steve

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 15 Apr 2008 11:48:35 -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/15/t1208281771q0q3lnlfd7zcr2g.htm/, Retrieved Tue, 15 Apr 2008 19:49:31 +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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.440051506383271 beta 0.000510357792765983 gamma 0.96961246768094 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14483 13950.0064127244 532.99358727564 14 14011 13710.3180276631 300.681972336923 15 15057 14858.4539887854 198.546011214616 16 14884 14757.8307940623 126.169205937656 17 15414 15346.8791948468 67.1208051532321 18 14440 14409.4965928749 30.5034071250557 19 14900 14882.3743789154 17.6256210845550 20 15074 15074.1789431871 -0.178943187094774 21 14442 14462.2002026381 -20.2002026381178 22 15307 15336.5931238976 -29.5931238976209 23 14938 14973.0809767451 -35.0809767451483 24 17193 17227.6015232390 -34.6015232389509 25 15528 15796.1793597407 -268.179359740729 26 14765 15019.3832309771 -254.383230977075 27 15838 15923.2660255571 -85.2660255571136 28 15723 15640.7630943442 82.2369056557509 29 16150 16200.2974877907 -50.2974877906727 30 15486 15138.1294300757 347.870569924342 31 15986 15765.3156185356 220.684381464374 32 15983 16042.5739394614 -59.5739394614156 33 15692 15349.5587830128 342.441216987201 34 16490 16436.5472822237 53.4527177762684 35 15686 16073.7925925926 -387.792592592596 36 18897 18313.7834502124 583.216549787649 37 16316 16895.9028379536 -579.902837953625 38 15636 15936.0503022295 -300.050302229527 39 17163 16983.0463333618 179.953666638183 40 16534 16889.6413325147 -355.641332514726 41 16518 17207.8578450826 -689.857845082581 42 16375 16035.9966343466 339.0033656534 43 16290 16603.8926137906 -313.892613790649 44 16352 16491.7088311064 -139.708831106396 45 15943 15964.7551711969 -21.7551711968772 46 16362 16746.0563229809 -384.056322980894 47 16393 15944.7054354089 448.294564591091 48 19051 19156.356226812 -105.356226812008 49 16747 16770.4584969015 -23.4584969015123 50 16320 16188.8764249218 131.123575078169 51 17910 17737.8757527058 172.124247294203 52 16961 17327.2676307849 -366.267630784881 53 17480 17460.0099751190 19.9900248809681 54 17049 17134.9256386618 -85.9256386617926 55 16879 17158.8465352256 -279.846535225559 56 17473 17157.4450247848 315.554975215218 57 16998 16867.0219923134 130.978007686579 58 17307 17547.9730593578 -240.973059357799 59 17418 17241.1132802831 176.886719716909 60 20169 20181.7132615435 -12.7132615435185 61 17871 17740.7680291172 130.231970882836 62 17226 17274.8412128554 -48.8412128553646 63 19062 18848.1932548180 213.806745181970 64 17804 18111.7650355626 -307.765035562628 65 19100 18504.8029249480 595.197075051976 66 18522 18340.3783130128 181.621686987244 67 18060 18365.5852249802 -305.585224980157 68 18869 18703.5773108711 165.422689128878 69 18127 18200.9628220799 -73.962822079895 70 18871 18612.3533893378 258.646610662221 71 18890 18747.3054779326 142.694522067351 72 21263 21783.5634715529 -520.563471552898 73 19547 19028.8903805263 518.1096194737 74 18450 18582.0878468767 -132.087846876704 75 20254 20385.1178385464 -131.117838546423 76 19240 19132.7870737035 107.212926296495 77 20216 20265.7094088722 -49.7094088721533 78 19420 19548.1138197171 -128.113819717128 79 19415 19150.0971746055 264.902825394514 80 20018 20037.3628166547 -19.3628166547314 81 18652 19274.9496496977 -622.949649697675 82 19978 19650.4021559329 327.597844067142 83 19509 19746.2597465847 -237.259746584718 84 21971 22352.5260978328 -381.526097832812 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20131.5438517072 19588.7640742271 20674.3236291872 86 19069.6244112468 18480.3925910819 19658.8562314118 87 20990.2274879787 20335.3577824417 21645.0971935157 88 19883.0625592060 19199.8579313310 20566.2671870810 89 20913.9942135408 20173.3622299424 21654.6261971393 90 20146.9728875164 19383.4761703426 20910.4696046901 91 20009.7882003458 19213.0630178796 20806.5133828120 92 20642.3306615505 19795.9350493784 21488.7262737226 93 19519.2896667351 18669.9101677230 20368.6691657471 94 20733.1598560548 19817.2561589609 21649.0635531486 95 20360.6555695008 19426.6869770710 21294.6241619306 96 23101.5535340852 22199.366344092 24003.7407240785

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/1zdog1208281709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/1zdog1208281709.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/217or1208281709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/217or1208281709.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/3hvq51208281709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/3hvq51208281709.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/4m2051208281709.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208281771q0q3lnlfd7zcr2g/4m2051208281709.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() bitmap(file="myhist.png") hist(myresid) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$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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