neerslag in Notingham

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 14:57:40 -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/May/26/t1211835514k4dirjiaqwxslvn.htm/, Retrieved Mon, 26 May 2008 22:58:37 +0200

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Dataseries X:

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29.90 28.77 15.64 23.73 25.65 21.81 28.97 24.29 25.33 28.84 19.99 19.75 22.70 23.28 24.15 20.38 27.75 27.31 25.61 22.64 26.05 28.07 21.02 25.00 17.93 35.45 17.70 28.53 26.55 26.51 30.78 26.83 27.49 25.89 20.44 19.79 18.14 27.98 35.90 34.38 21.58 21.53 31.14 28.25 25.16 20.51 30.05 20.17 32.37 22.46 25.40 19.82 18.14 20.10 20.25 19.73 24.74 26.17 20.14 31.71 26.66 20.75 20.01 26.67 23.91 26.81 29.31 31.76 22.99 23.94 27.04 20.28 23.32

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0059609824078949 beta 0 gamma 0.149848445764807 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 22.7 21.8376481264193 0.862351873580732 14 23.28 22.5953525621374 0.684647437862608 15 24.15 23.4818406671579 0.668159332842098 16 20.38 19.8212266395013 0.558773360498666 17 27.75 26.9815169182631 0.768483081736893 18 27.31 26.2719665527146 1.0380334472854 19 25.61 24.6221013177565 0.987898682243461 20 22.64 21.4990575198334 1.14094248016659 21 26.05 24.5076577523591 1.54234224764089 22 28.07 26.3428614075284 1.72713859247157 23 21.02 19.5076250050155 1.51237499498450 24 25 23.2889874444646 1.71101255553539 25 17.93 22.0404407121803 -4.1104407121803 26 35.45 22.7434911225064 12.7065088774936 27 17.7 23.7037352652812 -6.00373526528117 28 28.53 19.9741517810699 8.55584821893014 29 26.55 27.2557072182352 -0.705707218235155 30 26.51 26.5737299013003 -0.0637299013002917 31 30.78 24.9009469001368 5.87905309986323 32 26.83 21.8096356255930 5.02036437440704 33 27.49 24.9241941563657 2.56580584363426 34 25.89 26.8073718865538 -0.917371886553806 35 20.44 19.8747881316018 0.565211868398251 36 19.79 23.7062178522269 -3.91621785222694 37 18.14 21.5446794857404 -3.40467948574039 38 27.98 24.7688227606634 3.21117723933658 39 35.9 22.8782675449326 13.0217324550674 40 34.38 21.4153451395862 12.9646548604138 41 21.58 27.3966351700835 -5.81663517008354 42 21.53 26.7751943751373 -5.24519437513732 43 31.14 25.9501579013626 5.18984209863742 44 28.25 22.7044448535369 5.54555514646314 45 25.16 25.474351175511 -0.314351175510978 46 20.51 26.8295288302594 -6.31952883025937 47 30.05 20.0537268774894 9.99627312251055 48 20.17 23.2971649588303 -3.12716495883026 49 32.37 21.2000667055447 11.1699332944553 50 22.46 25.5463776645605 -3.08637766456047 51 25.4 25.0683455533426 0.331654446657375 52 19.82 23.5034081196583 -3.68340811965834 53 18.14 26.5944361904885 -8.45443619048846 54 20.1 26.0405573195039 -5.94055731950387 55 20.25 26.7660522996157 -6.51605229961571 56 19.73 23.5055920427926 -3.77559204279258 57 24.74 25.3407038205359 -0.600703820535934 58 26.17 25.7967425838865 0.373257416113482 59 20.14 21.4953500595627 -1.35535005956267 60 31.71 22.7094007860372 9.00059921396284 61 26.66 22.8089137664748 3.85108623352523 62 20.75 24.9784441593524 -4.22844415935237 63 20.01 25.0025068992166 -4.99250689921658 64 26.67 22.8199252106556 3.85007478934439 65 23.91 25.2333903694891 -1.32339036948913 66 26.81 25.0955748677195 1.71442513228055 67 29.31 25.7791793123355 3.53082068766451 68 31.76 22.9815099666945 8.7784900333055 69 22.99 25.3758643609065 -2.38586436090646 70 23.94 25.9690638901831 -2.02906389018307 71 27.04 21.3777246740052 5.6622753259948 72 20.28 24.1893790324116 -3.90937903241156 73 23.32 23.4424457585962 -0.122445758596172 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 24.3856235931428 22.8245543623943 25.9466928238913 75 24.3200272619453 22.7578811291134 25.8821733947772 76 23.4806394315950 21.9170197243302 25.0442591388597 77 25.1049244467477 23.5400554394732 26.6697934540223 78 25.4283783792798 23.8619822384734 26.9947745200862 79 26.3743961667159 24.8078121081939 27.940980225238 80 24.3306389040174 22.7625275223422 25.8987502856926 81 25.0091756938818 23.4394770228869 26.5788743648767 82 25.6696808972131 24.1012707652654 27.2380910291608 83 22.2327704172168 20.6621510338209 23.8033898006127 84 23.5830186533149 22.0113948229411 25.1546424836886 85 23.4234769289001 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/1v9er1211835452.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/1v9er1211835452.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/25ck61211835452.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/25ck61211835452.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/3i6dv1211835452.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211835514k4dirjiaqwxslvn/3i6dv1211835452.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$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$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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