| 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: |
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')
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