workshop 8

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 19 Dec 2010 23:02:46 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t.htm/, Retrieved Mon, 20 Dec 2010 00:00:51 +0100

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/2010/Dec/20/t1292799646w9q7loujsqqgn7t.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

40,7819 39,5915 38,8859 39,9068 41,47 41,5613 41,6005 41,4113 41,84 42,2892 43,1521 43,5998 43,116 42,4185 42,3687 42,2975 42,8528 43,535 44,7265 45,7293 45,7585 46,1685 46,5075 46,527 46,601 46,4607 46,7135 46,4113 45,55 44,6081 44,4395 44,9847 45,7558 45,3942 45,697 45,5664 46,0205 45,9195 45,8005 45,535 45,4977 45,5782 45,7697 45,2445 45,0615 45,2865 44,791 44,7625 44,7644 44,9973 44,7265 45,1465 44,7465 45,1795 45,6515 45,492 45,2775 45,2115 45,411 45,4005 44,7692 44,8913 45,032 44,879 44,833 44,8257 44,7815 44,479 44,6317 44,5043 44,3217 44,1005 44,047 43,6835 43,7864 44,1807 43,9595 43,937 43,991 43,865 43,671 43,93 43,863 43,7095 43,9435 43,736 43,6295 43,598 43,8726 43,8935 43,5957 43,7155 43,528 43,3415 43,3374 43,332 43,3869 43,5016 43,4875 43,6023 43,3886 43,3105 43,4455 43,5185 43,5755 43,6217 43,644 43,5789 43,5215 43,5033 43,632 43,263 43,3717 43,2745 43,2647 43,324 43,4455 43,409 etc...

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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.267907409590564 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 38.8859 38.4011 0.484799999999993 4 39.9068 37.8253815121695 2.08141848783049 5 41.47 39.4039089475181 2.06609105248192 6 41.5613 41.5206300493668 0.0406699506332515 7 41.6005 41.6228258304891 -0.0223258304890877 8 41.4113 41.6560445750758 -0.244744575075792 9 41.84 41.4012756899559 0.438724310044108 10 42.2892 41.9475131833842 0.341686816615777 11 43.1521 42.488253613315 0.663846386684995 12 43.5998 43.5290029791378 0.0707970208621731 13 43.116 43.9956700256038 -0.879670025603751 14 42.4185 43.2761999077498 -0.857699907749776 15 42.3687 42.3489157472585 0.0197842527415233 16 42.2975 42.3044160951611 -0.006916095161138 17 42.8528 42.2313632220220 0.621436777977962 18 43.535 42.9531507394344 0.581849260565576 19 44.7265 43.7912324676047 0.93526753239528 20 45.7293 45.2332975694829 0.496002430517095 21 45.7585 46.3689802957934 -0.610480295793366 22 46.1685 46.2346281011413 -0.0661281011412811 23 46.5075 46.6269118928634 -0.119411892863383 24 46.527 46.933920561972 -0.406920561972044 25 46.601 46.844403528305 -0.243403528304981 26 46.4607 46.8531939195516 -0.392493919551583 27 46.7135 46.6077418902845 0.105758109715524 28 46.4113 46.8888752715016 -0.477575271501564 29 45.55 46.4587293176291 -0.90872931762906 30 44.6081 45.3539740001241 -0.745874000124054 31 44.4395 44.2122488288699 0.227251171130128 32 44.9847 44.1045311014538 0.880168898546223 33 45.7558 44.8855348710655 0.870265128934541 34 45.3942 45.8897853474153 -0.495585347415322 35 45.697 45.3954143607582 0.301585639241765 36 45.5664 45.7790113881372 -0.212611388137219 37 46.0205 45.5914512218919 0.429048778108076 38 45.9195 46.1604965686228 -0.240996568622847 39 45.8005 45.9949318022029 -0.194431802202885 40 45.535 45.8238420817327 -0.288842081732689 41 45.4977 45.4809591478349 0.0167408521650714 42 45.5782 45.4481441461728 0.13005585382718 43 45.7697 45.5634870730738 0.206212926926248 44 45.2445 45.8102330441506 -0.565733044150647 45 45.0615 45.1334689697725 -0.0719689697724633 46 45.2865 44.9311879495098 0.35531205049017 47 44.791 45.2513786805530 -0.460378680552957 48 44.7625 44.6325398208153 0.129960179184714 49 44.7644 44.6388571157706 0.125542884229404 50 44.9973 44.674390984677 0.322909015322978 51 44.7265 44.9938007025056 -0.267300702505644 52 45.1465 44.6513888637156 0.495111136284386 53 44.7465 45.204032805697 -0.457532805697014 54 45.1795 44.68145637692 0.49804362307998 55 45.6515 45.2478859538425 0.403614046157529 56 45.492 45.8280171474229 -0.336017147422908 57 45.2775 45.5784956638788 -0.300995663878815 58 45.2115 45.2833566952711 -0.0718566952710589 59 45.411 45.1981057541793 0.212894245820749 60 45.4005 45.4546417000938 -0.0541417000938225 61 44.7692 45.4296367374709 -0.66043673747086 62 44.8913 44.6214008419366 0.26989915806341 63 45.032 44.815808826224 0.216191173775961 64 44.879 45.0144280435667 -0.135428043566698 65 44.833 44.8251458672288 0.00785413277117186 66 44.8257 44.7812500475941 0.0444499524058699 67 44.7815 44.7858585191996 -0.00435851919960584 68 44.479 44.7404908396112 -0.261490839611199 69 44.6317 44.3679355061393 0.263764493860705 70 44.5043 44.5912999684315 -0.0869999684314848 71 44.3217 44.4405920322545 -0.118892032254543 72 44.1005 44.2261399758723 -0.125639975872275 73 44.047 43.9712800953953 0.0757199046046892 74 43.6835 43.9380660188924 -0.254566018892390 75 43.7864 43.5063658962012 0.280034103798847 76 44.1807 43.6842891075469 0.496410892453085 77 43.9595 44.2115812638366 -0.252081263836565 78 43.937 43.9228468254358 0.0141531745642069 79 43.991 43.9041385657708 0.0868614342292275 80 43.865 43.9814093876084 -0.116409387608442 81 43.671 43.8242224501222 -0.15322245012225 82 43.93 43.5891730204189 0.340826979581124 83 43.863 43.939483093637 -0.0764830936370302 84 43.7095 43.8519927061433 -0.142492706143258 85 43.9435 43.6603178543549 0.283182145645135 86 43.736 43.970184449437 -0.234184449436960 87 43.6295 43.6999447002219 -0.0704447002219055 88 43.598 43.5745720430661 0.0234279569339293 89 43.8726 43.5493485663202 0.323251433679758 90 43.8935 43.9105500205638 -0.0170500205638149 91 43.5957 43.9268821937211 -0.331182193721105 92 43.7155 43.5403560300988 0.175143969901235 93 43.528 43.7070783973804 -0.179078397380408 94 43.3415 43.4716019678246 -0.130101967824586 95 43.3374 43.2502466866421 0.0871533133579234 96 43.332 43.269495705061 0.062504294938968 97 43.3869 43.2808410688064 0.10605893119358 98 43.5016 43.3641550423264 0.137444957673573 99 43.4875 43.5156775648980 -0.0281775648980513 100 43.6023 43.4940285864776 0.108271413522367 101 43.3886 43.6378353004071 -0.249235300407122 102 43.3105 43.3573633166965 -0.0468633166965233 103 43.4455 43.2667082869155 0.178791713084472 104 43.5185 43.4496079116243 0.0688920883757476 105 43.5755 43.5410646125623 0.0344353874377106 106 43.6217 43.607290108009 0.0144098919910292 107 43.644 43.6573506248448 -0.0133506248447617 108 43.5789 43.6760738935262 -0.0971738935261897 109 43.5215 43.5849402874318 -0.063440287431753 110 43.5033 43.5105441643622 -0.00724416436223407 111 43.632 43.4904033990533 0.141596600946691 112 43.263 43.6570381776198 -0.394038177619755 113 43.3717 43.1824724301739 0.189227569826137 114 43.2745 43.3418678982291 -0.0673678982290937 115 43.2647 43.226619539125 0.0380804608750083 116 43.324 43.227021576754 0.0969784232459787 117 43.4455 43.312302814912 0.133197185087973 118 43.4098 43.4694873277337 -0.0596873277337124 119 43.41 43.4177966503752 -0.00779665037518384 120 43.93 43.4159078699697 0.51409213003032 121 43.8104 44.073636960817 -0.263236960817004 122 43.54 43.883513828536 -0.343513828536032 123 43.858 43.5210839285744 0.336916071425598 124 43.8375 43.9293462405195 -0.0918462405194589 125 43.881 43.8842399521413 -0.00323995214125716 126 43.887 43.9268719449559 -0.0398719449558982 127 43.8009 43.9221899554674 -0.121289955467432 128 43.7877 43.8035954776888 -0.0158954776887938 129 43.811 43.786136961437 0.0248630385630122 130 44.0625 43.8160979536930 0.246402046307047 131 44.125 44.1336108876369 -0.008610887636884 132 44.52 44.1938039670358 0.326196032964191 133 45.4005 44.676194301246 0.72430569875403 134 45.89 45.7507411647508 0.139258835249159 135 45.189 46.2775496385650 -1.08854963856504 136 44.9035 45.2849191246863 -0.381419124686339 137 44.9351 44.8972341150233 0.0378658849766751 138 44.801 44.9389786661793 -0.137978666179272 139 43.98 44.7679131591444 -0.78791315914443 140 44.11 43.7358253856957 0.37417461430428 141 44.2661 43.9660695373485 0.300030462651470 142 44.361 44.2025499213958 0.158450078604247 143 44.099 44.339899871504 -0.240899871504034 144 43.8435 44.0133610109587 -0.169861010958684 145 43.8914 43.7123539875223 0.179046012477684 146 44.217 43.8082217409227 0.408778259077273 147 44.506 44.2433364654091 0.262663534590942 148 44.54 44.6027059725552 -0.0627059725552215 149 44.4465 44.6199065778821 -0.173406577882091 150 44.842 44.4799496707957 0.362050329204259 151 44.8946 44.9724456366343 -0.0778456366342652 152 44.951 45.0041902137756 -0.0531902137756433 153 45.445 45.0463401613874 0.398659838612552 154 45.0035 45.647144086058 -0.643644086057925 155 45.769 45.0332070662639 0.735792933736136 156 46.09 45.9958314451361 0.094168554863856 157 45.412 46.3420598987346 -0.930059898734619 158 45.12 45.4148899605006 -0.294889960500562 159 45.48 45.0438867550686 0.436113244931406 160 45.105 45.5207247248063 -0.415724724806303 161 45.056 45.0343489906807 0.0216510093193065 162 45.22 44.9911494565024 0.228850543497551 163 45.39 45.2164602127943 0.173539787205726 164 45.041 45.4329528076455 -0.39195280764546 165 44.9399 44.9789457462674 -0.039045746267405 166 44.9315 44.8673851015294 0.0641148984706206 167 45.1935 44.8761619578948 0.317338042105192 168 45.3466 45.2231791707198 0.123420829280249 169 45.4645 45.4093445253817 0.0551554746182603 170 45.5685 45.5420210857115 0.0264789142885391 171 45.3921 45.6531149830473 -0.261014983047275 172 45.34 45.4067871350748 -0.0667871350747475 173 45.1308 45.3367943667229 -0.205994366722905 174 45.1005 45.0724069495439 0.0280930504560786 175 45.37 45.0496332859191 0.320366714080897 176 45.2 45.4049619024076 -0.204961902407554 177 44.9614 45.1800510900688 -0.218651090068803 178 44.8015 44.8828728429243 -0.0813728429243099 179 44.9152 44.7011724553654 0.214027544634561 180 45.095 44.8722120204295 0.222787979570484 181 44.9271 45.1116985709242 -0.184598570924152 182 44.6026 44.8943432459738 -0.291743245973748 183 44.5 44.4916830686794 0.00831693132062128 184 44.54 44.3913112362052 0.148688763794773 185 44.5532 44.4711460577487 0.0820539422512923 186 44.407 44.5063289168639 -0.0993289168639464 187 44.259 44.3335179640495 -0.074517964049484 188 44.1365 44.165554049333 -0.029054049333034 189 44.112 44.0352702542381 0.0767297457619023 190 43.8814 44.0313267216637 -0.149926721663718 191 43.98 43.7605602420344 0.219439757965617 192 43.7294 43.9179497791521 -0.188549779152126 193 43.9119 43.6168358962406 0.295064103759394 194 43.955 43.8783857559420 0.0766142440580424 195 43.9 43.9420112796053 -0.0420112796052834 196 43.7065 43.8757561465126 -0.169256146512645 197 43.6939 43.6369111707432 0.0569888292568379 198 43.6587 43.6395789003650 0.0191210996350435 199 43.5885 43.6095015846367 -0.0210015846367071 200 43.8885 43.5336751044994 0.354824895500606 201 43.8216 43.9287353231112 -0.107135323111201 202 43.751 43.8331329762208 -0.0821329762208265 203 43.699 43.7405289433195 -0.0415289433195412 204 43.7425 43.6774030316918 0.0650969683082323 205 43.639 43.7383429918434 -0.0993429918434288 206 43.589 43.6082282682377 -0.0192282682376828 207 43.606 43.5530768727032 0.0529231272967934 208 43.5325 43.5842553706447 -0.0517553706447273 209 43.385 43.4968897233629 -0.1118897233629 210 43.3745 43.3194136374169 0.0550863625830615 211 43.236 43.3236716821203 -0.0876716821203303 212 43.1957 43.161683788869 0.0340162111309752 213 43.01 43.1304969838772 -0.120496983877217 214 43.1401 42.9125149490632 0.227585050936810 215 43.0487 43.1035866705212 -0.0548866705212063 216 43.1972 42.9974821248008 0.199717875199184 217 43.2461 43.1994880233944 0.0466119766056323 218 43.0866 43.2608757173027 -0.174275717302677 219 43.0865 43.0546859613256 0.0318140386744261 220 43.0194 43.0631091780155 -0.0437091780154617 221 43.08 42.984299165358 0.0957008346419954 222 43.007 43.0705381280626 -0.0635381280625964 223 42.9278 42.9805157927631 -0.0527157927631094 224 42.9545 42.8871928412794 0.067307158720574 225 42.7995 42.9319249278192 -0.132424927819166 226 42.9048 42.7414473084419 0.163352691558089 227 42.9468 42.8905107048869 0.0562892951131175 228 43.08 42.9475910241283 0.132408975871677 229 43.1274 43.1162643698606 0.0111356301393641 230 43.1625 43.1666476876854 -0.00414768768543894 231 43.45 43.2006364914218 0.249363508578163 232 43.831 43.5549428230514 0.276057176948569 233 43.7769 44.0099005862266 -0.233000586226609 234 43.98 43.8933780027375 0.0866219972624478 235 43.92 44.1196846776377 -0.199684677637691 236 44.11 44.0061876729169 0.103812327083141 237 44.03 44.2239997645493 -0.193999764549268 238 44.1582 44.0920257901677 0.0661742098323046 239 44.14 44.2379543513056 -0.0979543513055674 240 45.07 44.1935116547892 0.87648834521083 241 44.8737 45.3583293768909 -0.484629376890922 242 44.8505 45.0321935759166 -0.18169357591659 243 44.373 44.9603165206535 -0.587316520653523 244 44.075 44.3254700729955 -0.250470072995491 245 43.9725 43.9603672845593 0.0121327154406785 246 44.094 43.8611177289243 0.232882271075674 247 44.191 44.0450086149078 0.145991385092223 248 43.9685 44.1811207887104 -0.212620788710382 249 43.79 43.9016581039819 -0.111658103981874 250 43.6041 43.6932440705843 -0.0891440705842967 251 43.1707 43.4834617135537 -0.312761713553705 252 42.71 42.9662705330564 -0.256270533056416 253 42.755 42.4369137583909 0.318086241609116 254 43.3316 42.5671314194068 0.764468580593217 255 43.5 43.3485382165469 0.151461783453115 256 43.154 43.5575159506038 -0.403515950603769 257 43.16 43.1034110375491 0.0565889624509452 258 43.1 43.1245716398907 -0.0245716398906879 259 42.85 43.0579887154982 -0.207988715498189 260 42.6175 42.752266997505 -0.134766997505004 261 42.5 42.4836619203051 0.0163380796948616 262 42.6285 42.3705390129139 0.257960987086129 263 42.6974 42.5681486727395 0.129251327260455 264 43.04 42.671676061012 0.368323938987963 265 42.673 43.1129527733965 -0.439952773396492 266 42.5015 42.6280861655337 -0.126586165533659 267 42.538 42.4226727938355 0.115327206164466 268 42.3735 42.4900698068944 -0.116569806894368 269 42.014 42.2943398918928 -0.280339891892822 270 41.8618 41.8597347576509 0.0020652423490759 271 42.1824 41.7080880513788 0.474311948621157 272 42.605 42.1557597368718 0.449240263128210 273 42.7345 42.6987145320502 0.0357854679497507 274 42.615 42.8378017240696 -0.222801724069647 275 42.465 42.6586114913218 -0.193611491321839 276 42.34 42.4567415382148 -0.116741538214839 277 42.251 42.3004656151201 -0.0494656151200914 278 42.0475 42.1982134103095 -0.150713410309457 279 41.86 41.9543361709629 -0.0943361709628903 280 41.685 41.7415628117695 -0.0565628117695312 281 41.735 41.5514092153892 0.1835907846108 282 41.706 41.650594546919 0.055405453081029 283 41.764 41.6364380783311 0.127561921668892 284 41.58 41.7286128623278 -0.148612862327816 285 41.373 41.5047983753497 -0.131798375349732 286 41.088 41.2624886140215 -0.174488614021534 287 41.137 40.930741821436 0.206258178564021 288 41.1587 41.0349999157619 0.123700084238067 289 41.185 41.0898400848963 0.0951599151037072 290 40.819 41.1416341312486 -0.322634131248584 291 40.633 40.6891980569003 -0.0561980569002714 292 40.858 40.4881421810521 0.369857818947899 293 40.794 40.8122298312432 -0.0182298312432465 294 40.69 40.7433459243776 -0.0533459243775951 295 40.595 40.6250541559654 -0.0300541559653809 296 40.7305 40.5220024248933 0.208497575106733 297 40.5471 40.713360470146 -0.166260470146021 298 40.5145 40.4854180582719 0.0290819417281014 299 40.7 40.4606093259461 0.239390674053872 300 40.7 40.7102438613121 -0.0102438613120484 301 40.522 40.7074994549637 -0.185499454963733 302 40.6165 40.4798027765039 0.136697223496071 303 40.3985 40.610924975549 -0.212424975548991 304 40.2815 40.3360147506173 -0.0545147506173151 305 40.245 40.204409844995 0.0405901550050345 306 40.3055 40.1787842482772 0.126715751722770 307 40.2696 40.2732323370756 -0.00363233707560795 308 40.251 40.2363592070589 0.0146407929410799 309 40.127 40.2216815839701 -0.0946815839701145 310 39.95 40.0723156860728 -0.122315686072753 311 39.675 39.8625464074647 -0.187546407464716 312 39.954 39.5373013352628 0.416698664737183 313 39.8828 39.9279379951124 -0.0451379951124053 314 39.62 39.8446451917677 -0.224645191767735 315 39.5415 39.5216610803643 0.0198389196357383 316 39.525 39.4484760739329 0.076523926067054 317 39.8145 39.4524774007373 0.36202259926273 318 39.6675 39.838965937519 -0.171465937518995 319 39.695 39.6460289423653 0.0489710576347449 320 39.5985 39.6866486515611 -0.0881486515610916 321 39.2735 39.5665329746625 -0.293032974662466 322 39.1435 39.163027269496 -0.0195272694960167 323 39.1742 39.027795769309 0.146404230691026 324 39.2025 39.0977185475065 0.104781452493498 325 39.3946 39.1540902750172 0.240509724982829 326 39.5025 39.4106246124187 0.0918753875813394 327 39.4845 39.5431387095107 -0.0586387095107028 328 39.33 39.5094289647440 -0.179428964743956 329 39.295 39.3068586155939 -0.0118586155938871 330 39.2675 39.2686816046088 -0.0011816046088029 331 39.2535 39.2408650439789 0.0126349560211096 332 38.9845 39.2302500423168 -0.245750042316807 333 38.9285 38.8954117850729 0.0330882149270693 334 38.8592 38.848276363022 0.0109236369779779 335 38.77 38.7819028863081 -0.0119028863080999 336 38.79 38.6895140148706 0.100485985129353 337 38.8205 38.7364349548468 0.0840650451531957 338 38.7577 38.7894566033309 -0.0317566033309191 339 38.839 38.7181487739951 0.120851226004866 340 38.78 38.8318257128999 -0.0518257128999338 341 38.54 38.7589412204067 -0.218941220406734 342 38.511 38.4602852451950 0.0507147548050355 343 38.615 38.4448721037828 0.170127896217195 344 38.898 38.5944506277574 0.303549372242557 345 38.8691 38.9587737537578 -0.0896737537577934 346 38.384 38.9058494906803 -0.521849490680282 347 38.0277 38.280942145436 -0.253242145435969 348 37.72 37.8567966982531 -0.136796698253065 349 37.7325 37.5124478491835 0.220052150816464 350 37.626 37.5839014508836 0.0420985491163819 351 37.603 37.4886799641249 0.114320035875103 352 37.78 37.4963071488005 0.283692851199497 353 38.559 37.7493105656847 0.809689434315274 354 39.0459 38.745232364605 0.30066763539503 355 38.45 39.3126834519514 -0.862683451951376 356 38.505 38.4856641630424 0.0193358369575591 357 38.2885 38.545844377034 -0.257344377034009 358 37.795 38.2603999116101 -0.46539991161012 359 37.92 37.642215826867 0.277784173133021 360 38.034 37.8416362651163 0.192363734883692 361 38.029 38.0071719350282 0.0218280649718423 362 38.063 38.0080198353711 0.0549801646288586 363 37.9828 38.0567494288557 -0.0739494288557268 364 37.745 37.9567378289303 -0.211737828930282 365 37.969 37.6622116956692 0.306788304330766 366 38.007 37.9684025555752 0.0385974444248234 367 38.0615 38.0167430969278 0.0447569030721553 368 38.0912 38.0832338028912 0.00796619710879298 369 38.091 38.1150680061229 -0.0240680061229099 370 38.431 38.1084200089485 0.322579991051484 371 38.48 38.5348415787369 -0.0548415787368626 372 38.35 38.5691491134396 -0.219149113439606 373 38.214 38.3804374421439 -0.166437442143938 374 38.384 38.1998476181603 0.184152381839723 375 38.1375 38.4191834057489 -0.281683405748886 376 38.0075 38.0972183341901 -0.08971833419006 377 38.0524 37.9431821276844 0.109217872315583 378 38.235 38.0173424049375 0.217657595062526 379 38.31 38.2582544874084 0.0517455125916157 380 38.2615 38.3471174936447 -0.0856174936447474 381 38.13 38.2756799327067 -0.145679932706742 382 38.282 38.1051511993060 0.176848800694039 383 38.581 38.3045303033891 0.276469696610917 384 39.0801 38.6775985836384 0.402501416361588 385 39.0387 39.2845316954524 -0.245831695452381 386 39.1015 39.1772715627285 -0.0757715627284696 387 39.1503 39.2197717996373 -0.0694717996372631 388 39.14 39.2499597897569 -0.10995978975685 389 39.0275 39.210200747324 -0.182700747323963 390 38.7665 39.0487538633781 -0.282253863378145 391 38.691 38.7121359619936 -0.0211359619935720 392 38.849 38.6309734811667 0.218026518833319 393 39.1644 38.8473844010494 0.317015598950647 394 39.4907 39.247715228964 0.242984771035971 395 39.5095 39.6391126495422 -0.129612649542224 396 39.2795 39.6231884603532 -0.343688460353206 397 39.0437 39.3011117752338 -0.257411775233805 398 39.1355 38.9963492533328 0.139150746667191 399 39.143 39.125428769415 0.0175712305849913 400 39.185 39.1376362322844 0.0473637677156518 401 39.355 39.1923253366015 0.162674663398491 402 39.297 39.4059070842786 -0.108907084278606 403 39.4514 39.3187300694435 0.132669930556538 404 39.4173 39.5086733268694 -0.0913733268694301 405 39.4305 39.4500937355622 -0.0195937355621609 406 39.384 39.4580444286235 -0.0740444286235089 407 39.3261 39.3917073775564 -0.0656073775563684 408 39.301 39.3162306749852 -0.0152306749852045 409 39.35 39.2870502643036 0.0629497356963924 410 39.64 39.3529149649284 0.287085035071563 411 39.4723 39.7198271730067 -0.247527173006681 412 39.3685 39.4858128092832 -0.117312809283185 413 39.1906 39.3505838384363 -0.159983838436325 414 39.1183 39.1298229827045 -0.0115229827045056 415 39.1325 39.0544358902574 0.0780641097426198 416 39.1144 39.0895498436805 0.0248501563194807 417 39.1614 39.078107384688 0.0832926153120042 418 39.0908 39.1474220934943 -0.056622093494255 419 38.9199 39.0616526151006 -0.141752615100621 420 38.913 38.8527760391863 0.0602239608136799 421 38.9655 38.8620104845232 0.103489515476802 422 39.029 38.9422360925344 0.0867639074656381 423 39.089 39.0289807862294 0.060019213770552 424 39.07 39.1050603783164 -0.0350603783163734 425 39.0046 39.0766674431824 -0.0720674431823696 426 39.1038 38.9919600411636 0.111839958836427 427 39.3572 39.1211227948242 0.236077205175846 428 39.388 39.4377696273262 -0.0497696273261923 429 39.382 39.4552359753929 -0.0732359753929472 430 39.4398 39.4296155149366 0.0101844850634194 431 39.2537 39.4901440139479 -0.236444013947931 432 39.2301 39.2406989106580 -0.0105989106579543 433 39.2763 39.2142593839591 0.0620406160409033 434 39.282 39.277080524692 0.00491947530797887 435 39.3325 39.2840984885783 0.0484015114216803 436 39.557 39.3475656121236 0.209434387876428 437 40.1 39.6281746364587 0.471825363541264 438 40.5875 40.2975801473842 0.289919852615796 439 40.485 40.8627518240874 -0.377751824087376 440 40.55 40.659049311428 -0.109049311428016 441 40.7955 40.6948341928857 0.100665807114297 442 41.456 40.9673033085040 0.488696691495967 443 41.3557 41.7587287731982 -0.403028773198201 444 41.374 41.5504543785802 -0.176454378580203 445 41.2235 41.5214809431039 -0.297980943103873 446 41.15 41.2911496405296 -0.141149640529562 447 41.3725 41.1798346059706 0.192665394029355 448 41.6923 41.4539510926028 0.238348907397203 449 41.8 41.8376065309623 -0.0376065309623286 450 41.8045 41.9352314626685 -0.130731462668514 451 41.64 41.904707535153 -0.264707535153008 452 41.36 41.6692904251111 -0.309290425111065 453 41.5745 41.3064292285084 0.268070771491608 454 41.593 41.5927473744857 0.000252625514349347 455 41.575 41.6113150547328 -0.0363150547328033 456 41.68 41.5835859824902 0.096414017509801 457 42.0055 41.7144160121695 0.291083987830532 458 42.3188 42.1178995693224 0.200900430677571 459 42.565 42.4850222832909 0.0799777167091023 460 42.3575 42.7526489061994 -0.395148906199388 461 42.29 42.439285586337 -0.149285586336973 462 42.695 42.3317908716122 0.36320912838778 463 43.0028 42.8340972883382 0.168702711661759 464 42.4507 43.1870939948104 -0.736393994810449 465 42.4705 42.4377085872227 0.0327914127772715 466 42.2875 42.4662936496767 -0.178793649676706 467 42.3172 42.2353935061406 0.0818064938594247 468 42.55 42.2870100719981 0.262989928001858 469 42.7523 42.5902670223575 0.162032977642475 470 42.8993 42.835976857666 0.0633231423340277 471 43.1555 42.9999415966958 0.155558403304191 472 43.1885 43.2978168455651 -0.109316845565090 473 43.43 43.3015300526451 0.128469947354873 474 43.31 43.5774481034512 -0.267448103451208 475 42.815 43.3857967748557 -0.570796774855694 476 42.7017 42.7378760895014 -0.0361760895014456 477 42.28 42.614884247074 -0.334884247074001 478 41.922 42.1034662759277 -0.181466275927725 479 42.17 41.6968501160159 0.473149883984128 480 42.1962 42.0716104757821 0.124589524217853 481 42.3215 42.1311889324775 0.190311067522536 482 42.3173 42.3074746775938 0.00982532240615797 483 42.391 42.3059069542681 0.0850930457319237 484 42.463 42.4024040117243 0.0605959882757219 485 42.4125 42.4906381259748 -0.0781381259748102 486 42.304 42.4192043430546 -0.115204343054636 487 41.813 42.2798402459333 -0.466840245933284 488 41.651 41.6637702849527 -0.0127702849526798 489 41.539 41.4983490309913 0.0406509690087233 490 41.1575 41.3972397267957 -0.239739726795747 491 40.9545 40.9515116776140 0.00298832238605229 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 492 40.7493122713234 40.1615932413263 41.3370313013205 493 40.5441245426468 39.5950740042322 41.4931750810615 494 40.3389368139703 39.0291912275542 41.6486824003864 495 40.1337490852937 38.4487543996529 41.8187437709344 496 39.9285613566171 37.8497151873752 42.007407525859

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/1keas1292799756.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/1keas1292799756.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/2v5rd1292799756.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/2v5rd1292799756.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/3v5rd1292799756.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292799646w9q7loujsqqgn7t/3v5rd1292799756.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 5 ; par2 = Double ; 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=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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by