 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.914427070243967 beta 0.0344554406262715 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10812 10914.545 -102.545000000002 14 10738 10750.8917282676 -12.8917282676284 15 10171 10149.5219889536 21.4780110464035 16 9721 9703.09091042715 17.9090895728496 17 9897 9876.7939082906 20.2060917093950 18 9828 9803.8173135029 24.1826864970917 19 9924 9929.69728157403 -5.6972815740337 20 10371 10403.7413604695 -32.7413604695084 21 10846 10850.6073532273 -4.60735322731671 22 10413 10348.7213466474 64.2786533526305 23 10709 10643.5601293142 65.4398706857501 24 10662 10623.3559070742 38.6440929257624 25 10570 11034.7163831580 -464.71638315804 26 10297 10539.0955696924 -242.095569692427 27 10635 9715.39511183796 919.604888162043 28 10872 10102.5457909711 769.454209028861 29 10296 10999.9731063343 -703.973106334326 30 10383 10278.6055875396 104.394412460400 31 10431 10491.2814921564 -60.2814921563568 32 10574 10927.3833455591 -353.383345559088 33 10653 11087.6359689984 -434.635968998438 34 10805 10189.0488585829 615.951141417059 35 10872 10996.4667312719 -124.466731271887 36 10625 10802.3458574756 -177.345857475637 37 10407 10968.3521319551 -561.352131955147 38 10463 10395.5974743328 67.4025256671957 39 10556 9956.25410266609 599.745897333911 40 10646 10029.9239730652 616.076026934777 41 10702 10648.0358947517 53.9641052483403 42 11353 10699.8246351958 653.17536480418 43 11346 11428.4229118461 -82.4229118460953 44 11451 11846.6928711565 -395.692871156501 45 11964 11987.4668520811 -23.4668520810756 46 12574 11593.8837879629 980.116212037108 47 13031 12721.5361353658 309.463864634223 48 13812 12983.9517719481 828.04822805195 49 14544 14132.3976601841 411.602339815858 50 14931 14629.7387399561 301.261260043888 51 14886 14583.7599439579 302.240056042145 52 16005 14511.3699600888 1493.63003991117 53 17064 16036.0786698120 1027.92133018804 54 15168 17212.6821902173 -2044.68219021730 55 16050 15509.2634878286 540.736512171443 56 15839 16588.1180421682 -749.118042168222 57 15137 16543.9857647608 -1406.98576476078 58 14954 15033.9873988450 -79.9873988449799 59 15648 15164.2942507298 483.705749270222 60 15305 15665.3396333509 -360.339633350886 61 15579 15688.9339414398 -109.933941439775 62 16348 15680.9728258988 667.027174101157 63 15928 15962.1151315066 -34.1151315065963 64 16171 15666.077141574 504.922858425996 65 15937 16197.6555476122 -260.655547612248 66 15713 15843.2409942166 -130.240994216649 67 15594 16082.2224644933 -488.222464493265 68 15683 16047.9145111236 -364.914511123585 69 16438 16249.0398383683 188.960161631661 70 17032 16312.4833804945 719.516619505546 71 17696 17247.8157992586 448.184200741394 72 17745 17668.7332786633 76.2667213367349 73 19394 18151.3377547912 1242.66224520878 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 19527.6678272971 18384.6718971441 20670.6637574501 75 19198.8013910344 17625.4513045544 20772.1514775144 76 19041.0988899137 17111.4379820888 20970.7597977386 77 19090.5534094161 16842.5508182305 21338.5560006017 78 19038.9658020531 16495.7793033977 21582.1523007085 79 19423.8296431499 16600.8824686471 22246.7768176526 80 19919.3197728565 16827.4256965344 23011.2138491786 81 20585.8292652597 17232.8118131163 23938.846717403 82 20600.2300048159 16991.8542350923 24208.6057745394 83 20910.0746518975 17050.6249835388 24769.5243202562 84 20930.8897759767 16823.5490358477 25038.2305161057 85 21482.7183237706 17129.8275470264 25835.6091005148

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/1icw01212394093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/1icw01212394093.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/2gomh1212394093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/2gomh1212394093.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/32ef01212394093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394134e8brzgr32lt597f/32ef01212394093.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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