Exponentional smoothing - Niels Braspennincx - Inschrijvingen nieuwe personenwagens

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 16:02:42 -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/02/t1212357850a791zxnlayjvgps.htm/, Retrieved Sun, 01 Jun 2008 22:04:14 +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 120 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.269020114714124 beta 0.000794515688683651 gamma 0.647545306842965 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 39185.4976388889 -1483.49763888890 14 30364 31314.6139080416 -950.613908041567 15 32609 33267.3834347123 -658.383434712319 16 30212 30598.0864468371 -386.086446837056 17 29965 30082.9186368216 -117.918636821574 18 28352 28311.2014911403 40.7985088597452 19 25814 25711.1495038325 102.850496167539 20 22414 22088.4793992723 325.520600727661 21 20506 19881.531608786 624.468391213988 22 28806 27980.1819281687 825.818071831342 23 22228 21483.9675393295 744.032460670544 24 13971 13659.7018726807 311.298127319278 25 36845 37372.9275490270 -527.927549027037 26 35338 30011.4193196532 5326.58068034679 27 35022 33792.6186356372 1229.38136436279 28 34777 31761.8746560828 3015.12534391715 29 26887 32291.1799993386 -5404.17999933865 30 23970 29173.8934320633 -5203.89343206327 31 22780 25192.5782927666 -2412.57829276661 32 17351 20998.3614692181 -3647.36146921809 33 21382 17863.0390220230 3518.96097797702 34 24561 26835.1979310001 -2274.19793100015 35 17409 19465.1661502368 -2056.16615023684 36 11514 10681.0225058542 832.97749414576 37 31514 34135.7240364390 -2621.72403643896 38 27071 28980.0578886728 -1909.05788867276 39 29462 28871.7267237850 590.273276215034 40 26105 27510.5626871596 -1405.56268715955 41 22397 22860.6975028202 -463.697502820152 42 23843 21163.6595544677 2679.34044553231 43 21705 20622.3815018499 1082.61849815009 44 18089 16782.7547694347 1306.24523056534 45 20764 18372.0239310466 2391.97606895341 46 25316 24298.4575906587 1017.54240934132 47 17704 17917.4827076874 -213.482707687413 48 15548 10997.3153833704 4550.68461662957 49 28029 33818.3948130442 -5789.39481304424 50 29383 28148.7169794248 1234.28302057521 51 36438 30070.5397302820 6367.46026971804 52 32034 29321.5679356637 2712.43206433628 53 22679 26228.9581711308 -3549.95817113084 54 24319 25192.3351898077 -873.335189807669 55 18004 22941.7075003792 -4937.70750037923 56 17537 17589.2453249567 -52.2453249567079 57 20366 19327.58677841 1038.41322159000 58 22782 24239.6284255755 -1457.62842557547 59 19169 16609.8787474950 2559.12125250497 60 13807 12691.0661661552 1115.93383384485 61 29743 29693.3795670725 49.6204329274951 62 25591 28920.0192473646 -3329.01924736456 63 29096 32043.8970469899 -2947.89704698993 64 26482 27056.758868336 -574.758868335986 65 22405 20112.8026183063 2292.19738169368 66 27044 21913.2754015573 5130.72459844275 67 17970 19353.7820862700 -1383.78208626995 68 18730 17270.4163455906 1459.58365440935 69 19684 19932.5701621988 -248.57016219883 70 19785 23317.4742947894 -3532.47429478939 71 18479 17030.9743077256 1448.02569227435 72 10698 12130.0213606686 -1432.02136066862 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 27941.4961757071 22858.4634009673 33024.5289504469 74 25554.8664488543 20290.8298298049 30818.9030679036 75 29754.7638644583 24315.4701865707 35194.0575423458 76 26684.6518599757 21075.3090185481 32293.9947014034 77 21253.1678553524 15478.5234435685 27027.8122671364 78 23780.8973765084 17845.3021254256 29716.4926275912 79 16756.7539072319 10664.2135356125 22849.2942788513 80 16391.046727963 10145.2647890295 22636.8286668964 81 17851.1964814106 11455.6101211061 24246.7828417151 82 19747.8076738525 13205.6177399863 26289.9976077187 83 16769.1005314337 10083.2971312833 23454.903931584 84 10115.0445220726 3288.4288761681 16941.6601679771

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/1azdb1212357642.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/1azdb1212357642.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/267gh1212357642.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/267gh1212357642.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/38rby1212357642.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212357850a791zxnlayjvgps/38rby1212357642.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

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Software written by Ed van Stee & Patrick Wessa

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