opgave 10 oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:45:50 +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/18/t13057297213cihhqnape7ihb0.htm/, Retrieved Wed, 18 May 2011 16:42:04 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320 24977 25204 25739 26434 27525 30695 32436 30160 30236 31293 31077 32226 33865 32810

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.750102276552439 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14544 12099.2186826727 2444.78131732733 14 14931 14291.259502767 639.740497233011 15 14886 14765.9690523822 120.030947617797 16 16005 16100.4734136235 -95.4734136235274 17 17064 17248.8405028966 -184.840502896604 18 15168 15385.4286115819 -217.428611581863 19 16050 15329.3374432133 720.66255678666 20 15839 15873.6076945031 -34.6076945031036 21 15137 16406.8319429242 -1269.83194292422 22 14954 16074.9307559364 -1120.93075593644 23 15648 15552.0102109901 95.9897890098891 24 15305 16401.9298589301 -1096.92985893007 25 15579 17070.6652162102 -1491.6652162102 26 16348 15808.8014881881 539.198511811861 27 15928 16036.041507764 -108.041507763966 28 16171 17204.1981776734 -1033.19817767338 29 15937 17647.8114703688 -1710.81147036876 30 15713 14716.2093422803 996.790657719728 31 15594 15799.0279129557 -205.027912955695 32 15683 15473.2452562242 209.754743775791 33 16438 15862.8434427541 575.156557245855 34 17032 16959.926136745 72.0738632550274 35 17696 17674.1825611747 21.8174388253137 36 17745 18171.4009909518 -426.400990951781 37 19394 19384.3237992793 9.67620072072168 38 20148 19750.8963904935 397.103609506477 39 20108 19552.9503332592 555.049666740753 40 18584 21137.1105538536 -2553.1105538536 41 18441 20357.3900045254 -1916.39000452539 42 18391 17686.5619729097 704.438027090298 43 19178 18200.1027579782 977.897242021772 44 18079 18778.4634748238 -699.463474823802 45 18483 18571.2639401369 -88.263940136887 46 19644 19070.336672515 573.663327484977 47 19195 20192.2929897825 -997.292989782534 48 19650 19813.3870639623 -163.387063962331 49 20830 21472.1276817113 -642.127681711321 50 23595 21452.0386576346 2142.96134236536 51 22937 22482.4865559503 454.513444049659 52 21814 23147.2133687415 -1333.21336874153 53 21928 23575.1447561781 -1647.14475617815 54 21777 21558.0800507517 218.919949248277 55 21383 21711.350736046 -328.350736046024 56 21467 20777.1487256761 689.851274323933 57 22052 21789.0561450684 262.943854931636 58 22680 22787.2031352412 -107.203135241176 59 24320 22988.4735947557 1331.52640524428 60 24977 24622.8935853504 354.106414649643 61 25204 26890.8567459665 -1686.85674596648 62 25739 26916.3592139628 -1177.35921396278 63 26434 24892.2543770244 1541.74562297558 64 27525 25844.5431985053 1680.45680149475 65 30695 28665.0377216608 2029.96227833919 66 32436 29619.8249595258 2816.17504047418 67 30160 31357.4522765505 -1197.45227655049 68 30236 29694.2412564194 541.758743580576 69 31293 30509.0212752618 783.978724738154 70 31077 31956.4878608999 -879.48786089995 71 32226 32031.7211939538 194.278806046157 72 33865 32582.6146056672 1282.38539433278 73 32810 35397.227656543 -2587.22765654298 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 35202.9967992786 32961.9907673702 37444.002831187 75 34415.0904381421 31646.3155373123 37183.8653389719 76 34061.7109278284 30857.2000375182 37266.2218181387 77 35980.3797374516 32259.5393329338 39701.2201419693 78 35427.7659214053 31417.0642666674 39438.4675761432 79 33881.6530844962 29701.9465994304 38061.3595695621 80 33467.1115850566 29036.8414622514 37897.3817078617 81 33946.0995362555 29191.970181954 38700.228890557 82 34393.7768333893 29338.0850325368 39449.4686342417 83 35467.0882073697 30046.1984108696 40887.9780038697 84 36167.1349638553 30444.0278239371 41890.2421037734 85 37048.9624582011 31440.2803854036 42657.6445309987

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/14ark1305729947.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/14ark1305729947.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/261wl1305729947.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/261wl1305729947.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/3vpl81305729947.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057297213cihhqnape7ihb0/3vpl81305729947.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=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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