test kuleuven

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 17 Apr 2008 07:27:08 -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/17/t1208438934da4lvnmdyh0073a.htm/, Retrieved Thu, 17 Apr 2008 15:28:58 +0200

User-defined keywords:

EXPONENTIAL SMOOTHING

Dataseries X:

» Textbox « » Textfile « » CSV «

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.257593917038981 beta 0.275620602016356 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 14000 12418 1582 4 13477 12482.8327141109 994.167285889096 5 14237 12466.8273751728 1770.17262482716 6 13674 12776.3953443527 897.604655647281 7 13529 12924.9234187952 604.076581204808 8 14058 13040.7287909641 1017.27120903593 9 12975 13335.1950008946 -360.195000894586 10 14326 13249.2611009332 1076.73889906681 11 14008 13609.9191462529 398.080853747075 12 16193 13824.0220276335 2368.97797236650 13 14483 14714.0091672289 -231.009167228871 14 14011 14917.8542024250 -906.854202425036 15 15057 14883.2206602832 173.779339716792 16 14884 15139.2897638098 -255.289763809847 17 15414 15266.7081649975 147.291835002472 18 14440 15508.2865909102 -1068.28659091022 19 14900 15360.8929937446 -460.892993744594 20 15074 15337.2377238919 -263.237723891854 21 14442 15345.8078471588 -903.807847158841 22 15307 15125.2022815364 181.797718463629 23 14938 15197.1494149680 -259.149414968046 24 17193 15137.1121095627 2055.88789043734 25 15528 15819.3786518194 -291.378651819447 26 14765 15876.3162540952 -1111.31625409515 27 15838 15643.1414745702 194.858525429809 28 15723 15760.2639755477 -37.2639755476648 29 16150 15814.9474574311 335.052542568883 30 15486 15989.325533836 -503.325533836001 31 15986 15912.0073154504 73.992684549643 32 15983 15988.6561050292 -5.65610502916206 33 15692 16044.3862776907 -352.386277690657 34 16490 15985.7820789511 504.21792104888 35 15686 16183.6324711241 -497.632471124056 36 18897 16088.0812915112 2808.91870848877 37 16316 17043.7057276810 -727.705727681048 38 15636 17036.6514323675 -1400.65143236751 39 17163 16756.8066998239 406.193300176132 40 16534 16971.2331687191 -437.233168719074 41 16518 16937.3553459559 -419.35534595593 42 16375 16878.3092708513 -503.309270851274 43 16290 16761.9031278947 -471.903127894733 44 16352 16620.0827481543 -268.082748154338 45 15943 16511.7318683831 -568.731868383089 46 16362 16285.5566705486 76.443329451422 47 16393 16231.0020171667 161.997982833258 48 19051 16209.9872857146 2841.01271428535 49 16747 17080.7772146159 -333.777214615868 50 16320 17110.062991691 -790.062991690986 51 17910 16965.7192853769 944.280714623052 52 16961 17335.1741899171 -374.174189917117 53 17480 17338.4374407453 141.562559254660 54 17049 17484.6020265019 -435.602026501892 55 16879 17451.1655701818 -572.165570181805 56 17473 17341.9284555769 131.071544423117 57 16998 17423.146786409 -425.146786409005 58 17307 17330.9020061455 -23.9020061455049 59 17418 17340.3184413361 77.6815586638913 60 20169 17381.4174349923 2787.58256500767 61 17871 18318.4837616176 -447.483761617645 62 17226 18390.4461439381 -1164.44614393811 63 19062 18195.0498086843 866.950191315664 64 17804 18584.4807073156 -780.480707315615 65 19100 18494.1307097856 605.869290214378 66 18522 18803.9116617851 -281.911661785070 67 18060 18864.9904230216 -804.990423021602 68 18869 18734.1744138350 134.825586165025 69 18127 18855.0216644002 -728.021664400152 70 18871 18701.9164910760 169.083508924028 71 18890 18791.9047765196 98.0952234803808 72 21263 18870.5714948148 2392.42850518523 73 19547 19710.1026048821 -163.102604882108 74 18450 19879.7644563814 -1429.76445638138 75 20254 19621.6312307591 632.368769240937 76 19240 19939.5880185195 -699.588018519546 77 20216 19864.7713565907 351.228643409253 78 19420 20085.5752728283 -665.575272828344 79 19415 19997.202045416 -582.202045415997 80 20018 19888.9699625048 129.030037495155 81 18652 19973.1078369356 -1321.10783693559 82 19978 19589.9027501805 388.097249819497 83 19509 19674.5326992170 -165.532699216954 84 21971 19604.7984189797 2366.20158102032 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20355.2195194777 18446.2449522395 22264.1940867159 86 20496.1214862168 18486.7294041021 22505.5135683316 87 20637.023452956 18487.7137610757 22786.3331448364 88 20777.9254196952 18448.4298683930 23107.4209709973 89 20918.8273864343 18370.2106155603 23467.4441573083 90 21059.7293531735 18255.6315116779 23863.8271946691 91 21200.6313199126 18107.7620868906 24293.5005529347 92 21341.5332866518 17929.6698078764 24753.3967654272 93 21482.4352533910 17724.1616590796 25240.7088477024 94 21623.3372201301 17493.6879713920 25752.9864688683 95 21764.2391868693 17240.3361473629 26288.1422263757 96 21905.1411536084 16965.8652371616 26844.4170700553

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/1himy1208438824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/1himy1208438824.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/27n4d1208438824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/27n4d1208438824.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/3z4m41208438824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208438934da4lvnmdyh0073a/3z4m41208438824.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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