marlies smulders eigen reeks exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 05:22:57 -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/25/t1211714736xskov2vo9z0u3pi.htm/, Retrieved Sun, 25 May 2008 13:25:36 +0200

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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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.421222314791007 beta 0.00099345799369076 gamma 0.768751783081094 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1839 1771.23347222222 67.7665277777769 14 2609 2532.95961119811 76.0403888018895 15 2417 2342.20270543556 74.797294564442 16 2394 2348.45348081602 45.5465191839844 17 2372 2352.94390324843 19.0560967515726 18 2717 2680.95060963219 36.0493903678062 19 2998 2948.13035595746 49.869644042536 20 2538 2517.65237031077 20.3476296892345 21 3007 3008.37256824583 -1.3725682458321 22 2475 2468.40149308823 6.59850691176689 23 2175 2172.74910724848 2.25089275152413 24 2465 2473.84968456526 -8.84968456526394 25 2279 2143.71420776375 135.285792236248 26 2323 2937.75297110593 -614.752971105929 27 2746 2455.36697713888 290.633022861118 28 2601 2539.50975137465 61.49024862535 29 2486 2538.92805555715 -52.9280555571531 30 2718 2844.14282193609 -126.142821936087 31 2646 3049.05330747937 -403.053307479365 32 2551 2414.36970120493 136.630298795074 33 2712 2944.16635998225 -232.166359982251 34 2606 2310.18954340422 295.810456595778 35 2365 2134.20943081216 230.790569187843 36 3533 2526.51676326994 1006.48323673006 37 3509 2688.49796404187 820.502035958134 38 2912 3438.03698676852 -526.036986768515 39 3599 3396.48785159841 202.512148401586 40 2719 3342.14985767164 -623.14985767164 41 2869 3002.57877308779 -133.578773087785 42 4085 3241.51716235907 843.482837640932 43 2686 3732.3252381571 -1046.3252381571 44 2545 3067.21399489408 -522.213994894081 45 3071 3155.53196733373 -84.5319673337344 46 3388 2818.85220515374 569.14779484626 47 2652 2729.38660990147 -77.3866099014654 48 3190 3337.19620546927 -147.19620546927 49 2884 2930.16878520631 -46.1687852063087 50 3295 2714.85655656415 580.143443435847 51 3818 3463.21024850511 354.789751494895 52 3226 3105.5085727968 120.491427203198 53 3953 3297.17562139202 655.82437860798 54 3810 4303.86067100086 -493.860671000857 55 2877 3390.44800908055 -513.448009080553 56 3515 3183.15824520286 331.84175479714 57 3708 3826.48714866684 -118.487148666835 58 3450 3766.85933806598 -316.85933806598 59 3360 3016.65905314433 343.340946855669 60 4098 3770.94167772287 327.058322277132 61 4374 3609.14410377887 764.855896221132 62 3703 4014.97453174642 -311.974531746417 63 4257 4287.75871686254 -30.7587168625396 64 3487 3663.72478309449 -176.724783094489 65 3659 3968.5796685894 -309.579668589402 66 3904 4056.86713288802 -152.867132888015 67 2957 3278.30497701392 -321.304977013923 68 3320 3528.06225466171 -208.062254661705 69 3420 3743.38984196395 -323.389841963947 70 3500 3508.88970774994 -8.88970774994368 71 2791 3181.98936814293 -390.989368142926 72 2919 3619.23279439654 -700.23279439654 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 3218.60130663492 2438.83560718261 3998.36700608723 74 2821.90822867353 1975.66269431790 3668.15376302916 75 3350.12864009986 2442.14012933611 4258.11715086361 76 2673.02066891636 1707.11712674463 3638.9242110881 77 2992.19327598954 1971.55069963344 4012.83585234563 78 3279.72853247323 2207.03650010661 4352.42056483984 79 2489.79608939324 1367.36985634845 3612.22232243803 80 2924.59724472618 1754.45672385065 4094.73776560171 81 3175.65616960676 1959.58340074907 4391.72893846444 82 3216.84724349160 1956.42934324371 4477.26514373948 83 2723.22476830616 1419.88676000965 4026.56277660266 84 3187.27496733121 1842.3053639857 4532.24457067673

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/1l5q21211714568.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/1l5q21211714568.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/2olo81211714568.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/2olo81211714568.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/3p7gz1211714568.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211714736xskov2vo9z0u3pi/3p7gz1211714568.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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')

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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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