Exponential smoothing- Inschrijving personenwagens - Kristof Vermeulen

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 08:46:13 -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/Jun/01/t12123317998gmheytbylz5ew3.htm/, Retrieved Sun, 01 Jun 2008 14:50:02 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.562783761271795 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 43129 39690 3439 4 37863 41625.4133550137 -3762.41335501370 5 35953 39507.9882156199 -3554.98821561986 6 29133 37507.2985763564 -8374.2985763564 7 24693 32794.3793255415 -8101.3793255415 8 22205 28235.0545972237 -6030.0545972237 9 21725 24841.4377903239 -3116.43779032386 10 27192 23087.5572089158 4104.44279108416 11 21790 25397.4709608071 -3607.47096080709 12 13253 23367.2448848053 -10114.2448848053 13 37702 17675.1121061106 20026.8878938894 14 30364 28945.9194016022 1418.08059839776 15 32609 29743.9921345551 2865.00786544491 16 30212 31356.3720371435 -1144.37203714345 17 29965 30712.3380377856 -747.338037785594 18 28352 30291.7483259391 -1939.74832593914 19 25814 29200.0894671464 -3386.08946714644 20 22414 27294.4533008230 -4880.45330082296 21 20506 24547.8134354745 -4041.81343547447 22 28806 22273.1464678993 6532.85353210073 23 22228 25949.7303505327 -3721.73035053265 24 13971 23855.2009454205 -9884.2009454205 25 36845 18292.5331601905 18552.4668398095 26 35338 28733.5602291688 6604.43977083125 27 35022 32450.4316844902 2571.56831550981 28 34777 33897.6685734602 879.331426539822 29 26887 34392.5420210928 -7505.54202109276 30 23970 30168.5448520787 -6198.54485207866 31 22780 26680.1044658139 -3900.10446581391 32 17351 24485.1890051902 -7134.18900519023 33 21382 20470.1832832254 911.816716774614 34 24561 20983.3389246823 3577.6610753177 35 17409 22996.7884812053 -5587.78848120529 36 11514 19852.0718625614 -8338.07186256137 37 31514 15159.5404179946 16354.4595820054 38 27071 24363.5646951231 2707.43530487687 39 29462 25887.2653194018 3574.73468059822 40 26105 27899.0679484976 -1794.06794849758 41 22397 26889.3956404649 -4492.39564046494 42 23843 24361.1483248031 -518.148324803064 43 21705 24069.5428616737 -2364.54286167372 44 18089 22738.8165362926 -4649.81653629261 45 20764 20121.9752967741 642.024703225936 46 25316 20483.2963740850 4832.70362591503 47 17704 23203.0634977893 -5499.06349778927 48 15548 20108.279859031 -4560.27985903099 49 28029 17541.8284075135 10487.1715924865 50 29383 23443.8382814358 5939.16171856422 51 36438 26786.3020522108 9651.69794778919 52 32034 32218.1209259269 -184.12092592688 53 22679 32114.5006587049 -9435.5006587049 54 24319 26804.3541085165 -2485.35410851645 55 18004 25405.6371752333 -7401.63717523326 56 17537 21240.1159661863 -3703.11596618634 57 20366 19156.0624343104 1209.93756568964 58 22782 19836.9956484332 2945.00435156679 59 19169 21494.3962743698 -2325.39627436977 60 13807 20185.7010126325 -6378.70101263253 61 29743 16595.871664715 13147.128335285 62 25591 23994.8619991697 1596.13800083032 63 29096 24893.1425467858 4202.85745321419 64 26482 27258.4424723949 -776.44247239489 65 22405 26821.4732573693 -4416.47325736932 66 27044 24335.9538260307 2708.04617396928 67 17970 25859.9982375148 -7889.99823751485 68 18730 21419.6353529784 -2689.63535297841 69 19684 19905.9522525796 -221.952252579627 70 19785 19781.0411290501 3.95887094988211 71 18479 19783.2691173337 -1304.26911733368 72 10698 19049.24763777 -8351.24763776999 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 14349.3010808736 1752.95244691226 26945.6497148349 74 14349.3010808736 -104.840541035601 28803.4427027828 75 14349.3010808736 -1749.65606374034 30448.2582254875 76 14349.3010808736 -3241.33939245836 31939.9415542056 77 14349.3010808736 -4616.05795553625 33314.6601172834 78 14349.3010808736 -5897.65065260571 34596.2528143529 79 14349.3010808736 -7102.81456341074 35801.4167251579 80 14349.3010808736 -8243.78362957834 36942.3857913255 81 14349.3010808736 -9329.8392720101 38028.4414337573 82 14349.3010808736 -10368.2210232831 39066.8231850303 83 14349.3010808736 -11364.7050264482 40063.3071881954 84 14349.3010808736 -12323.9874528879 41022.5896146351

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/1yvww1212331567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/1yvww1212331567.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/2vgv71212331567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/2vgv71212331567.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/3c2ec1212331567.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123317998gmheytbylz5ew3/3c2ec1212331567.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=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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