Aantal inschrijvingen personenwagens - Frederic Germanes

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 13:25:04 -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/t121182997174ssj75q6v3l738.htm/, Retrieved Mon, 26 May 2008 21:26:11 +0200

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Dataseries X:

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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 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 42553

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.341201512395321 beta 0 gamma 0.875658744185353 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 31514 32478.5095713308 -964.509571330844 14 27071 27633.7742594754 -562.774259475369 15 29462 29858.9789157948 -396.9789157948 16 26105 26330.1648576729 -225.164857672855 17 22397 22481.3197176804 -84.3197176803551 18 23843 23715.7001246415 127.299875358458 19 21705 21607.2815873868 97.718412613176 20 18089 18073.5089854424 15.4910145576068 21 20764 20410.3324553078 353.667544692154 22 25316 24471.6530318003 844.346968199708 23 17704 17130.465137269 573.534862730987 24 15548 15196.4047532664 351.595246733594 25 28029 32385.0996593921 -4356.09965939209 26 29383 26706.8140996103 2676.18590038965 27 36438 30178.3345167915 6259.66548320847 28 32034 28704.5535327993 3329.44646720072 29 22679 25624.5654854751 -2945.56548547514 30 24319 26141.6085232899 -1822.60852328993 31 18004 23197.1778014374 -5193.17780143743 32 17537 17855.9746353464 -318.974635346352 33 20366 20225.0132730322 140.986726967789 34 22782 24397.1990318382 -1615.19903183815 35 19169 16489.0091286967 2679.99087130333 36 13807 15176.5023585576 -1369.50235855757 37 29743 28198.4941922787 1544.50580772126 38 25591 28537.0398580175 -2946.03985801748 39 29096 31673.3359923962 -2577.33599239617 40 26482 26188.2974754638 293.702524536151 41 22405 19745.3536927891 2659.64630721086 42 27044 22584.9679411960 4459.03205880396 43 17970 19658.4315366501 -1688.43153665009 44 18730 18296.8927127078 433.107287292172 45 19684 21325.3733064043 -1641.37330640427 46 19785 23917.1321619439 -4132.1321619439 47 18479 17634.8709733806 844.12902661939 48 10698 13583.343321264 -2885.34332126400 49 31956 26315.3719089867 5640.62809101327 50 29506 25530.9977282663 3975.00227173373 51 34506 31375.086724741 3130.913275259 52 27165 29177.6260856717 -2012.62608567174 53 26736 22842.1460200893 3893.85397991068 54 23691 27229.5888103522 -3538.58881035217 55 18157 18195.9314115922 -38.9314115921807 56 17328 18620.8733458202 -1292.87334582016 57 18205 19792.5103910492 -1587.51039104924 58 20995 20771.6103722955 223.389627704488 59 17382 18766.0220572724 -1384.02205727244 60 9367 11714.4535764689 -2347.45357646895 61 31124 29291.6111066964 1832.38889330356 62 26551 26320.8841670277 230.115832972329 63 30651 29965.1716088314 685.828391168558 64 25859 24678.6598101251 1180.34018987493 65 25100 22911.0624731174 2188.93752688256 66 25778 22472.6562283452 3305.34377165479 67 20418 17885.1604298823 2532.83957011771 68 18688 18436.2810108908 251.718989109249 69 20424 20027.6501251368 396.349874863205 70 24776 22983.5565836467 1792.44341635329 71 19814 20187.2471478846 -373.247147884569 72 12738 11764.9277139464 973.072286053635 73 42553 38377.2105815039 4175.78941849613 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 33992.8708694808 29630.5562980431 38355.1854409185 75 38894.2104441205 34329.775006056 43458.6458821849 76 32224.9159335975 27437.4505040004 37012.3813631946 77 30188.0817330271 25165.9696283209 35210.1938377332 78 29422.0632344738 24516.0972055354 34328.0292634122 79 22237.8774064778 17187.1093247631 27288.6454881925 80 20444.6985991207 14990.0062697214 25899.3909285200 81 22183.2168494132 16058.5457043549 28307.8879944714 82 26098.7133897929 20362.0528535090 31835.3739260767 83 21162.1390539612 16123.9964042967 26200.2817036257 84 13128.2394533178 2550.88033000855 23705.5985766271 85 42210.9367385439 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/1t1jl1211829897.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/1t1jl1211829897.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/2dic01211829897.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/2dic01211829897.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/3jgw41211829897.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t121182997174ssj75q6v3l738/3jgw41211829897.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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