*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 15:03:30 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz.htm/, Retrieved Wed, 18 May 2011 16:59:34 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,202 1,2271 1,277 1,265 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,457 1,4718 1,4748 1,5527 1,5751 1,5557 1,5553 1,577 1,4975 1,437 1,3322 1,2732 1,3449 1,3239 1,2785 1,305 1,319 1,365 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614 1,4272 1,3686 1,3569 1,3406 1,2565 1,2209 1,277 1,2894 1,3067 1,3898 1,3661 1,322 1,336

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 1 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0526243027716168 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.2938 1.3388 -0.0450000000000002 4 1.2694 1.31013190637528 -0.0407319063752773 5 1.2165 1.28358841820172 -0.0670884182017197 6 1.2037 1.2271579369698 -0.0234579369698034 7 1.2292 1.21312347939231 0.0160765206076929 8 1.2256 1.23946949508028 -0.0138694950802805 9 1.2015 1.23513962257189 -0.0336396225718862 10 1.1786 1.20926936088854 -0.0306693608885404 11 1.1856 1.18475540715533 0.000844592844670089 12 1.2103 1.19179985326491 0.0185001467350934 13 1.1938 1.21747341058801 -0.0236734105880134 14 1.202 1.19972761386159 0.00227238613840686 15 1.2271 1.20804719659775 0.0190528034022455 16 1.277 1.23414983709264 0.0428501629073574 17 1.265 1.28630479703929 -0.0213047970392923 18 1.2684 1.27318364694941 -0.00478364694940869 19 1.2811 1.27633191086399 0.00476808913600935 20 1.2727 1.28928282823033 -0.016582828230326 21 1.2611 1.28001016845672 -0.0189101684567234 22 1.2881 1.26741503402639 0.0206849659736053 23 1.3213 1.29550356593861 0.0257964340613897 24 1.2999 1.33006108529508 -0.0301610852950849 25 1.3074 1.3070738792106 0.000326120789404083 26 1.3242 1.31459104108976 0.0096089589102426 27 1.3516 1.33189670585277 0.0197032941472297 28 1.3511 1.36033357796957 -0.00923357796957225 29 1.3419 1.35934766736684 -0.017447667366836 30 1.3716 1.34922949603667 0.0223705039633346 31 1.3622 1.38010672821039 -0.0179067282103853 32 1.3896 1.36976439912339 0.0198356008766067 33 1.4227 1.39820823378958 0.0244917662104196 34 1.4684 1.43259709591005 0.0358029040899506 35 1.457 1.48018119877498 -0.0231811987749819 36 1.4718 1.46756130435204 0.00423869564796164 37 1.4748 1.48258436275517 -0.00778436275517325 38 1.5527 1.48517471609266 0.0675252839073388 39 1.5751 1.56662818707774 0.00847181292225963 40 1.5557 1.58947401032599 -0.0337740103259856 41 1.5553 1.56829667658078 -0.0129966765807796 42 1.577 1.56721273553737 0.00978726446263245 43 1.4975 1.58942778350576 -0.091927783505755 44 1.437 1.50509014799342 -0.0680901479934246 45 1.3322 1.44100695142965 -0.108806951429654 46 1.2732 1.33048106147396 -0.0572810614739636 47 1.3449 1.26846668555188 0.0764333144481215 48 1.3239 1.34418893543323 -0.0202889354332343 49 1.2785 1.32212124435208 -0.0436212443520823 50 1.305 1.27442570678202 0.0305742932179764 51 1.319 1.30253465764535 0.0164653423546457 52 1.365 1.31740113480666 0.0475988651933363 53 1.4016 1.36590599190018 0.0356940080998169 54 1.4088 1.40438436418956 0.00441563581043969 55 1.4268 1.41181673394538 0.0149832660546219 56 1.4562 1.43060521787474 0.0255947821252556 57 1.4816 1.46135212543868 0.0202478745613228 58 1.4914 1.48781765572007 0.00358234427992588 59 1.4614 1.49780617409009 -0.0364061740900932 60 1.4272 1.46589032456202 -0.0386903245620198 61 1.3686 1.42965427320794 -0.061054273207936 62 1.3569 1.36784133464914 -0.0109413346491405 63 1.3406 1.35556555454184 -0.0149655545418386 64 1.2565 1.33847800266848 -0.0819780026684838 65 1.2209 1.25006396743545 -0.0291639674354449 66 1.277 1.2129292339831 0.0640707660168993 67 1.2894 1.27240091337278 0.0169990866272169 68 1.3067 1.2856954784543 0.0210045215457049 69 1.3898 1.30410082675569 0.0856991732443109 70 1.3661 1.39171068599577 -0.0256106859957748 71 1.322 1.36666294150174 -0.0446629415017445 72 1.336 1.32021258534549 0.0157874146545143 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.33504338703425 1.26114016918015 1.40894660488835 74 1.33408677406849 1.22678658230355 1.44138696583343 75 1.33313016110274 1.19827769760627 1.4679826245992 76 1.33217354813698 1.17246286231958 1.49188423395439 77 1.33121693517123 1.14815811896001 1.51427575138244 78 1.33026032220548 1.12477426847802 1.53574637593293 79 1.32930370923972 1.10197197433231 1.55663544414713 80 1.32834709627397 1.07953717136842 1.57715702117952 81 1.32739048330821 1.05732613604406 1.59745483057237 82 1.32643387034246 1.03523791094158 1.61762982974334 83 1.3254772573767 1.01319912119628 1.63775539355713 84 1.32452064441095 0.991155012351751 1.65788627647015

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/1i66m1305731009.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/1i66m1305731009.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/2avyn1305731009.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/2avyn1305731009.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/35cbu1305731009.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730771ihmo1b7mtaylwgz/35cbu1305731009.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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