Opdracht 10 - Oefening 2 - Katrien De Soomer

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 23 May 2008 09:03:26 -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/23/t1211555070baie2hjit7tdlku.htm/, Retrieved Fri, 23 May 2008 17:04:30 +0200

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Dataseries X:

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464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565 1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722 832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753 2258 1208 1241 1265 1828 809 997 1164 1205 1538 1513 1378 2083 1357 1536 1526 1376 779 1005 1193 1522 1539 1546 2116 2326 1596 1356 1553 1613 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

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.138188790941126 beta 0.0173529526220280 gamma 0.352954520634182 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 530 515.414440622897 14.5855593771033 14 883 842.900916696941 40.0990833030589 15 894 849.831695972678 44.1683040273223 16 1045 1003.88195914183 41.1180408581650 17 1199 1159.86209042234 39.1379095776585 18 1287 1245.40579874525 41.5942012547489 19 1565 1514.88900184722 50.1109981527823 20 1577 1547.77796739094 29.2220326090567 21 1076 1073.17576868511 2.82423131488827 22 918 921.817194474754 -3.81719447475382 23 1008 1021.83640049345 -13.8364004934452 24 1063 1093.45753715863 -30.4575371586332 25 544 538.498317646241 5.50168235375861 26 635 883.992724365653 -248.992724365653 27 804 851.857147113964 -47.8571471139639 28 980 987.59009966451 -7.59009966451094 29 1018 1130.24715952532 -112.247159525323 30 1064 1190.1075296698 -126.107529669800 31 1404 1417.85280514777 -13.8528051477679 32 1286 1431.92714643595 -145.92714643595 33 1104 969.842429086618 134.157570913382 34 999 845.741333206727 153.258666793273 35 996 957.871967176254 38.1280328237459 36 1015 1027.20670939209 -12.2067093920882 37 615 512.53138942575 102.46861057425 38 722 783.740616251253 -61.7406162512533 39 832 838.814780352263 -6.81478035226257 40 977 994.104798817453 -17.1047988174529 41 1270 1104.29767508664 165.702324913364 42 1437 1201.89594875293 235.104051247072 43 1520 1540.82757247366 -20.8275724736561 44 1708 1513.34948377193 194.650516228073 45 1151 1140.03853934925 10.9614606507496 46 934 990.346571583594 -56.3465715835944 47 1159 1043.96730162844 115.032698371563 48 1209 1114.44601855681 94.5539814431922 49 699 600.001372009354 98.9986279906462 50 830 842.553030410869 -12.5530304108687 51 996 931.645389058085 64.3546109419151 52 1124 1114.86198600448 9.13801399552221 53 1458 1307.69773088421 150.302269115788 54 1270 1436.98934543368 -166.989345433682 55 1753 1663.18078654273 89.8192134572671 56 2258 1721.34750618056 536.652493819438 57 1208 1285.52525758474 -77.5252575847376 58 1241 1085.02930910613 155.970690893874 59 1265 1238.38964605712 26.6103539428761 60 1828 1298.64872216196 529.35127783804 61 809 748.425917469025 60.5740825309753 62 997 987.91562981621 9.08437018378993 63 1164 1126.23341659803 37.7665834019715 64 1205 1319.64954701957 -114.649547019575 65 1538 1578.99607270820 -40.996072708195 66 1513 1588.41846016296 -75.4184601629597 67 1378 1959.87732467204 -581.877324672038 68 2083 2074.32800424228 8.6719957577152 69 1357 1337.26902261079 19.7309773892086 70 1536 1212.28145653055 323.718543469453 71 1526 1358.52293692570 167.477063074303 72 1376 1605.00054003904 -229.000540039041 73 779 786.704150391548 -7.70415039154796 74 1005 1003.53588179346 1.46411820654123 75 1193 1150.67415811311 42.3258418868861 76 1522 1299.02917640314 222.970823596856 77 1539 1641.75527564294 -102.755275642938 78 1546 1632.17732282556 -86.1773228255631 79 2116 1849.7002749325 266.299725067501 80 2326 2303.43211973339 22.5678802666107 81 1596 1492.1581417881 103.841858211899 82 1356 1464.53209893504 -108.532098935041 83 1553 1506.77149580913 46.228504190874 84 1613 1620.35062075642 -7.3506207564185 85 814 844.989947423514 -30.9899474235139 86 1150 1077.90995655504 72.090043444965 87 1225 1261.00424991122 -36.0042499112217 88 1691 1466.87921964820 224.120780351797 89 1759 1726.10905115275 32.8909488472527 90 1754 1741.65874264454 12.3412573554633 91 2100 2110.94886589595 -10.9488658959508 92 2062 2477.55816342208 -415.55816342208 93 2012 1593.56220187514 418.437798124862 94 1897 1536.99236609413 360.007633905866 95 1964 1704.92823507691 259.071764923093 96 2186 1846.2276936445 339.772306355501 97 966 979.48087993079 -13.4808799307898 98 1549 1295.00860664629 253.991393353711 99 1538 1500.51669504191 37.4833049580895 100 1612 1857.75200730189 -245.752007301893 101 2078 2024.13904383593 53.8609561640656 102 2137 2039.43470380867 97.5652961913308 103 2907 2479.46702292777 427.532977072227 104 2249 2834.49200953365 -585.492009533651 105 1883 2063.45276691845 -180.452766918448 106 1739 1884.57385781799 -145.573857817994 107 1828 1959.24821911067 -131.248219110666 108 1868 2076.73532015479 -208.735320154794 109 1138 999.77958578803 138.22041421197 110 1430 1433.49724354292 -3.49724354292471 111 1809 1538.29530880992 270.704691190080 112 1763 1849.57217747235 -86.5721774723452 113 2200 2143.11707099246 56.8829290075419 114 2067 2172.30985888696 -105.309858886960 115 2503 2699.27317331618 -196.273173316180 116 2141 2652.32820928588 -511.328209285884 117 2103 2010.92994372578 92.0700562742206 118 1972 1875.74272327381 96.2572767261868 119 2181 1990.75869314381 190.241306856194 120 2344 2134.76078172848 209.239218271524 121 970 1135.37809966138 -165.378099661379 122 1199 1501.71162455123 -302.711624551229 123 1718 1649.2085568589 68.7914431410995 124 1683 1822.23219311813 -139.232193118133 125 2025 2148.50714589241 -123.507145892408 126 2051 2101.45775991581 -50.4577599158069 127 2439 2597.53863841864 -158.538638418635 128 2353 2454.95815170453 -101.958151704525 129 2230 2049.68111829082 180.318881709178 130 1852 1924.91609796578 -72.9160979657772 131 2147 2042.54671457936 104.453285420636 132 2286 2176.70038756706 109.299612432936 133 1007 1065.76441805878 -58.7644180587797 134 1665 1399.86768449305 265.132315506950 135 1642 1753.86990491781 -111.869904917812 136 1518 1841.29283465705 -323.292834657047 137 1831 2152.87654567507 -321.876545675072 138 2207 2099.26981765408 107.730182345915 139 2822 2590.67641554791 231.323584452090 140 2393 2514.71789350983 -121.717893509827 141 2306 2180.37736497262 125.622635027382 142 1785 1963.20155076723 -178.201550767232 143 2047 2123.72126457589 -76.7212645758927 144 2171 2234.38742977834 -63.3874297783386 145 1212 1047.34686346252 164.653136537481 146 1335 1521.24424765127 -186.244247651267 147 2011 1693.60188388355 317.39811611645 148 1860 1773.69759448320 86.3024055167957 149 1954 2158.71790165912 -204.717901659125 150 2152 2259.47994712112 -107.479947121125 151 2835 2781.29868587681 53.7013141231869 152 2224 2565.19655021878 -341.196550218777 153 2182 2269.16895953021 -87.1689595302146 154 1992 1925.45701889331 66.5429811066938 155 2389 2155.82426469756 233.175735302438 156 2724 2319.33331671591 404.666683284094 157 891 1180.84303141773 -289.843031417725 158 1247 1490.02323328043 -243.023233280426 159 2017 1808.76868858983 208.231311410165 160 2257 1802.22079463206 454.779205367938 161 2255 2156.79215504739 98.2078449526139 162 2255 2336.8751785537 -81.8751785537015 163 3057 2941.71486638894 115.285133611055 164 3330 2593.72160894797 736.278391052027 165 1896 2506.1698416447 -610.169841644698 166 2096 2113.62988175086 -17.6298817508573 167 2374 2404.83255512033 -30.8325551203279 168 2535 2593.07494193432 -58.0749419343183 169 1041 1127.23701253264 -86.237012532636 170 1728 1498.94107698729 229.058923012706 171 2201 2073.26056298899 127.739437011011 172 2455 2130.9507934861 324.049206513899 173 2204 2375.75501482807 -171.755014828069 174 2660 2472.00954440677 187.990455593228 175 3670 3233.47028240361 436.529717596392 176 2665 3093.8830706459 -428.883070645898 177 2639 2405.05907050405 233.940929495951 178 2226 2299.06592121852 -73.0659212185169 179 2586 2604.97460965133 -18.9746096513300 180 2684 2804.10579678828 -120.105796788276 181 1185 1195.61768993792 -10.6176899379157 182 1749 1719.32980817409 29.6701918259105 183 2459 2274.99162656601 184.008373433991 184 2618 2406.76323322972 211.236766770282 185 2585 2488.59953884362 96.4004611563769 186 3310 2751.98684954933 558.013150450666 187 3923 3726.79165528676 196.208344713244 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 188 3245.24034646890 3066.81539186405 3423.66530107374 189 2768.00438666639 2583.19389650866 2952.81487682413 190 2513.58291499792 2322.72582558653 2704.44000440931 191 2883.95863801343 2678.45825816188 3089.45901786499 192 3075.49477620287 2857.36160067387 3293.62795173188 193 1333.95454445120 1145.61501090122 1522.29407800119 194 1937.25726544019 1721.80514037392 2152.70939050645 195 2607.53714105196 2353.18523366474 2861.88904843918 196 2734.89089155822 2465.84668254851 3003.93510056792 197 2755.00833155814 2477.11899686146 3032.89766625481 198 3175.78355309347 2863.00213568801 3488.56497049893 199 4008.98763225839 3672.26979929807 4345.70546521871

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/1eej21211554995.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/1eej21211554995.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/2j8l31211554995.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/2j8l31211554995.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/3a5q41211554995.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/23/t1211555070baie2hjit7tdlku/3a5q41211554995.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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