Bouwvergunningen

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 15:18:24 -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/t1211836738ike7q9actoi48gd.htm/, Retrieved Mon, 26 May 2008 23:19:05 +0200

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Dataseries X:

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2434 2637 1831 1851 1839 2609 2417 2394 2372 2717 2998 2538 3007 2475 2175 2465 2279 2323 2746 2601 2486 2718 2646 2551 2712 2606 2365 3533 3509 2912 3599 2719 2869 4085 2686 2545 3071 3388 2652 3190 2884 3295 3818 3226 3953 3810 2877 3515 3708 3450 3360 4098 4374 3703 4257 3487 3659 3904 2957 3320 3420 3500 2791 2919 3179 3016 3492 3034 2612 3525 2846 3212 2591

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 0.316502668649575 beta 0 gamma 0.528977938320109 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3007 2814.83245828937 192.167541710630 14 2475 2346.15707822244 128.842921777562 15 2175 2086.66316988123 88.336830118767 16 2465 2392.09901966454 72.9009803354616 17 2279 2245.72407879384 33.2759212061646 18 2323 2312.61230778536 10.387692214641 19 2746 2750.33626105096 -4.33626105095573 20 2601 2610.86732589147 -9.8673258914664 21 2486 2479.28826734839 6.71173265161497 22 2718 2657.99387082264 60.0061291773568 23 2646 2513.02444948422 132.975550515780 24 2551 2395.66833476417 155.331665235834 25 2712 3220.69674991596 -508.696749915957 26 2606 2484.98686513470 121.013134865305 27 2365 2196.31504635075 168.684953649246 28 3533 2534.40126092563 998.59873907437 29 3509 2635.8395787133 873.160421286698 30 2912 2973.92027841379 -61.9202784137888 31 3599 3500.84090696903 98.1590930309671 32 2719 3351.80258342192 -632.802583421921 33 2869 3003.31573747574 -134.315737475743 34 4085 3194.07975342453 890.920246575472 35 2686 3297.82852383102 -611.828523831017 36 2545 2922.34636456097 -377.346364560975 37 3071 3392.53186261917 -321.531862619173 38 3388 2892.895773122 495.104226877997 39 2652 2679.9164505143 -27.9164505143021 40 3190 3300.76210031538 -110.762100315378 41 2884 2970.88063058456 -86.8806305845555 42 3295 2691.245919822 603.754080178 43 3818 3476.20039091554 341.799609084459 44 3226 3123.2672425134 102.732757486599 45 3953 3189.61068681413 763.389313185874 46 3810 4112.02243901921 -302.022439019214 47 2877 3238.81968436346 -361.819684363456 48 3515 3012.81964887572 502.180351124277 49 3708 3892.83302755833 -184.833027558333 50 3450 3699.28367624962 -249.283676249624 51 3360 2993.75921767905 366.24078232095 52 4098 3810.02542963601 287.974570363994 53 4374 3554.6912773051 819.308722694897 54 3703 3791.86137645289 -88.8613764528909 55 4257 4365.11356828438 -108.113568284378 56 3487 3690.91090344476 -203.910903444762 57 3659 3914.00915901374 -255.009159013744 58 3904 4136.25452737725 -232.254527377247 59 2957 3226.71755646372 -269.717556463722 60 3320 3342.62735554049 -22.6273555404928 61 3420 3804.61274158354 -384.612741583543 62 3500 3526.16686034411 -26.1668603441094 63 2791 3110.30266521900 -319.302665219004 64 2919 3630.76990994799 -711.76990994799 65 3179 3257.11363729289 -78.1136372928936 66 3016 2956.56200048966 59.4379995103413 67 3492 3449.08214296858 42.9178570314225 68 3034 2917.31766935173 116.682330648272 69 2612 3176.45842738926 -564.458427389258 70 3525 3245.94498526019 279.055014739807 71 2846 2620.0921158609 225.907884139099 72 3212 2948.55932692633 263.440673073671 73 2591 3335.99363177502 -744.993631775016 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 3076.45921200473 2564.62740377124 3588.29102023821 75 2622.72401152168 2040.69408265355 3204.75394038981 76 3041.99531079612 2407.35214881864 3676.63847277361 77 3119.7870762464 2461.8398975783 3777.7342549145 78 2899.51161021889 2146.72524315946 3652.29797727831 79 3351.99331947265 2628.24305582365 4075.74358312165 80 2851.62472075925 2094.50543446716 3608.74400705134 81 2817.15365429601 1928.47307232875 3705.83423626326 82 3372.21323439456 2582.79597289754 4161.63049589158 83 2650.13203956863 1775.49992957307 3524.76414956419 84 2906.15353512492 2015.41861213911 3796.88845811073 85 2830.84497981207 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/1ojqw1211836695.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/1ojqw1211836695.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/244c31211836695.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/244c31211836695.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/3ts0b1211836695.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836738ike7q9actoi48gd/3ts0b1211836695.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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