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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 10 Mar 2008 11:43:04 -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/Mar/10/t1205171047i3xo7gva8f85ux9.htm/, Retrieved Mon, 10 Mar 2008 18:44:12 +0100

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.283890683571503 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 12873 13328 -455 3 14000 13198.8297389750 801.170261025034 4 13477 13426.2745120345 50.7254879654774 5 14237 13440.6750054875 796.324994512461 6 13674 13666.7442525248 7.25574747524479 7 13529 13668.8040916353 -139.804091635324 8 14058 13629.1150124949 428.884987505124 9 12975 13750.8714647713 -775.87146477126 10 14326 13530.6087842737 795.391215726278 11 14008 13756.4129402130 251.587059786978 12 16193 13827.8361625937 2365.16383740631 13 14483 14499.2841411536 -16.2841411535665 14 14011 14494.6612251901 -483.661225190106 15 15057 14357.3543093539 699.645690646146 16 14884 14555.9772027292 328.022797270754 17 15414 14649.0998188735 764.900181126524 18 14440 14866.2478541575 -426.247854157451 19 14900 14745.2400594698 154.759940530195 20 15074 14789.1749647764 284.825035223594 21 14442 14870.0341387243 -428.03413872431 22 15307 14748.5192344899 558.480765510074 23 14938 14907.0667207721 30.9332792278838 24 17193 14915.8483905572 2277.15160944277 25 15528 15562.3105175579 -34.3105175578839 26 14765 15552.5700812747 -787.570081274684 27 15838 15328.9862725411 509.013727458852 28 15723 15473.4905275767 249.509472423280 29 16150 15544.3239422605 605.676057739471 30 15486 15716.2697323151 -230.269732315079 31 15986 15650.8983006023 335.101699397677 32 15983 15746.0305511103 236.969448889700 33 15692 15813.3039699412 -121.303969941160 34 16490 15778.8669029946 711.133097005375 35 15686 15980.7509640138 -294.750964013800 36 18897 15897.0739113566 2999.92608864344 37 16316 16748.7249793255 -432.724979325532 38 15636 16625.8783891463 -989.878389146343 39 17163 16344.8611365989 818.138863401073 40 16534 16577.1231377863 -43.1231377862714 41 16518 16564.8808807224 -46.8808807223795 42 16375 16551.5718354477 -176.571835447670 43 16290 16501.4447363830 -211.444736382953 44 16352 16441.4175456336 -89.4175456335979 45 15943 16416.0327374804 -473.032737480389 46 16362 16281.7431502854 80.2568497146203 47 16393 16304.5273222122 88.4726777878423 48 19051 16329.6438911867 2721.35610881325 49 16747 17102.2115371592 -355.21153715923 50 16320 17001.3702910626 -681.370291062609 51 17910 16807.9356133675 1102.06438663247 52 16961 17120.8014254284 -159.801425428432 53 17480 17075.4352895279 404.564710472147 54 17049 17190.2874417327 -141.287441732697 55 16879 17150.1772533191 -271.177253319132 56 17473 17073.1925575053 399.807442494679 57 16998 17186.6941656521 -188.694165652108 58 17307 17133.1256499792 173.874350020822 59 17418 17182.4869580621 235.513041937862 60 20169 17249.3469165279 2919.65308347212 61 17871 18078.2092261864 -207.209226186427 62 17226 18019.3844573220 -793.384457322041 63 19062 17794.1500013979 1267.84999860212 64 17804 18154.0808041672 -350.080804167166 65 19100 18054.6961253669 1045.30387463311 66 18522 18351.4481568764 170.551843123576 67 18060 18399.8662362052 -339.866236205155 68 18869 18303.381378086 565.618621914 69 18127 18463.9552353019 -336.955235301935 70 18871 18368.2967832191 502.70321678093 71 18890 18511.0095430646 378.990456935397 72 21263 18618.6014029511 2644.39859704893 73 19547 19369.3215283028 177.678471697189 74 18450 19419.7627910889 -969.762791088866 75 20254 19144.4561694244 1109.54383057556 76 19240 19459.4453259391 -219.445325939076 77 20216 19397.1468423517 818.85315764834 78 19420 19629.6116250211 -209.611625021127 79 19415 19570.1048375093 -155.104837509345 80 20018 19526.0720191636 491.92798083643 81 18652 19665.7257899112 -1013.72578991117 82 19978 19377.9384824592 600.061517540773 83 19509 19548.2903568588 -39.2903568588299 84 21971 19537.1361905924 2433.86380940759 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20228.0874511651 18517.5865739587 21938.5883283714 86 20228.0874511651 18449.9940872937 22006.1808150364 87 20228.0874511651 18384.8786267604 22071.2962755697 88 20228.0874511651 18321.9863179397 22134.1885843904 89 20228.0874511651 18261.1039001910 22195.0710021392 90 20228.0874511651 18202.0501737384 22254.1247285917 91 20228.0874511651 18144.6696319934 22311.5052703368 92 20228.0874511651 18088.8276331528 22367.3472691773 93 20228.0874511651 18034.4066793385 22421.7682229916 94 20228.0874511651 17981.3035077470 22474.8713945832 95 20228.0874511651 17929.4267871868 22526.7481151434 96 20228.0874511651 17878.6952727834 22577.4796295467

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/1hxbj1205170981.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/1hxbj1205170981.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/27rv61205170981.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/27rv61205170981.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/34rys1205170981.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171047i3xo7gva8f85ux9/34rys1205170981.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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