test

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 27 Apr 2008 15:45:34 -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/Apr/27/t1209332797uek53m1r4zj46e7.htm/, Retrieved Sun, 27 Apr 2008 23:46:38 +0200

User-defined keywords:

Dataseries X:

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13328 12873 14000 13477 14237 13674 13529 14058 12975 14326 14008 16193 14483 14011 15057 14884 15414 14440 14900 15074 14442 15307 14938 17193 15528 14765 15838 15723 16150 15486 15986 15983 15692 16490 15686 18897 16316 15636 17163 16534 16518 16375 16290 16352 15943 16362 16393 19051 16747 16320 17910 16961 17480 17049 16879 17473 16998 17307 17418 20169 17871 17226 19062 17804 19100 18522 18060 18869 18127 18871 18890 21263 19547 18450 20254 19240 20216 19420 19415 20018 18652 19978 19509 21971

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.283890683571533 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 12873 13328 -455 3 14000 13198.8297389750 801.170261025047 4 13477 13426.2745120345 50.7254879654629 5 14237 13440.6750054876 796.324994512448 6 13674 13666.7442525248 7.25574747521205 7 13529 13668.8040916353 -139.804091635348 8 14058 13629.1150124949 428.884987505109 9 12975 13750.8714647713 -775.871464771284 10 14326 13530.6087842737 795.391215726282 11 14008 13756.4129402130 251.587059786954 12 16193 13827.8361625937 2365.16383740628 13 14483 14499.2841411537 -16.2841411536556 14 14011 14494.6612251902 -483.66122519017 15 15057 14357.3543093539 699.645690646114 16 14884 14555.9772027293 328.022797270711 17 15414 14649.0998188735 764.900181126482 18 14440 14866.2478541575 -426.247854157504 19 14900 14745.2400594698 154.759940530170 20 15074 14789.1749647764 284.82503522357 21 14442 14870.0341387243 -428.034138724335 22 15307 14748.5192344899 558.480765510069 23 14938 14907.0667207721 30.9332792278619 24 17193 14915.8483905572 2277.15160944276 25 15528 15562.3105175580 -34.3105175579658 26 14765 15552.5700812747 -787.570081274742 27 15838 15328.9862725412 509.013727458832 28 15723 15473.4905275767 249.509472423251 29 16150 15544.3239422606 605.676057739442 30 15486 15716.2697323151 -230.269732315121 31 15986 15650.8983006023 335.101699397654 32 15983 15746.0305511103 236.969448889671 33 15692 15813.3039699412 -121.303969941187 34 16490 15778.8669029946 711.133097005357 35 15686 15980.7509640138 -294.750964013836 36 18897 15897.0739113566 2999.92608864342 37 16316 16748.7249793256 -432.724979325634 38 15636 16625.8783891464 -989.8783891464 39 17163 16344.8611365989 818.138863401058 40 16534 16577.1231377863 -43.1231377863041 41 16518 16564.8808807224 -46.8808807224013 42 16375 16551.5718354477 -176.571835447685 43 16290 16501.4447363830 -211.444736382960 44 16352 16441.4175456336 -89.417545633598 45 15943 16416.0327374804 -473.032737480386 46 16362 16281.7431502854 80.2568497146349 47 16393 16304.5273222122 88.4726777878495 48 19051 16329.6438911867 2721.35610881325 49 16747 17102.2115371593 -355.211537159306 50 16320 17001.3702910627 -681.370291062656 51 17910 16807.9356133675 1102.06438663246 52 16961 17120.8014254285 -159.801425428472 53 17480 17075.4352895279 404.564710472121 54 17049 17190.2874417327 -141.287441732729 55 16879 17150.1772533192 -271.177253319151 56 17473 17073.1925575053 399.807442494675 57 16998 17186.6941656521 -188.694165652123 58 17307 17133.1256499792 173.874350020818 59 17418 17182.4869580621 235.513041937851 60 20169 17249.3469165279 2919.65308347211 61 17871 18078.2092261865 -207.209226186525 62 17226 18019.3844573221 -793.384457322103 63 19062 17794.1500013979 1267.84999860210 64 17804 18154.0808041672 -350.080804167217 65 19100 18054.6961253669 1045.30387463309 66 18522 18351.4481568765 170.551843123529 67 18060 18399.8662362052 -339.866236205195 68 18869 18303.381378086 565.618621913982 69 18127 18463.9552353020 -336.955235301968 70 18871 18368.2967832191 502.703216780916 71 18890 18511.0095430646 378.990456935375 72 21263 18618.6014029511 2644.39859704890 73 19547 19369.3215283029 177.678471697087 74 18450 19419.7627910889 -969.762791088946 75 20254 19144.4561694245 1109.54383057553 76 19240 19459.4453259391 -219.445325939130 77 20216 19397.1468423517 818.853157648307 78 19420 19629.6116250212 -209.611625021178 79 19415 19570.1048375094 -155.104837509374 80 20018 19526.0720191636 491.927980836415 81 18652 19665.7257899112 -1013.72578991120 82 19978 19377.9384824592 600.061517540784 83 19509 19548.2903568588 -39.2903568588408 84 21971 19537.1361905924 2433.86380940758 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20228.0874511651 18517.5865739588 21938.5883283715 86 20228.0874511651 18449.9940872937 22006.1808150366 87 20228.0874511651 18384.8786267605 22071.2962755698 88 20228.0874511651 18321.9863179398 22134.1885843905 89 20228.0874511651 18261.1039001910 22195.0710021393 90 20228.0874511651 18202.0501737384 22254.1247285919 91 20228.0874511651 18144.6696319934 22311.5052703369 92 20228.0874511651 18088.8276331528 22367.3472691775 93 20228.0874511651 18034.4066793385 22421.7682229918 94 20228.0874511651 17981.3035077469 22474.8713945834 95 20228.0874511651 17929.4267871867 22526.7481151436 96 20228.0874511651 17878.6952727834 22577.4796295469

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/1ck471209332726.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/1ck471209332726.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/2zhq11209332726.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/2zhq11209332726.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/3vls71209332726.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/27/t1209332797uek53m1r4zj46e7/3vls71209332726.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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