Opdracht 10 - Frederik Degrave

*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 21:40:08 +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/t1305840995ftvzuulj9kxs3st.htm/, Retrieved Thu, 19 May 2011 23:36:39 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

101397 97994 94044 91159 87239 89235 118647 125620 125154 117529 109459 108483 107137 104699 100804 96066 91971 93228 120144 127233 127166 118194 109940 106683 102834 99882 96666 92540 88744 89321 115870 122401 122030 113802 105791 103076 98658 96945 92497 90687 88796 90015 113228 118711 117460 106556 97347 92657 93118 89037 83570 81693 75956 73993 97088 102394 96549 89727 82336 82653 82303 79596 74472 73562 66618 69029 89899 93774 90305 83799 80320 82497 84420 84646 84186 83269 77793 81145 101691 107357 104253 95963 91432 94324 93855 92183 87600 83641 78195 79604 100846 105293 102518 93132 87479 85476

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 0.900408097789281 beta 0.0913871909632014 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 107137 104619.120362699 2517.87963730095 14 104699 104788.600903621 -89.6009036205942 15 100804 101107.044012316 -303.044012315717 16 96066 96386.2418227676 -320.241822767552 17 91971 92309.220569077 -338.220569077064 18 93228 93634.1045092177 -406.10450921765 19 120144 122385.200894548 -2241.20089454768 20 127233 127026.648110507 206.351889492697 21 127166 126297.101235628 868.898764372294 22 118194 119071.112083861 -877.112083861415 23 109940 109936.739574641 3.260425358676 24 106683 108778.639780748 -2095.63978074784 25 102834 105602.799011237 -2768.79901123731 26 99882 100189.850993115 -307.850993115338 27 96666 95816.083271503 849.916728497075 28 92540 91796.5158977738 743.484102226226 29 88744 88399.5644798924 344.435520107581 30 89321 89906.1450994609 -585.14509946086 31 115870 116615.235722145 -745.235722144673 32 122401 122198.509350494 202.490649505969 33 122030 121160.191647546 869.808352453896 34 113802 113723.644186166 78.355813833914 35 105791 105567.788681764 223.211318235582 36 103076 104192.210454025 -1116.21045402451 37 98658 101690.265688471 -3032.26568847099 38 96945 96181.177528213 763.822471787091 39 92497 92895.7512132914 -398.751213291398 40 90687 87741.892688304 2945.10731169602 41 88796 86365.1794318254 2430.82056817465 42 90015 89813.0884135216 201.911586478367 43 113228 117711.978961515 -4483.9789615154 44 118711 119881.489988966 -1170.48998896581 45 117460 117571.564277521 -111.564277521087 46 106556 109282.327540962 -2726.32754096226 47 97347 98716.4097847291 -1369.40978472913 48 92657 95381.3184261404 -2724.31842614038 49 93118 90740.7921326635 2377.20786733653 50 89037 90403.0112230851 -1366.01122308514 51 83570 85030.5374366513 -1460.53743665128 52 81693 79214.1369402668 2478.86305973321 53 75956 77325.3747977432 -1369.37479774318 54 73993 76233.3805450807 -2240.38054508073 55 97088 95444.6149444653 1643.3850555347 56 102394 101691.388380141 702.611619859439 57 96549 100651.459162345 -4102.45916234482 58 89727 89026.4971809714 700.50281902864 59 82336 82293.2226965751 42.7773034248821 60 82653 79892.3846401612 2760.61535983883 61 82303 80791.1851834754 1511.81481652455 62 79596 79495.9221631644 100.07783683564 63 74472 75849.6665180149 -1377.66651801491 64 73562 70905.86070602 2656.13929398003 65 66618 69263.4236282681 -2645.42362826811 66 69029 66804.2172141097 2224.78278589029 67 89899 89254.2266601605 644.773339839463 68 93774 94445.8340541212 -671.83405412118 69 90305 92023.1095263779 -1718.10952637788 70 83799 83829.4686167014 -30.4686167014152 71 80320 77121.0441343703 3198.9558656297 72 82497 78436.3897714538 4060.61022854624 73 84420 81063.6142171169 3356.3857828831 74 84646 82051.2082498839 2594.79175011608 75 84186 81278.4897796768 2907.51022032321 76 83269 81537.2780940697 1731.7219059303 77 77793 79128.9254372178 -1335.92543721777 78 81145 79776.9975841016 1368.0024158984 79 101691 106489.155519651 -4798.15551965068 80 107357 108517.851037485 -1160.85103748459 81 104253 106482.644097461 -2229.64409746086 82 95963 98107.6606378548 -2144.66063785483 83 91432 89747.9885446511 1684.01145534891 84 94324 90266.9926940846 4057.00730591537 85 93855 93303.7147578206 551.285242179409 86 92183 91819.453980905 363.546019094982 87 87600 88951.4032495159 -1351.40324951588 88 83641 84976.6796240965 -1335.67962409648 89 78195 79089.8023914219 -894.802391421894 90 79604 80062.2492385634 -458.249238563352 91 100846 103405.854953713 -2559.85495371318 92 105293 107280.903532959 -1987.90353295897 93 102518 103862.126563669 -1344.12656366943 94 93132 95938.0798448168 -2806.07984481685 95 87479 87048.8786534814 430.121346518601 96 85476 86129.19066623 -653.190666229959 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 83765.8906281664 79993.1919019317 87538.5893544011 98 81073.7387605628 75853.826683935 86293.6508371907 99 77223.7846884003 70831.8656940452 83615.7036827553 100 74029.8251557248 66555.3006065391 81504.3497049105 101 69294.4154352096 60975.530511596 77613.3003588231 102 70334.2605424694 60605.8470241242 80062.6740608145 103 90435.4231941782 76592.3904681818 104278.455920175 104 95480.657784422 79408.2751073703 111553.040461474 105 93668.7291357959 76418.8715391528 110918.586732439 106 87123.6021231756 69620.3753603256 104626.828886026 107 81425.4808461684 63634.284937798 99216.6767545387 108 80026.6956231044 61478.1530265631 98575.2382196458

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/155yf1305841206.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/155yf1305841206.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/22dl21305841206.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/22dl21305841206.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/3hm7q1305841206.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305840995ftvzuulj9kxs3st/3hm7q1305841206.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')

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Software written by Ed van Stee & Patrick Wessa

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