Exponential smoothing-omzetcijfers carefour droge voeding-Angelique Vigar

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 05:17:34 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74.htm/, Retrieved Sat, 06 Jun 2009 13:20:00 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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831581 808744 899237 929532 883165 908232 955613 937590 849396 978630 868513 1156102 1505713 1415151 1545021 1681193 1457973 1638575 1688972 1563924 1596359 1722061 1549332 2264959 1420268 1415099 1597279 1605693 1575400 1654752 1553966 1570959 1642414 1664774 1551560 2304365 1644081 1425600 1569344 1456489 1610786 1601519 1496600 1486452 1637939 1605759 1504221 1993384 1507620 1477037 1679184 1504731 1570141 1734191 1657498 1652164 1610941 1813765 1711573 2165466 1492778 1385488 1470589 1514657 1641395 1606185 1581162 1517847 1630080 1604623 1548973 2125558

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' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.570561730922535 beta 0.0317962765371711 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1505713 1167726.14903846 337986.850961538 14 1415151 1277413.81662595 137737.183374055 15 1545021 1495210.64589795 49810.3541020476 16 1681193 1665166.39602192 16026.6039780800 17 1457973 1459501.18165776 -1528.18165776460 18 1638575 1632388.07120978 6186.92879022006 19 1688972 1665078.6075113 23893.3924886987 20 1563924 1675604.82540275 -111680.825402748 21 1596359 1537761.66519362 58597.3348063775 22 1722061 1709511.51434114 12549.4856588582 23 1549332 1618822.22579524 -69490.2257952369 24 2264959 1878657.7939676 386301.206032401 25 1420268 2606118.88249658 -1185850.88249658 26 1415099 1748078.10687168 -332979.106871677 27 1597279 1638713.39982424 -41434.3998242447 28 1605693 1719615.32194655 -113922.321946545 29 1575400 1407424.99918752 167975.000812479 30 1654752 1658569.63649736 -3817.63649735716 31 1553966 1671206.83851959 -117240.838519592 32 1570959 1518477.14217451 52481.8578254941 33 1642414 1525891.71588907 116522.284110931 34 1664774 1690436.30587636 -25662.3058763589 35 1551560 1521540.30152900 30019.6984710027 36 2304365 2014518.45271201 289846.547287987 37 1644081 1990685.82219720 -346604.822197204 38 1425600 1971849.78273390 -546249.782733903 39 1569344 1856239.61547470 -286895.615474703 40 1456489 1751746.75192061 -295257.751920608 41 1610786 1439646.20894040 171139.791059598 42 1601519 1601374.97468156 144.025318435859 43 1496600 1550188.91024660 -53588.9102466037 44 1486452 1490441.37032732 -3989.37032732344 45 1637939 1475891.92702859 162047.072971410 46 1605759 1588932.50880658 16826.4911934154 47 1504221 1452542.58394701 51678.4160529862 48 1993384 2054202.50385244 -60818.503852441 49 1507620 1535360.10774845 -27740.1077484528 50 1477037 1596888.51312674 -119851.513126736 51 1679184 1827844.71895860 -148660.718958596 52 1504731 1793043.43084426 -288312.430844256 53 1570141 1679731.63104864 -109590.631048643 54 1734191 1597298.35285094 136892.647149056 55 1657498 1592985.81497687 64512.1850231325 56 1652164 1615989.71519410 36174.2848059025 57 1610941 1690454.69205969 -79513.6920596892 58 1813765 1593720.51085287 220044.489147129 59 1711573 1582346.31724677 129226.682753228 60 2165466 2175449.25655232 -9983.2565523237 61 1492778 1696246.30475591 -203468.304755910 62 1385488 1611196.41682829 -225708.416828286 63 1470589 1760704.17413304 -290115.174133042 64 1514657 1573977.59322021 -59320.5932202067 65 1641395 1660979.05849022 -19584.0584902212 66 1606185 1730291.61965435 -124106.619654351 67 1581162 1535787.14868838 45374.8513116229 68 1517847 1525162.65604943 -7315.65604942641 69 1630080 1513804.12551696 116275.874483040 70 1604623 1649644.7213236 -45021.7213236007 71 1548973 1435447.48459165 113525.515408353 72 2125558 1946939.25114092 178618.748859081 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1482806.4579273 1037968.42248131 1927644.49337329 74 1498539.26782313 982340.851678332 2014737.68396793 75 1747505.85174281 1164983.20338478 2330028.50010084 76 1829020.07373594 1183553.86624906 2474486.28122281 77 1971608.32838715 1265582.10616038 2677634.55061392 78 2012240.44532605 1247386.14912835 2777094.74152375 79 1968611.43068087 1146210.01835388 2791012.84300785 80 1915930.42442828 1036937.11023477 2794923.73862179 81 1968413.5393073 1033540.37209177 2903286.70652283 82 1973127.44312561 982900.138758262 2963354.74749296 83 1858004.13341973 812802.560912754 2903205.70592671 84 2335916.56554240 1236004.41836064 3435828.71272416

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/1ti1j1244287052.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/1ti1j1244287052.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/2eekc1244287052.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/2eekc1244287052.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/38j3x1244287052.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244287196ohmemb4qw55up74/38j3x1244287052.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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