IKO opdracht 10 werknemers x1000 Marin Peeters MAR 201B

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 17:08:50 +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/19/t1305824721tgbo67h6o6a1z5v.htm/, Retrieved Thu, 19 May 2011 19:05:21 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

3893.9 3799.2 3769.6 3768.6 3854.9 3778.5 3779.7 3803.2 3900.3 3792.6 3767.4 3752.6 3829.6 3722.6 3692.9 3681 3762.9 3661.7 3633.1 3621.5 3710 3619.4 3595.2 3573.2 3650.1 3554.2 3537 3528.6 3597.1 3521.9 3516.5 3515.7 3600.2 3517.1 3513.7 3528.2 3608.3 3502.5 3502.5 3495.3 3543.8 3425.3 3418.4 3406.4 3446.1 3341.1 3347 3354.9 3399 3288.9 3279 3275.2 3314 3227.1 3225.3 3228.6 3287.1 3210.1 3213.1 3228 3287 3211 3199.8 3166.3 3164 3156.7 3156 3165.5 3179.2 3182.5 3179.5 3193.5 3219.6 3221.9 3210.1

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.445237169833869 beta 0.612003677861392 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 3769.6 3704.5 65.1000000000004 4 3768.6 3656.52382948956 112.076170510439 5 3854.9 3660.00247161576 194.897528384241 6 3778.5 3753.4632617268 25.0367382732024 7 3779.7 3778.11789471349 1.58210528650579 8 3803.2 3792.76075607348 10.4392439265207 9 3900.3 3814.19170079453 86.1082992054698 10 3792.6 3892.77669518382 -100.176695183817 11 3767.4 3861.12386024016 -93.7238602401621 12 3752.6 3806.80555386658 -54.2055538665822 13 3829.6 3755.31196925228 74.288030747723 14 3722.6 3781.27101128997 -58.6710112899746 15 3692.9 3732.04467048096 -39.1446704809555 16 3681 3680.84577696375 0.154223036247913 17 3762.9 3647.18623531314 115.713764686859 18 3661.7 3696.50856870722 -34.8085687072203 19 3633.1 3669.32788939067 -36.2278893906732 20 3621.5 3631.64365462591 -10.1436546259124 21 3710 3602.80907888328 107.190921116724 22 3619.4 3655.42432709343 -36.0243270934257 23 3595.2 3634.45867042543 -39.2586704254254 24 3573.2 3601.3554949804 -28.1554949803985 25 3650.1 3565.52386562647 84.5761343735298 26 3554.2 3602.93042685883 -48.7304268588314 27 3537 3567.70555467901 -30.7055546790061 28 3528.6 3532.13916768493 -3.53916768492809 29 3597.1 3507.70388952504 89.396110474961 30 3521.9 3549.00611036664 -27.1061103666352 31 3516.5 3531.05115524126 -14.5511552412599 32 3515.7 3514.72113528689 0.97886471310676 33 3600.2 3505.57238516355 94.627614836454 34 3517.1 3563.90431408603 -46.8043140860273 35 3513.7 3546.51193416001 -32.8119341600068 36 3528.2 3526.40866340754 1.79133659246281 37 3608.3 3522.20017054165 86.0998294583528 38 3502.5 3578.99001818999 -76.4900181899939 39 3502.5 3542.54630305138 -40.0463030513847 40 3495.3 3511.41659611134 -16.1165961113352 41 3543.8 3486.54972469731 57.2502753026897 42 3425.3 3509.9484549551 -84.6484549550992 43 3418.4 3447.10301076511 -28.7030107651117 44 3406.4 3401.34536667499 5.05463332500585 45 3446.1 3371.99520128622 74.1047987137754 46 3341.1 3393.58131450031 -52.4813145003081 47 3347 3344.50612024184 2.49387975816398 48 3354.9 3320.5874751647 34.3125248353044 49 3399 3320.185383163 78.8146168369981 50 3288.9 3361.07321824492 -72.1732182449191 51 3279 3315.06940871984 -36.0694087198367 52 3275.2 3275.31191993245 -0.111919932451201 53 3314 3251.53354498447 62.4664550155285 54 3227.1 3272.63867211733 -45.538672117329 55 3225.3 3233.24721573869 -7.94721573868628 56 3228.6 3208.42736173802 20.1726382619786 57 3287.1 3201.62428930299 85.4757106970142 58 3210.1 3247.18757366303 -37.0875736630287 59 3213.1 3228.07525444115 -14.9752544411522 60 3228 3214.72760270399 13.2723972960116 61 3287 3217.57340835526 69.4265916447443 62 3211 3264.3389773553 -53.3389773552994 63 3199.8 3241.91058538151 -42.1105853815075 64 3166.3 3213.00691282751 -46.7069128275116 65 3164 3169.32976791475 -5.32976791474857 66 3156.7 3142.62297457242 14.0770254275817 67 3156 3128.39261038096 27.6073896190378 68 3165.5 3127.70911610114 37.7908838988646 69 3179.2 3141.85720846673 37.3427915332682 70 3182.5 3165.98121068061 16.5187893193915 71 3179.5 3185.33474488548 -5.83474488547881 72 3193.5 3193.14576390737 0.35423609262898 73 3219.6 3203.80887195829 15.7911280417143 74 3221.9 3225.6479318105 -3.74793181049927 75 3210.1 3237.76621406174 -27.6662140617373 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 3231.69651028064 3119.25703905153 3344.13598150976 77 3237.94483334842 3099.5425005761 3376.34716612074 78 3244.19315641619 3066.56565885864 3421.82065397374 79 3250.44147948396 3023.04533089798 3477.83762806995 80 3256.68980255174 2971.198901799 3542.18070330448 81 3262.93812561951 2912.48545672196 3613.39079451707 82 3269.18644868728 2847.85229180891 3690.52060556566 83 3275.43477175506 2777.9424025233 3772.92714098681 84 3281.68309482283 2703.21698743372 3860.14920221194 85 3287.9314178906 2624.0240306739 3951.83880510731 86 3294.17974095838 2540.63743369283 4047.72204822392 87 3300.42806402615 2453.28025242616 4147.57587562614

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/1hjvo1305824926.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/1hjvo1305824926.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/2pzpl1305824926.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/2pzpl1305824926.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/3trem1305824926.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305824721tgbo67h6o6a1z5v/3trem1305824926.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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