Sarah Geerts - extrapolation - eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 04:09:55 +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/20/t13058645333g0v37u54s4f8qc.htm/, Retrieved Fri, 20 May 2011 06:08:56 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

31.514 27.071 29.462 26.105 22.397 23.843 21.705 18.089 20.764 25.316 17.704 15.548 28.029 29.383 36.438 32.034 22.679 24.319 18.004 17.537 20.366 22.782 19.169 13.807 29.743 25.591 29.096 26.482 22.405 27.044 17.970 18.730 19.684 19.785 18.479 10.698 31.956 29.506 34.506 27.165 26.736 23.691 18.157 17.328 18.205 20.995 17.382 9.367 31.124 26.551 30.651 25.859 25.100 25.778 20.418 18.688 20.424 24.776 19.814 12.738 31.566 30.111 30.019 31.934 25.826 26.835 20.205 17.789 20.520 22.518 15.572 11.509 25.447 24.090 27.786 26.195 20.516 22.759 19.028 16.971 20.036 22.485 18.730 14.538 27.561 25.985 34.670 32.066 27.186 29.586 21.359 21.553 19.573 24.256 22.380 16.167 27.297 28.287

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 2 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.217005798442115 beta 0 gamma 0.706425518435226 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 28.029 26.7390885139169 1.28991148608307 14 29.383 28.5940642052635 0.788935794736517 15 36.438 35.8063116244493 0.631688375550702 16 32.034 31.8277553359329 0.206244664067089 17 22.679 22.6541904039938 0.0248095960061718 18 24.319 24.3606438174574 -0.0416438174574054 19 18.004 22.3785573631892 -4.37455736318921 20 17.537 17.9358310666813 -0.398831066681261 21 20.366 20.1950829353151 0.170917064684858 22 22.782 24.1677453379306 -1.38574533793059 23 19.169 16.5489957245019 2.62000427549815 24 13.807 15.0451672854309 -1.23816728543092 25 29.743 27.5525481225535 2.19045187744652 26 25.591 29.3363868270661 -3.74538682706612 27 29.096 35.3166826509825 -6.22068265098245 28 26.482 29.8987923348675 -3.41679233486748 29 22.405 20.6670836851791 1.73791631482094 30 27.044 22.5925865154812 4.45141348451877 31 17.97 19.2246774176737 -1.25467741767373 32 18.73 17.6610060544764 1.06899394552358 33 19.684 20.5929863670096 -0.908986367009586 34 19.785 23.4708488064628 -3.68584880646277 35 18.479 17.6170165394614 0.861983460538628 36 10.698 13.7597193612411 -3.06171936124105 37 31.956 26.7157218480834 5.24027815191662 38 29.506 25.9182442849889 3.5877557150111 39 34.506 32.0322840875248 2.47371591247516 40 27.165 29.8280998545382 -2.66309985453818 41 26.736 23.1790286874342 3.55697131256579 42 23.691 27.1549251810745 -3.46392518107453 43 18.157 18.792354147262 -0.635354147262028 44 17.328 18.6395403988487 -1.31154039884874 45 18.205 19.9450910340095 -1.74009103400945 46 20.995 21.0114609964673 -0.0164609964672984 47 17.382 18.4173870906547 -1.03538709065473 48 9.367 11.9226303211818 -2.55563032118179 49 31.124 29.4088255032548 1.71517449674517 50 26.551 26.9681106631271 -0.417110663127108 51 30.651 31.2834339745109 -0.632433974510921 52 25.859 26.0011792503858 -0.142179250385752 53 25.1 23.4549710702516 1.64502892974842 54 25.778 23.1418399804271 2.63616001957285 55 20.418 17.8572495544256 2.56075044557444 56 18.688 18.0101116660372 0.677888333962766 57 20.424 19.5304891228528 0.893510877147204 58 24.776 22.2632223183168 2.51277768168317 59 19.814 19.3715394653399 0.442460534660068 60 12.738 11.5323619850402 1.2056380149598 61 31.566 35.9404540057861 -4.37445400578605 62 30.111 30.4358634100249 -0.324863410024946 63 30.019 35.2387052155291 -5.21970521552911 64 31.934 28.7019085366913 3.23209146330866 65 25.826 27.6463850319208 -1.82038503192077 66 26.835 27.072576409823 -0.23757640982301 67 20.205 20.6404261132437 -0.435426113243729 68 17.789 19.0448944892686 -1.25589448926862 69 20.52 20.2787759913562 0.241224008643751 70 22.518 23.751046718997 -1.23304671899702 71 15.572 19.0367214045529 -3.46472140455286 72 11.509 11.3038864382713 0.205113561728723 73 25.447 30.4742403876788 -5.02724038767878 74 24.09 27.3001174930027 -3.21011749300272 75 27.786 28.4355003726381 -0.649500372638094 76 26.195 27.6009196306679 -1.40591963066795 77 20.516 23.3065826792077 -2.79058267920771 78 22.759 23.3108481180279 -0.55184811802792 79 19.028 17.59848563769 1.42951436231003 80 16.971 16.1800667536419 0.790933246358104 81 20.036 18.4670434811774 1.56895651882258 82 22.485 21.1977921895663 1.28720781043368 83 18.73 16.0537676205067 2.67623237949332 84 14.538 11.6020986194158 2.9359013805842 85 27.561 29.4574897396373 -1.89648973963727 86 25.985 27.812886453676 -1.82788645367602 87 34.67 30.9945888307834 3.67541116921661 88 32.066 30.5082906724925 1.55770932750752 89 27.186 25.2590379366929 1.92696206330707 90 29.586 27.9066766605854 1.67932333941459 91 21.359 22.6892116506813 -1.33021165068127 92 21.553 19.8935365801293 1.65946341987074 93 19.573 23.2965843081304 -3.72358430813045 94 24.256 25.0248703741857 -0.768870374185678 95 22.38 19.5805325941406 2.79946740585943 96 16.167 14.6423232141706 1.52467678582936 97 27.297 30.6626089672762 -3.3656089672762 98 28.287 28.6351311159572 -0.348131115957226 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 99 35.6615998937544 32.0626992275137 39.2605005599952 100 33.0596948994055 29.3404852821502 36.7789045166608 101 27.4268531422471 23.6504958350133 31.2032104494809 102 29.5591489806745 25.6023165666403 33.5159813947087 103 22.213356827946 18.333642354358 26.0930713015341 104 21.3206572071175 17.3428045463768 25.2985098678582 105 21.3117352487873 17.2088357234468 25.4146347741278 106 25.6575630607364 21.180718310071 30.1344078114018 107 22.137189441296 17.7813965694034 26.4929823131886 108 15.7516073179311 11.6886346653409 19.8145799705212 109 28.6377664616738 23.3417480860619 33.9337848372857 110 29.0155966083571 -46.9237224842763 104.95491570099

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/1s8ut1305864593.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/1s8ut1305864593.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/2239v1305864593.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/2239v1305864593.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/3ja731305864593.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058645333g0v37u54s4f8qc/3ja731305864593.ps (open in new window)

Parameters (Session):

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=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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