| ws8ExponentialSmoothing | | *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, 26 Dec 2010 02:13:11 +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/26/t1293329474zmvy5tqb16emd5n.htm/, Retrieved Sun, 26 Dec 2010 03:11:15 +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/26/t1293329474zmvy5tqb16emd5n.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 « | | 1,3866
1,3582
1,3332
1,3595
1,3617
1,3684
1,3394
1,3262
1,3173
1,3085
1,327
1,3182
1,293
1,291
1,2984
1,2795
1,299
1,3174
1,326
1,3111
1,2816
1,276
1,2849
1,2818
1,2829
1,2796
1,3008
1,2967
1,2938
1,2833
1,2823
1,2765
1,2634
1,2596
1,2705
1,2591
1,2798
1,2763
1,2795
1,2782
1,2644
1,2596
1,2615
1,2555
1,2555
1,2658
1,2565
1,2783
1,2786
1,2782
1,2905
1,3042
1,2942
1,313
1,3671
1,3549
1,3558
1,3507
1,3494
1,3607
1,3295
1,3193
1,3308
1,3246
1,3392
1,3425
1,3496
1,3255
1,3231
1,3273
1,3276
1,3173
1,3196
1,3058
1,2966
1,2932
1,2947
1,305
1,3232
1,3125
1,2992
1,3266
1,3275
1,3223
1,3403
1,3322
1,3363
1,3425
1,3574
1,3683
1,3623
1,3563
1,3518
1,3494
1,3612
1,369
1,3771
1,3972
1,401
1,3908
1,3901
1,3856
1,4098
1,422
1,4238
1,4207
1,4095
1,4177
1,3866
1,3959
1,4102
1,3969
1,4004
1,385
1,389
1,384
1,392
1,3932
1,3858
1,3978
1,4029
1,394
1,4096
1,4058
1,4134
1,4096
1,4049
1,4009
1,3897
1,4019
etc... | | | | Output produced by software: |
| Estimated Parameters of Exponential Smoothing | | Parameter | Value | | alpha | 0.978425156332075 | | beta | 0.110824791228909 | | gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 3 | 1.3332 | 1.3298 | 0.00339999999999985 | | 4 | 1.3595 | 1.30509532032805 | 0.0544046796719466 | | 5 | 1.3617 | 1.33619420651663 | 0.0255057934833709 | | 6 | 1.3684 | 1.34178338465146 | 0.0266166153485365 | | 7 | 1.3394 | 1.35134555862214 | -0.0119455586221409 | | 8 | 1.3262 | 1.32188222961635 | 0.00431777038364878 | | 9 | 1.3173 | 1.30879954292895 | 0.00850045707104785 | | 10 | 1.3085 | 1.3007310386708 | 0.0077689613291958 | | 11 | 1.327 | 1.29278923829392 | 0.0342107617060843 | | 12 | 1.3182 | 1.31442836223476 | 0.00377163776524037 | | 13 | 1.293 | 1.30669405445331 | -0.0136940544533084 | | 14 | 1.291 | 1.28038597616801 | 0.010614023831985 | | 15 | 1.2984 | 1.27901245173107 | 0.0193875482689281 | | 16 | 1.2795 | 1.28832542914033 | -0.0088254291403258 | | 17 | 1.299 | 1.26907714521953 | 0.0299228547804713 | | 18 | 1.3174 | 1.29098580481554 | 0.0264141951844583 | | 19 | 1.326 | 1.31232569419633 | 0.0136743058036661 | | 20 | 1.3111 | 1.32268331176212 | -0.0115833117621238 | | 21 | 1.2816 | 1.30707221882224 | -0.0254722188222418 | | 22 | 1.276 | 1.27510982126451 | 0.000890178735485803 | | 23 | 1.2849 | 1.26903758208913 | 0.0158624179108657 | | 24 | 1.2818 | 1.27933458004476 | 0.00246541995523586 | | 25 | 1.2829 | 1.27679095294608 | 0.00610904705391668 | | 26 | 1.2796 | 1.27847476922562 | 0.00112523077437854 | | 27 | 1.3008 | 1.2754043072906 | 0.0253956927093992 | | 28 | 1.2967 | 1.29883442641044 | -0.00213442641043704 | | 29 | 1.2938 | 1.29509694053762 | -0.00129694053761731 | | 30 | 1.2833 | 1.29203823976707 | -0.00873823976706967 | | 31 | 1.2823 | 1.28075126440872 | 0.00154873559128177 | | 32 | 1.2765 | 1.27969725975266 | -0.00319725975265928 | | 33 | 1.2634 | 1.2736529629518 | -0.0102529629517984 | | 34 | 1.2596 | 1.25959342128352 | 6.57871648490627e-06 | | 35 | 1.2705 | 1.25557278663091 | 0.0149272133690941 | | 36 | 1.2591 | 1.26776949019777 | -0.00866949019776886 | | 37 | 1.2798 | 1.25593851993694 | 0.0238614800630599 | | 38 | 1.2763 | 1.2785240594295 | -0.00222405942949599 | | 39 | 1.2795 | 1.27534568773145 | 0.004154312268555 | | 40 | 1.2782 | 1.278858543074 | -0.00065854307400004 | | 41 | 1.2644 | 1.27759097137155 | -0.0131909713715503 | | 42 | 1.2596 | 1.26263100988039 | -0.00303100988038962 | | 43 | 1.2615 | 1.25728314649045 | 0.00421685350954726 | | 44 | 1.2555 | 1.25948402426783 | -0.00398402426783107 | | 45 | 1.2555 | 1.25322895417785 | 0.00227104582214999 | | 46 | 1.2658 | 1.25334026006452 | 0.0124597399354796 | | 47 | 1.2565 | 1.26477149707757 | -0.00827149707756814 | | 48 | 1.2783 | 1.25502186071575 | 0.0232781392842514 | | 49 | 1.2786 | 1.27866531849761 | -6.53184976051602e-05 | | 50 | 1.2782 | 1.27946186721938 | -0.00126186721938404 | | 51 | 1.2905 | 1.27895085355913 | 0.0115491464408692 | | 52 | 1.3042 | 1.2922267753581 | 0.0119732246419004 | | 53 | 1.2942 | 1.30721592774856 | -0.0130159277485602 | | 54 | 1.313 | 1.29634369877117 | 0.0166563012288321 | | 55 | 1.3671 | 1.31630963050099 | 0.050790369499008 | | 56 | 1.3549 | 1.37518058423797 | -0.0202805842379716 | | 57 | 1.3558 | 1.36231482887555 | -0.00651482887555166 | | 58 | 1.3507 | 1.36221140744091 | -0.0115114074409055 | | 59 | 1.3494 | 1.35597098260821 | -0.00657098260821476 | | 60 | 1.3607 | 1.35385187733949 | 0.00684812266051216 | | 61 | 1.3295 | 1.3656049299554 | -0.0361049299553982 | | 62 | 1.3193 | 1.33141664190805 | -0.0121166419080494 | | 63 | 1.3308 | 1.31938524525827 | 0.0114147547417296 | | 64 | 1.3246 | 1.33161530387243 | -0.00701530387243454 | | 65 | 1.3392 | 1.32505223370355 | 0.0141477662964464 | | 66 | 1.3425 | 1.34072973932037 | 0.00177026067963371 | | 67 | 1.3496 | 1.34448873809724 | 0.00511126190275801 | | 68 | 1.3255 | 1.35207088988345 | -0.0265708898834474 | | 69 | 1.3231 | 1.32577324576081 | -0.00267324576081296 | | 70 | 1.3273 | 1.32256778772574 | 0.00473221227426057 | | 71 | 1.3276 | 1.32712114771379 | 0.00047885228620892 | | 72 | 1.3173 | 1.32756483704624 | -0.010264837046239 | | 73 | 1.3196 | 1.31638357554948 | 0.00321642445051973 | | 74 | 1.3058 | 1.31874148844902 | -0.0129414884490155 | | 75 | 1.2966 | 1.30388679859363 | -0.00728679859362802 | | 76 | 1.2932 | 1.2937746645473 | -0.000574664547295933 | | 77 | 1.2947 | 1.29016753826485 | 0.00453246173515076 | | 78 | 1.305 | 1.29204882469841 | 0.0129511753015925 | | 79 | 1.3232 | 1.3035715369514 | 0.0196284630485957 | | 80 | 1.3125 | 1.32375586363582 | -0.0112558636358209 | | 81 | 1.2992 | 1.31250167249828 | -0.0133016724982851 | | 82 | 1.3266 | 1.29780346009239 | 0.0287965399076089 | | 83 | 1.3275 | 1.32741771494428 | 8.22850557176125e-05 | | 84 | 1.3223 | 1.32894614298204 | -0.00664614298203925 | | 85 | 1.3403 | 1.32317064146756 | 0.0171293585324372 | | 86 | 1.3322 | 1.34251508955442 | -0.0103150895544195 | | 87 | 1.3363 | 1.33388869524833 | 0.00241130475167317 | | 88 | 1.3425 | 1.33797559213033 | 0.00452440786967134 | | 89 | 1.3574 | 1.34462060083465 | 0.0127793991653482 | | 90 | 1.3683 | 1.36072821903708 | 0.00757178096291877 | | 91 | 1.3623 | 1.37256160929328 | -0.0102616092932781 | | 92 | 1.3563 | 1.365833656983 | -0.0095336569830038 | | 93 | 1.3518 | 1.35878418121738 | -0.00698418121737654 | | 94 | 1.3494 | 1.35347185562065 | -0.00407185562064916 | | 95 | 1.3612 | 1.35056749602107 | 0.0106325039789337 | | 96 | 1.369 | 1.36320317418529 | 0.00579682581471475 | | 97 | 1.3771 | 1.37173607482621 | 0.00536392517378537 | | 98 | 1.3972 | 1.38042704518458 | 0.0167729548154227 | | 99 | 1.401 | 1.40209965177239 | -0.0010996517723878 | | 100 | 1.3908 | 1.40616601108504 | -0.0153660110850367 | | 101 | 1.3901 | 1.39460761114216 | -0.00450761114216292 | | 102 | 1.3856 | 1.39318456561954 | -0.00758456561954457 | | 103 | 1.4098 | 1.38792852743533 | 0.0218714725646652 | | 104 | 1.422 | 1.41386462410392 | 0.00813537589607649 | | 105 | 1.4238 | 1.42724312766955 | -0.00344312766954835 | | 106 | 1.4207 | 1.42891958078183 | -0.00821958078183282 | | 107 | 1.4095 | 1.42503135193094 | -0.0155313519309421 | | 108 | 1.4177 | 1.41230497930545 | 0.005395020694547 | | 109 | 1.3866 | 1.42063849848658 | -0.0340384984865818 | | 110 | 1.3959 | 1.38669834799715 | 0.00920165200284795 | | 111 | 1.4102 | 1.39606321826894 | 0.0141367817310594 | | 112 | 1.3969 | 1.41178964806605 | -0.0148896480660459 | | 113 | 1.4004 | 1.39750134817143 | 0.00289865182856941 | | 114 | 1.385 | 1.40093188010947 | -0.0159318801094666 | | 115 | 1.389 | 1.38421059216939 | 0.0047894078306121 | | 116 | 1.384 | 1.38828286713837 | -0.00428286713837167 | | 117 | 1.392 | 1.38301419264937 | 0.0089858073506306 | | 118 | 1.3932 | 1.39170228798235 | 0.0014977120176467 | | 119 | 1.3858 | 1.39322624501952 | -0.0074262450195206 | | 120 | 1.3978 | 1.38521352229999 | 0.0125864777000064 | | 121 | 1.4029 | 1.39814655008448 | 0.0047534499155184 | | 122 | 1.394 | 1.4039309808992 | -0.00993098089919986 | | 123 | 1.4096 | 1.39427094156241 | 0.0153290584375907 | | 124 | 1.4058 | 1.41098814766279 | -0.00518814766278664 | | 125 | 1.4134 | 1.40706823279928 | 0.00633176720071749 | | 126 | 1.4096 | 1.41510626978538 | -0.00550626978537672 | | 127 | 1.4049 | 1.410964608026 | -0.00606460802600117 | | 128 | 1.4009 | 1.40561904581273 | -0.0047190458127313 | | 129 | 1.3897 | 1.40107831161986 | -0.0113783116198649 | | 130 | 1.4019 | 1.38878819108529 | 0.01311180891471 | | 131 | 1.3901 | 1.40188158335267 | -0.0117815833526702 | | 132 | 1.399 | 1.38934113297412 | 0.00965886702587926 | | 133 | 1.3901 | 1.39882590591357 | -0.00872590591356959 | | 134 | 1.3975 | 1.38937637169585 | 0.00812362830414926 | | 135 | 1.3991 | 1.39729372122101 | 0.00180627877898809 | | 136 | 1.4089 | 1.39922587865568 | 0.00967412134431966 | | 137 | 1.413 | 1.40990513257003 | 0.00309486742997378 | | 138 | 1.409 | 1.41448266706821 | -0.00548266706821376 | | 139 | 1.4217 | 1.41007321980884 | 0.0116267801911623 | | 140 | 1.4223 | 1.42366482169462 | -0.00136482169462182 | | 141 | 1.4191 | 1.4243971207212 | -0.00529712072119848 | | 142 | 1.4229 | 1.42070757272147 | 0.00219242727853364 | | 143 | 1.4227 | 1.42458372003564 | -0.00188372003564297 | | 144 | 1.4269 | 1.42426740342352 | 0.0026325965764773 | | 145 | 1.4229 | 1.42865542695371 | -0.00575542695370945 | | 146 | 1.4104 | 1.42421231464386 | -0.0138123146438591 | | 147 | 1.4053 | 1.41038841947421 | -0.00508841947420824 | | 148 | 1.4138 | 1.40454844632496 | 0.00925155367504171 | | 149 | 1.4303 | 1.41374224443097 | 0.0165577555690333 | | 150 | 1.4384 | 1.4318800340218 | 0.00651996597819893 | | 151 | 1.441 | 1.4409035822131 | 9.64177869000604e-05 | | 152 | 1.437 | 1.44365262420464 | -0.00665262420464052 | | 153 | 1.4357 | 1.43907686464963 | -0.00337686464963438 | | 154 | 1.4202 | 1.43734002450593 | -0.0171400245059314 | | 155 | 1.4166 | 1.4202784051614 | -0.00367840516140006 | | 156 | 1.417 | 1.41598910951252 | 0.00101089048747904 | | 157 | 1.4293 | 1.41639755335221 | 0.0129024466477872 | | 158 | 1.4294 | 1.42984005573783 | -0.000440055737832568 | | 159 | 1.4072 | 1.43018020124106 | -0.0229802012410574 | | 160 | 1.4101 | 1.40597467164577 | 0.00412532835423285 | | 161 | 1.4112 | 1.40873719896209 | 0.00246280103790752 | | 162 | 1.4243 | 1.41014011851478 | 0.0141598814852197 | | 163 | 1.433 | 1.42452316507551 | 0.00847683492448548 | | 164 | 1.4323 | 1.43426495103161 | -0.00196495103160665 | | 165 | 1.4324 | 1.43357716389541 | -0.00117716389541211 | | 166 | 1.427 | 1.43353252319945 | -0.00653252319945286 | | 167 | 1.4268 | 1.42753971816236 | -0.000739718162356295 | | 168 | 1.4364 | 1.42713452887487 | 0.00926547112512721 | | 169 | 1.4272 | 1.43752335838653 | -0.0103233583865263 | | 170 | 1.4314 | 1.42762658371717 | 0.00377341628282779 | | 171 | 1.422 | 1.43193161373695 | -0.00993161373695117 | | 172 | 1.4335 | 1.42175037536014 | 0.0117496246398576 | | 173 | 1.4262 | 1.43405666205321 | -0.00785666205320523 | | 174 | 1.433 | 1.4263277371871 | 0.00667226281290279 | | 175 | 1.4473 | 1.43353777647354 | 0.0137622235264627 | | 176 | 1.4522 | 1.44917710137316 | 0.00302289862683991 | | 177 | 1.4545 | 1.45463658490431 | -0.000136584904310677 | | 178 | 1.4594 | 1.45698993985233 | 0.0024100601476702 | | 179 | 1.4561 | 1.46209632827597 | -0.00599632827597163 | | 180 | 1.4611 | 1.45832749034878 | 0.00277250965122278 | | 181 | 1.4671 | 1.46343893769768 | 0.00366106230231988 | | 182 | 1.4712 | 1.46981675007766 | 0.0013832499223374 | | 183 | 1.4705 | 1.47411588451886 | -0.00361588451885986 | | 184 | 1.4658 | 1.47313165609548 | -0.00733165609547792 | | 185 | 1.478 | 1.46771682422188 | 0.010283175778117 | | 186 | 1.4783 | 1.48065183043021 | -0.00235183043021459 | | 187 | 1.4768 | 1.48096941088881 | -0.00416941088880907 | | 188 | 1.467 | 1.47905651998804 | -0.0120565199880398 | | 189 | 1.465 | 1.46811934929462 | -0.00311934929461777 | | 190 | 1.4549 | 1.46558828844981 | -0.0106882884498145 | | 191 | 1.4643 | 1.45449261578487 | 0.00980738421512939 | | 192 | 1.4539 | 1.46451387643359 | -0.010613876433593 | | 193 | 1.4537 | 1.45340355937062 | 0.000296440629376171 | | 194 | 1.4616 | 1.45300031515877 | 0.00859968484122531 | | 195 | 1.4722 | 1.46165367015679 | 0.0105463298432054 | | 196 | 1.4694 | 1.47335524983315 | -0.00395524983314743 | | 197 | 1.4763 | 1.47043923652189 | 0.00586076347811448 | | 198 | 1.475 | 1.47776296221124 | -0.00276296221124417 | | 199 | 1.4765 | 1.47634941935335 | 0.00015058064665352 | | 200 | 1.4864 | 1.47780288814792 | 0.00859711185207801 | | 201 | 1.4881 | 1.48845287275256 | -0.000352872752558575 | | 202 | 1.4864 | 1.49030770395057 | -0.00390770395057261 | | 203 | 1.4869 | 1.48826067183121 | -0.00136067183121358 | | 204 | 1.4918 | 1.48855817724362 | 0.0032418227563753 | | 205 | 1.4971 | 1.49371040218508 | 0.0033895978149161 | | 206 | 1.4921 | 1.49937476080974 | -0.00727476080974299 | | 207 | 1.5 | 1.49381601298539 | 0.00618398701460987 | | 208 | 1.502 | 1.50209619559168 | -9.6195591678283e-05 | | 209 | 1.5019 | 1.50422125869956 | -0.00232125869955957 | | 210 | 1.4874 | 1.50391756127099 | -0.0165175612709867 | | 211 | 1.4785 | 1.48793278294414 | -0.0094327829441403 | | 212 | 1.4788 | 1.47785709780267 | 0.000942902197327067 | | 213 | 1.48 | 1.47803548645184 | 0.0019645135481603 | | 214 | 1.4772 | 1.47942646494449 | -0.00222646494449052 | | 215 | 1.4658 | 1.47647546067664 | -0.0106754606766446 | | 216 | 1.4761 | 1.46410016605849 | 0.0119998339415082 | | 217 | 1.4867 | 1.47521213727984 | 0.0114878627201629 | | 218 | 1.4862 | 1.48706885517033 | -0.000868855170327976 | | 219 | 1.4984 | 1.48674123619085 | 0.0116587638091505 | | 220 | 1.4966 | 1.49993515840956 | -0.00333515840956045 | | 221 | 1.5037 | 1.49809700615857 | 0.0056029938414317 | | 222 | 1.4922 | 1.5056117206312 | -0.0134117206311957 | | 223 | 1.4868 | 1.49306767677782 | -0.00626767677781914 | | 224 | 1.4965 | 1.48683391736595 | 0.00966608263404578 | | 225 | 1.4875 | 1.49723827871769 | -0.0097382787176874 | | 226 | 1.4957 | 1.48760096656717 | 0.00809903343283191 | | 227 | 1.4863 | 1.49629433802339 | -0.009994338023386 | | 228 | 1.4815 | 1.48620097599658 | -0.00470097599657748 | | 229 | 1.4968 | 1.48077702801808 | 0.0160229719819236 | | 230 | 1.4969 | 1.49736734323765 | -0.00046734323765496 | | 231 | 1.5083 | 1.49777244342436 | 0.0105275565756389 | | 232 | 1.5071 | 1.51007677276163 | -0.00297677276163344 | | 233 | 1.4918 | 1.50884534388175 | -0.0170453438817508 | | 234 | 1.5023 | 1.49200058031392 | 0.0102994196860815 | | 235 | 1.5074 | 1.50302742615513 | 0.00437257384487499 | | 236 | 1.509 | 1.50872943156658 | 0.000270568433422547 | | 237 | 1.512 | 1.51044727044562 | 0.00155272955437558 | | 238 | 1.5068 | 1.51358797632945 | -0.0067879763294465 | | 239 | 1.4787 | 1.50783187993377 | -0.029131879933773 | | 240 | 1.4774 | 1.47705506677657 | 0.000344933223430877 | | 241 | 1.4768 | 1.47515651154851 | 0.00164348845148976 | | 242 | 1.473 | 1.47470670506084 | -0.00170670506083592 | | 243 | 1.4757 | 1.47079392050888 | 0.00490607949112243 | | 244 | 1.4647 | 1.47388323538011 | -0.0091832353801129 | | 245 | 1.4541 | 1.46219143737079 | -0.00809143737078966 | | 246 | 1.456 | 1.4506904969917 | 0.00530950300830346 | | 247 | 1.4343 | 1.45287710319249 | -0.0185771031924944 | | 248 | 1.4337 | 1.42967806776953 | 0.00402193223046732 | | 249 | 1.4368 | 1.42902661036227 | 0.00777338963773366 | | 250 | 1.4279 | 1.43288857115018 | -0.00498857115017648 | | 251 | 1.4276 | 1.42372297891385 | 0.00387702108614518 | | 252 | 1.4398 | 1.42365210513558 | 0.016147894864416 | | 253 | 1.4405 | 1.43733833996786 | 0.00316166003213514 | | 254 | 1.4433 | 1.43866134665098 | 0.00463865334902125 | | 255 | 1.4338 | 1.44193246739213 | -0.00813246739212636 | | 256 | 1.4406 | 1.43182616827822 | 0.00877383172178203 | | 257 | 1.4389 | 1.43921279711335 | -0.000312797113352081 | | 258 | 1.4442 | 1.43767492194167 | 0.00652507805833147 | | 259 | 1.435 | 1.44353493462601 | -0.00853493462601285 | | 260 | 1.4304 | 1.43373437696102 | -0.00333437696102257 | | 261 | 1.4273 | 1.42866061669899 | -0.00136061669899035 | | 262 | 1.4528 | 1.4253704963403 | 0.0274295036597032 | | 263 | 1.4481 | 1.45322363831217 | -0.00512363831217244 | | 264 | 1.4563 | 1.44867039187517 | 0.00762960812482683 | | 265 | 1.4486 | 1.45742254970144 | -0.00882254970144203 | | 266 | 1.4374 | 1.44912084016513 | -0.0117208401651312 | | 267 | 1.4369 | 1.43671243551615 | 0.000187564483850045 | | 268 | 1.4279 | 1.43597585187043 | -0.00807585187043136 | | 269 | 1.4132 | 1.42627843877318 | -0.0130784387731755 | | 270 | 1.4064 | 1.41026822446426 | -0.00386822446425628 | | 271 | 1.4135 | 1.40285006939296 | 0.0106499306070391 | | 272 | 1.4151 | 1.41079165452564 | 0.00430834547435843 | | 273 | 1.4085 | 1.41299564334852 | -0.00449564334851993 | | 274 | 1.4072 | 1.40609810850257 | 0.00110189149743145 | | 275 | 1.3999 | 1.40479682480558 | -0.00489682480557896 | | 276 | 1.3966 | 1.39709526502826 | -0.000495265028256142 | | 277 | 1.3913 | 1.39364659861313 | -0.0023465986131308 | | 278 | 1.3937 | 1.38813209032633 | 0.00556790967367471 | | 279 | 1.3984 | 1.3909650854491 | 0.00743491455090428 | | 280 | 1.3847 | 1.39643100087816 | -0.011731000878163 | | 281 | 1.3691 | 1.3818724659303 | -0.0127724659303028 | | 282 | 1.3675 | 1.36490996882364 | 0.00259003117635515 | | 283 | 1.376 | 1.36325937217873 | 0.0127406278212703 | | 284 | 1.374 | 1.37292188886933 | 0.00107811113066814 | | 285 | 1.3718 | 1.37129040949127 | 0.000509590508725788 | | 286 | 1.3572 | 1.36915793205161 | -0.0119579320516128 | | 287 | 1.3607 | 1.35353027332355 | 0.00716972667645077 | | 288 | 1.3649 | 1.35739503752487 | 0.00750496247513177 | | 289 | 1.3726 | 1.3624015961924 | 0.0101984038075975 | | 290 | 1.3567 | 1.37114933692515 | -0.014449336925149 | | 291 | 1.3519 | 1.3542143120927 | -0.00231431209269894 | | 292 | 1.3626 | 1.34890155125848 | 0.0136984487415173 | | 293 | 1.3577 | 1.36074145280046 | -0.00304145280046253 | | 294 | 1.3547 | 1.35587281738503 | -0.00117281738502673 | | 295 | 1.3489 | 1.35270532886489 | -0.00380532886489449 | | 296 | 1.357 | 1.34654949875765 | 0.0104505012423477 | | 297 | 1.3525 | 1.35547511863382 | -0.00297511863382005 | | 298 | 1.3548 | 1.35094217097292 | 0.00385782902707699 | | 299 | 1.3641 | 1.3535130701164 | 0.0105869298835981 | | 300 | 1.3668 | 1.36381587147053 | 0.00298412852947028 | | 301 | 1.3582 | 1.36700348100895 | -0.00880348100894945 | | 302 | 1.3662 | 1.35770320226264 | 0.00849679773735823 | | 303 | 1.3557 | 1.3662512912112 | -0.0105512912111989 | | 304 | 1.361 | 1.35501813453468 | 0.00598186546531543 | | 305 | 1.3657 | 1.3606100704503 | 0.00508992954969534 | | 306 | 1.3765 | 1.3658812340462 | 0.0106187659537962 | | 307 | 1.3705 | 1.37771338302317 | -0.00721338302316554 | | 308 | 1.3723 | 1.37131593457951 | 0.00098406542048668 | | 309 | 1.3756 | 1.37304578182812 | 0.00255421817188006 | | 310 | 1.366 | 1.37658886951762 | -0.0105888695176195 | | 311 | 1.3548 | 1.36612423860488 | -0.0113242386048844 | | 312 | 1.3471 | 1.3537121742652 | -0.00661217426520144 | | 313 | 1.3519 | 1.34519352927201 | 0.00670647072798847 | | 314 | 1.3338 | 1.35043338945049 | -0.0166333894504851 | | 315 | 1.3356 | 1.33103332226414 | 0.00456667773586461 | | 316 | 1.3353 | 1.33287111618327 | 0.00242888381672968 | | 317 | 1.3471 | 1.33288061176667 | 0.0142193882333319 | | 318 | 1.3482 | 1.34596809526053 | 0.00223190473946744 | | 319 | 1.3479 | 1.34756873717397 | 0.000331262826031686 | | 320 | 1.3468 | 1.34734566330111 | -0.000545663301114496 | | 321 | 1.3396 | 1.34620541451977 | -0.00660541451977226 | | 322 | 1.334 | 1.33841990274791 | -0.00441990274791171 | | 323 | 1.3296 | 1.33229348398303 | -0.00269348398302816 | | 324 | 1.3384 | 1.32756417216237 | 0.010835827837631 | | 325 | 1.3585 | 1.33724724896997 | 0.0212527510300342 | | 326 | 1.3583 | 1.35942702126341 | -0.00112702126340625 | | 327 | 1.3615 | 1.35958765419462 | 0.00191234580538135 | | 328 | 1.3544 | 1.3629294431784 | -0.00852944317840176 | | 329 | 1.3535 | 1.35512984351738 | -0.00162984351738094 | | 330 | 1.3432 | 1.35390425566652 | -0.010704255666518 | | 331 | 1.3486 | 1.34263933196066 | 0.00596066803933826 | | 332 | 1.3373 | 1.34832612650654 | -0.0110261265065441 | | 333 | 1.3339 | 1.33619700954733 | -0.00229700954733425 | | 334 | 1.3311 | 1.33235960682315 | -0.00125960682314608 | | 335 | 1.3321 | 1.32940064111296 | 0.00269935888704476 | | 336 | 1.329 | 1.33060792869033 | -0.00160792869032655 | | 337 | 1.3245 | 1.32742650398681 | -0.00292650398681404 | | 338 | 1.3256 | 1.32263762020097 | 0.00296237979902503 | | 339 | 1.3315 | 1.32393179044499 | 0.00756820955501447 | | 340 | 1.3238 | 1.33055306983444 | -0.00675306983443513 | | 341 | 1.3089 | 1.32242978841982 | -0.0135297884198216 | | 342 | 1.2924 | 1.30620890918368 | -0.0138089091836782 | | 343 | 1.2727 | 1.28821757917537 | -0.0155175791753717 | | 344 | 1.2746 | 1.26687181395008 | 0.00772818604992165 | | 345 | 1.2969 | 1.26910828649924 | 0.0277917135007584 | | 346 | 1.2698 | 1.29398897912517 | -0.0241889791251666 | | 347 | 1.2686 | 1.26538755239612 | 0.00321244760388462 | | 348 | 1.2587 | 1.26394470868248 | -0.00524470868248339 | | 349 | 1.2492 | 1.25365846700537 | -0.00445846700537111 | | 350 | 1.2349 | 1.24365805560645 | -0.0087580556064506 | | 351 | 1.2428 | 1.2285011496264 | 0.0142988503736021 | | 352 | 1.227 | 1.23745417864677 | -0.0104541786467702 | | 353 | 1.2334 | 1.2210546354413 | 0.0123453645586975 | | 354 | 1.2497 | 1.22830139320409 | 0.0213986067959098 | | 355 | 1.236 | 1.2467264023906 | -0.0107264023906009 | | 356 | 1.2223 | 1.23255639025963 | -0.0102563902596327 | | 357 | 1.2309 | 1.21773411082372 | 0.0131658891762751 | | 358 | 1.2255 | 1.22725640572217 | -0.00175640572217373 | | 359 | 1.2384 | 1.22198789821876 | 0.016412101781236 | | 360 | 1.2307 | 1.2362755414758 | -0.00557554147579609 | | 361 | 1.2155 | 1.2284453444949 | -0.0129453444948979 | | 362 | 1.2218 | 1.21200063441714 | 0.0097993655828641 | | 363 | 1.2268 | 1.2188725029448 | 0.00792749705520257 | | 364 | 1.206 | 1.22477249655793 | -0.018772496557935 | | 365 | 1.1959 | 1.20251297229056 | -0.00661297229055857 | | 366 | 1.1942 | 1.19143356298081 | 0.00276643701918711 | | 367 | 1.201 | 1.18983117886924 | 0.0111688211307583 | | 368 | 1.2045 | 1.19766097605671 | 0.00683902394328606 | | 369 | 1.2127 | 1.20199597186024 | 0.0107040281397597 | | 370 | 1.2249 | 1.21127326305669 | 0.0136267369433052 | | 371 | 1.2258 | 1.22488780444466 | 0.000912195555339057 | | 372 | 1.2277 | 1.2261610314847 | 0.00153896851530355 | | 373 | 1.2363 | 1.22821438510437 | 0.0080856148956252 | | 374 | 1.2372 | 1.237549895887 | -0.000349895886998963 | | 375 | 1.2391 | 1.23859395018547 | 0.000506049814531506 | | 376 | 1.2258 | 1.24053035617677 | -0.0147303561767709 | | 377 | 1.2271 | 1.22596181129345 | 0.00113818870655313 | | 378 | 1.2262 | 1.22704286800359 | -0.000842868003585462 | | 379 | 1.2294 | 1.22609421364249 | 0.00330578635751344 | | 380 | 1.2339 | 1.22956316592989 | 0.0043368340701071 | | 381 | 1.2198 | 1.23451118047737 | -0.0147111804773725 | | 382 | 1.2271 | 1.21922694974603 | 0.00787305025397167 | | 383 | 1.2328 | 1.22689340296935 | 0.00590659703065222 | | 384 | 1.2548 | 1.23327630343682 | 0.0215236965631829 | | 385 | 1.2531 | 1.25727326238259 | -0.00417326238258608 | | 386 | 1.2579 | 1.2556751477076 | 0.00222485229240066 | | 387 | 1.2567 | 1.26057835849142 | -0.00387835849142237 | | 388 | 1.266 | 1.25908948930182 | 0.00691051069818394 | | 389 | 1.2637 | 1.26890605381968 | -0.00520605381967676 | | 390 | 1.2572 | 1.26630295479534 | -0.00910295479533496 | | 391 | 1.2569 | 1.25889996217557 | -0.00199996217557441 | | 392 | 1.2703 | 1.25822985279431 | 0.0120701472056941 | | 393 | 1.2828 | 1.27263510387374 | 0.0101648961262568 | | 394 | 1.3 | 1.28627842731235 | 0.013721572687647 | | 395 | 1.2957 | 1.30488957434174 | -0.00918957434174361 | | 396 | 1.2844 | 1.30008741862463 | -0.0156874186246301 | | 397 | 1.2817 | 1.28722656275526 | -0.00552656275526275 | | 398 | 1.285 | 1.28370807787856 | 0.00129192212143803 | | 399 | 1.2897 | 1.28700105811131 | 0.00269894188869135 | | 400 | 1.2931 | 1.29196335830675 | 0.00113664169325323 | | 401 | 1.3033 | 1.29552031502598 | 0.00777968497401504 | | 402 | 1.2992 | 1.30642057292773 | -0.00722057292772837 | | 403 | 1.3069 | 1.30186124724843 | 0.00503875275156851 | | 404 | 1.3028 | 1.30984312513855 | -0.0070431251385501 | | 405 | 1.3073 | 1.30524007719838 | 0.00205992280162315 | | 406 | 1.3221 | 1.30976704554444 | 0.0123329544555566 | | 407 | 1.3206 | 1.32568271516147 | -0.00508271516146896 | | 408 | 1.3184 | 1.32400731757614 | -0.00560731757613864 | | 409 | 1.3176 | 1.32121061324227 | -0.00361061324227285 | | 410 | 1.3253 | 1.31997602227535 | 0.00532397772464677 | | 411 | 1.3133 | 1.32806055881446 | -0.0147605588144564 | | 412 | 1.3016 | 1.31489333660411 | -0.0132933366041053 | | 413 | 1.279 | 1.30172023499439 | -0.0227202349943947 | | 414 | 1.2799 | 1.27685997826122 | 0.00304002173878004 | | 415 | 1.282 | 1.27753384574817 | 0.00446615425182784 | | 416 | 1.286 | 1.28008735907687 | 0.00591264092312938 | | 417 | 1.288 | 1.28469728126167 | 0.00330271873832588 | | 418 | 1.2836 | 1.28711171614798 | -0.00351171614798185 | | 419 | 1.2711 | 1.28247794791642 | -0.0113779479164251 | | 420 | 1.2704 | 1.26891390692151 | 0.00148609307848924 | | 421 | 1.2611 | 1.26809750991379 | -0.00699750991379244 | | 422 | 1.2613 | 1.25822177598573 | 0.00307822401427416 | | 423 | 1.2693 | 1.25853817701672 | 0.0107618229832829 | | 424 | 1.2713 | 1.26753934954033 | 0.00376065045967189 | | 425 | 1.27 | 1.27009818022626 | -9.8180226257849e-05 | | 426 | 1.268 | 1.2688707878436 | -0.000870787843595178 | | 427 | 1.28 | 1.26679303392891 | 0.0132069660710949 | | 428 | 1.2818 | 1.27992138962693 | 0.00187861037306924 | | 429 | 1.2834 | 1.28216950192338 | 0.0012304980766229 | | 430 | 1.2874 | 1.28391691238251 | 0.00348308761749405 | | 431 | 1.2744 | 1.28824599741492 | -0.0138459974149185 | | 432 | 1.2697 | 1.27411849610375 | -0.00441849610374745 | | 433 | 1.2715 | 1.26873598507443 | 0.00276401492557077 | | 434 | 1.2725 | 1.27068073606309 | 0.00181926393691412 | | 435 | 1.2801 | 1.27189838855378 | 0.00820161144621556 | | 436 | 1.285 | 1.28025002200142 | 0.0047499779985789 | | 437 | 1.2989 | 1.28573954844525 | 0.013160451554747 | | 438 | 1.3078 | 1.30088513108696 | 0.00691486891303783 | | 439 | 1.306 | 1.31066968381769 | -0.00466968381769184 | | 440 | 1.3074 | 1.30861326734026 | -0.00121326734025584 | | 441 | 1.312 | 1.30980713655105 | 0.00219286344895497 | | 442 | 1.3364 | 1.31457143024877 | 0.0218285697512302 | | 443 | 1.3323 | 1.34091474692895 | -0.00861474692894504 | | 444 | 1.3412 | 1.33653742729437 | 0.00466257270563419 | | 445 | 1.3477 | 1.34565655150584 | 0.00204344849415894 | | 446 | 1.346 | 1.35243463751237 | -0.0064346375123654 | | 447 | 1.3611 | 1.35021981892915 | 0.0108801810708457 | | 448 | 1.3648 | 1.36612603340815 | -0.00132603340815396 | | 449 | 1.3726 | 1.3699455937841 | 0.00265440621590085 | | 450 | 1.3705 | 1.37794754367782 | -0.00744754367781586 | | 451 | 1.378 | 1.37525792647633 | 0.00274207352366962 | | 452 | 1.3856 | 1.38283542043064 | 0.00276457956935916 | | 453 | 1.397 | 1.39073470863393 | 0.00626529136606813 | | 454 | 1.3874 | 1.40273855044759 | -0.0153385504475889 | | 455 | 1.3936 | 1.39194143320286 | 0.00165856679713783 | | 456 | 1.3833 | 1.39795456769564 | -0.0146545676956358 | | 457 | 1.3958 | 1.38641747109166 | 0.00938252890834268 | | 458 | 1.4101 | 1.3994162574126 | 0.0106837425874022 | | 459 | 1.4089 | 1.41484666234987 | -0.00594666234987207 | | 460 | 1.3896 | 1.41336064175658 | -0.0237606417565761 | | 461 | 1.3859 | 1.39186851976418 | -0.00596851976417567 | | 462 | 1.3861 | 1.38713746845202 | -0.00103746845201913 | | 463 | 1.4016 | 1.38711858518189 | 0.0144814148181143 | | 464 | 1.3934 | 1.40385404201362 | -0.0104540420136234 | | 465 | 1.4031 | 1.39505844947531 | 0.00804155052468714 | | 466 | 1.3912 | 1.405231385547 | -0.0140313855469969 | | 467 | 1.3803 | 1.39228612974748 | -0.0119861297474786 | | 468 | 1.3857 | 1.38004230251282 | 0.00565769748717582 | | 469 | 1.3857 | 1.38567512513085 | 2.48748691498157e-05 | | 470 | 1.3926 | 1.38579934967393 | 0.0068006503260738 | | 471 | 1.4018 | 1.39329058348807 | 0.00850941651193327 | | 472 | 1.4014 | 1.40337642518388 | -0.00197642518388186 | | 473 | 1.4244 | 1.40298834435787 | 0.0214116556421315 | | 474 | 1.4084 | 1.42780549657833 | -0.0194054965783284 | | 475 | 1.3917 | 1.41058190922632 | -0.0188819092263171 | | 476 | 1.3945 | 1.39182317642811 | 0.00267682357189125 | | 477 | 1.377 | 1.39444830819293 | -0.0174483081929262 | | 478 | 1.37 | 1.37549051903728 | -0.00549051903727782 | | 479 | 1.3711 | 1.36763717396184 | 0.00346282603815751 | | 480 | 1.3626 | 1.36891949420183 | -0.00631949420183364 | | 481 | 1.3612 | 1.35994529969084 | 0.00125470030916053 | | 482 | 1.3481 | 1.35851793950517 | -0.0104179395051716 | | 483 | 1.3647 | 1.34454011849398 | 0.020159881506016 | | 484 | 1.3674 | 1.36266641861307 | 0.00473358138692537 | | 485 | 1.3647 | 1.36621251867201 | -0.00151251867200553 | | 486 | 1.3496 | 1.36348326921206 | -0.0138832692120641 | | 487 | 1.3339 | 1.34714475108812 | -0.0132447510881235 | | 488 | 1.3321 | 1.32999479694988 | 0.00210520305011719 | | 489 | 1.3225 | 1.32809189917908 | -0.00559189917908287 | | 490 | 1.3146 | 1.31805161228225 | -0.00345161228224633 | | 491 | 1.2998 | 1.3097311646165 | -0.0099311646165019 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 492 | 1.29399408638802 | 1.27293570752493 | 1.31505246525112 | | 493 | 1.287973909452 | 1.25687258508591 | 1.3190752338181 | | 494 | 1.28195373251599 | 1.2419428852072 | 1.32196457982477 | | 495 | 1.27593355557997 | 1.22740923090323 | 1.3244578802567 | | 496 | 1.26991337864395 | 1.21300163015482 | 1.32682512713307 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/1y1mh1293329583.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/1y1mh1293329583.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/2rb321293329583.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/2rb321293329583.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/3rb321293329583.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/26/t1293329474zmvy5tqb16emd5n/3rb321293329583.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 <- 5
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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