*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 12:40:59 +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/18/t1305722278m5c0hvaoa58n7gh.htm/, Retrieved Wed, 18 May 2011 14:38:01 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

814 1150 1225 1691 1759 1754 2100 2062 2012 1897 1964 2186 966 1549 1538 1612 2078 2137 2907 2249 1883 1739 1828 1868 1138 1430 1809 1763 2200 2067 2503 2141 2103 1972 2181 2344 970 1199 1718 1683 2025 2051 2439 2353 2230 1852 2147 2286 1007 1665 1642 1518 1831 2207 2822 2393 2306 1785 2047 2171 1212 1335 2011 1860 1954 2152 2835 2224 2182 1992 2389 2724 891 1247 2017 2257 2255 2255 3057 3330 1896 2096 2374 2535 1041 1728 2201 2455 2204 2660 3670 2665 2639 2226 2586 2684 1185 1749 2459 2618 2585 3310 3923

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.171837101246772 beta 0 gamma 0.386851263600274 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 966 890.374871020695 75.6251289793047 14 1549 1431.26540160807 117.734598391932 15 1538 1453.2507909226 84.7492090774037 16 1612 1562.7181909336 49.2818090664045 17 2078 2057.46930817417 20.530691825832 18 2137 2160.60990815768 -23.6099081576813 19 2907 2327.02923601584 579.970763984157 20 2249 2371.90374660748 -122.903746607481 21 1883 2275.09132018145 -392.09132018145 22 1739 2088.5556874905 -349.555687490495 23 1828 2107.37328273892 -279.373282738923 24 1868 2276.15735192144 -408.157351921438 25 1138 983.685964199098 154.314035800902 26 1430 1597.94935199721 -167.949351997213 27 1809 1558.76134094957 250.23865905043 28 1763 1690.12384086734 72.8761591326563 29 2200 2213.09042200071 -13.0904220007133 30 2067 2300.85738822245 -233.857388222445 31 2503 2634.22289608979 -131.222896089791 32 2141 2331.4449766286 -190.444976628596 33 2103 2133.963224215 -30.9632242150019 34 1972 2016.97246438246 -44.9724643824586 35 2181 2112.45532363131 68.5446763686859 36 2344 2307.50951007982 36.4904899201788 37 970 1149.31718857444 -179.317188574435 38 1199 1628.10390677362 -429.103906773623 39 1718 1678.61608633526 39.3839136647357 40 1683 1716.7851533595 -33.785153359499 41 2025 2189.84203542125 -164.842035421247 42 2051 2179.49365273091 -128.493652730908 43 2439 2558.50852518634 -119.508525186343 44 2353 2241.83984809527 111.160151904734 45 2230 2145.88273047273 84.1172695272658 46 1852 2041.50208807352 -189.502088073515 47 2147 2149.25232240628 -2.25232240627884 48 2286 2322.03079251129 -36.0307925112884 49 1007 1085.80783155629 -78.8078315562923 50 1665 1499.65495782406 165.345042175942 51 1642 1822.70552670598 -180.705526705982 52 1518 1799.1924568875 -281.192456887499 53 1831 2199.51454663209 -368.514546632086 54 2207 2165.52914687751 41.4708531224892 55 2822 2586.49209911449 235.507900885514 56 2393 2392.08585396447 0.914146035534031 57 2306 2262.40113921286 43.5988607871395 58 1785 2053.94526409419 -268.945264094192 59 2047 2213.59360536566 -166.593605365655 60 2171 2349.72746842407 -178.72746842407 61 1212 1066.95664625435 145.043353745648 62 1335 1617.56743478251 -282.567434782512 63 2011 1750.50001777202 260.499982227984 64 1860 1766.65882919478 93.341170805217 65 1954 2229.20033358206 -275.20033358206 66 2152 2354.07089111243 -202.070891112428 67 2835 2821.78438699214 13.2156130078597 68 2224 2499.17192715494 -275.171927154935 69 2182 2332.32640922816 -150.326409228161 70 1992 1985.12130297315 6.87869702685134 71 2389 2231.67363751923 157.326362480774 72 2724 2427.23706486073 296.762935139272 73 891 1217.94263141972 -326.942631419722 74 1247 1555.33432394767 -308.33432394767 75 2017 1861.20428215139 155.795717848615 76 2257 1805.07154481788 451.928455182124 77 2255 2221.2309765631 33.7690234368979 78 2255 2432.88275703902 -177.882757039023 79 3057 3009.67146125636 47.3285387436449 80 3330 2569.47036879694 760.529631203062 81 1896 2606.04087332991 -710.040873329906 82 2096 2184.33339151501 -88.333391515012 83 2374 2487.07905491054 -113.079054910535 84 2535 2692.03977051495 -157.039770514949 85 1041 1147.34045999992 -106.340459999922 86 1728 1551.32916861704 176.670831382963 87 2201 2150.87765346461 50.1223465353878 88 2455 2164.4052766606 290.594723339399 89 2204 2436.13220717465 -232.132207174655 90 2660 2542.01819880033 117.981801199671 91 3670 3302.50843006674 367.491569933263 92 2665 3106.32350670552 -441.323506705517 93 2639 2436.59954952698 202.400450473016 94 2226 2359.57132754962 -133.571327549615 95 2586 2673.00752314577 -87.0075231457672 96 2684 2885.60415105108 -201.604151051084 97 1185 1212.50477919223 -27.5047791922266 98 1749 1771.11376805478 -22.113768054784 99 2459 2336.29249633475 122.707503665255 100 2618 2442.56242295145 175.437577048554 101 2585 2528.42353153446 56.5764684655405 102 3310 2818.10536968948 491.894630310517 103 3923 3813.00610020984 109.993899790165 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 104 3255.69245115611 3030.53319934678 3480.85170296544 105 2815.64874514931 2580.56978501259 3050.72770528603 106 2569.84893869539 2325.84255583369 2813.8553215571 107 2961.11377095788 2695.78119734107 3226.44634457468 108 3172.69174871154 2889.74738535243 3455.63611207065 109 1369.41431843186 1130.16675758807 1608.66187927566 110 2013.10160675149 1734.05861985703 2292.14459364596 111 2714.19281636516 2381.61692333664 3046.76870939369 112 2826.83374181122 2478.19161277593 3175.47587084651 113 2844.52522159072 2487.03994440019 3202.01049878125 114 3303.99254769061 2901.79949019966 3706.18560518156 115 4152.70462836921 3724.44797162474 4580.96128511368

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/1pz0w1305722456.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/1pz0w1305722456.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/2a1ln1305722456.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/2a1ln1305722456.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/3vodi1305722456.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305722278m5c0hvaoa58n7gh/3vodi1305722456.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')

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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