| Exponential Smoothing | | *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: Tue, 14 Dec 2010 14:19:11 +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/14/t1292336278r7iwkh5a7dkf82c.htm/, Retrieved Tue, 14 Dec 2010 15:17:58 +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/14/t1292336278r7iwkh5a7dkf82c.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 | 0.994202437987405 | | beta | FALSE | | gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 2 | 1.3582 | 1.3866 | -0.0284 | | 3 | 1.3332 | 1.35836465076116 | -0.0251646507611578 | | 4 | 1.3595 | 1.33334589362331 | 0.0261541063766868 | | 5 | 1.3617 | 1.35934836994640 | 0.00235163005360284 | | 6 | 1.3684 | 1.36168636627893 | 0.0067136337210667 | | 7 | 1.3394 | 1.36836107729217 | -0.0289610772921725 | | 8 | 1.3262 | 1.33956790364155 | -0.0133679036415528 | | 9 | 1.3173 | 1.32627750125034 | -0.00897750125034036 | | 10 | 1.3085 | 1.31735204762022 | -0.00885204762021696 | | 11 | 1.327 | 1.30855132029502 | 0.0184486797049832 | | 12 | 1.3182 | 1.32689304263536 | -0.00869304263535975 | | 13 | 1.293 | 1.31825039845376 | -0.0252503984537567 | | 14 | 1.291 | 1.29314639075088 | -0.0021463907508783 | | 15 | 1.2984 | 1.29101244383348 | 0.00738755616651865 | | 16 | 1.2795 | 1.29835717018500 | -0.0188571701850031 | | 17 | 1.299 | 1.27960932561353 | 0.0193906743864702 | | 18 | 1.3174 | 1.29888758136278 | 0.0185124186372216 | | 19 | 1.326 | 1.31729267310495 | 0.0087073268950526 | | 20 | 1.3111 | 1.32594951873236 | -0.0148495187323621 | | 21 | 1.2816 | 1.31118609100571 | -0.029586091005708 | | 22 | 1.276 | 1.28177152719732 | -0.005771527197316 | | 23 | 1.2849 | 1.27603346078683 | 0.00886653921316616 | | 24 | 1.2818 | 1.28484859568907 | -0.00304859568907445 | | 25 | 1.2829 | 1.28181767442256 | 0.00108232557744103 | | 26 | 1.2796 | 1.28289372515035 | -0.00329372515034687 | | 27 | 1.3008 | 1.27961909557581 | 0.0211809044241884 | | 28 | 1.2967 | 1.30067720239312 | -0.00397720239311794 | | 29 | 1.2938 | 1.29672305807751 | -0.00292305807751059 | | 30 | 1.2833 | 1.29381694661047 | -0.0105169466104706 | | 31 | 1.2823 | 1.28336097265016 | -0.00106097265015737 | | 32 | 1.2765 | 1.28230615105473 | -0.00580615105473292 | | 33 | 1.2634 | 1.27653366152079 | -0.0131336615207942 | | 34 | 1.2596 | 1.26347614321712 | -0.00387614321711927 | | 35 | 1.2705 | 1.25962247218067 | 0.0108775278193289 | | 36 | 1.2591 | 1.27043693685792 | -0.0113369368579235 | | 37 | 1.2798 | 1.25916572659447 | 0.0206342734055334 | | 38 | 1.2763 | 1.27968037152035 | -0.00338037152034665 | | 39 | 1.2795 | 1.27631959791351 | 0.00318040208648518 | | 40 | 1.2782 | 1.27948156142168 | -0.00128156142167879 | | 41 | 1.2644 | 1.27820742993182 | -0.0138074299318152 | | 42 | 1.2596 | 1.26448004943126 | -0.00488004943126419 | | 43 | 1.2615 | 1.25962829238920 | 0.00187170761079769 | | 44 | 1.2555 | 1.26148914865906 | -0.00598914865905686 | | 45 | 1.2555 | 1.25553472246075 | -3.47224607535335e-05 | | 46 | 1.2658 | 1.25550020130562 | 0.0102997986943805 | | 47 | 1.2565 | 1.26574028627835 | -0.00924028627835227 | | 48 | 1.2783 | 1.25655357113271 | 0.0217464288672871 | | 49 | 1.2786 | 1.27817392373009 | 0.000426076269910647 | | 50 | 1.2782 | 1.27859752979640 | -0.000397529796402951 | | 51 | 1.2905 | 1.27820230470365 | 0.0122976952963534 | | 52 | 1.3042 | 1.29042870334891 | 0.0137712966510926 | | 53 | 1.2942 | 1.30412016005367 | -0.00992016005367136 | | 54 | 1.313 | 1.29425751274309 | 0.0187424872569140 | | 55 | 1.3671 | 1.31289133926786 | 0.0542086607321424 | | 56 | 1.3549 | 1.36678572192779 | -0.0118857219277857 | | 57 | 1.3558 | 1.35496890820994 | 0.000831091790059135 | | 58 | 1.3507 | 1.35579518169381 | -0.00509518169380896 | | 59 | 1.3494 | 1.35072953963184 | -0.00132953963183535 | | 60 | 1.3607 | 1.34940770808846 | 0.0112922919115364 | | 61 | 1.3295 | 1.36063453223738 | -0.0311345322373786 | | 62 | 1.3193 | 1.32968050438138 | -0.0103805043813794 | | 63 | 1.3308 | 1.31936018161787 | 0.0114398183821269 | | 64 | 1.3246 | 1.33073367694352 | -0.00613367694351674 | | 65 | 1.3392 | 1.32463556037245 | 0.0145644396275546 | | 66 | 1.3425 | 1.33911556175808 | 0.00338443824191947 | | 67 | 1.3496 | 1.34248037850941 | 0.00711962149058532 | | 68 | 1.3255 | 1.34955872355290 | -0.0240587235529022 | | 69 | 1.3231 | 1.32563948194174 | -0.00253948194174169 | | 70 | 1.3273 | 1.32311472280404 | 0.00418527719596296 | | 71 | 1.3276 | 1.32727573559592 | 0.000324264404083507 | | 72 | 1.3173 | 1.32759812005701 | -0.0102981200570089 | | 73 | 1.3196 | 1.31735970398964 | 0.00224029601035647 | | 74 | 1.3058 | 1.31958701174495 | -0.0137870117449534 | | 75 | 1.2966 | 1.30587993105556 | -0.0092799310555598 | | 76 | 1.2932 | 1.29665380097577 | -0.00345380097576720 | | 77 | 1.2947 | 1.29322002362534 | 0.00147997637466379 | | 78 | 1.305 | 1.29469141974519 | 0.0103085802548093 | | 79 | 1.3232 | 1.30494023536671 | 0.0182597646332892 | | 80 | 1.3125 | 1.32309413788220 | -0.0105941378822030 | | 81 | 1.2992 | 1.31256142017134 | -0.0133614201713421 | | 82 | 1.3266 | 1.29927746366202 | 0.0273225363379803 | | 83 | 1.3275 | 1.32644159590124 | 0.00105840409876068 | | 84 | 1.3223 | 1.32749386383660 | -0.00519386383660292 | | 85 | 1.3403 | 1.32233011174768 | 0.0179698882523223 | | 86 | 1.3322 | 1.34019581845850 | -0.00799581845849784 | | 87 | 1.3363 | 1.33224635625335 | 0.00405364374664541 | | 88 | 1.3425 | 1.33627649874900 | 0.00622350125099813 | | 89 | 1.3574 | 1.34246391886556 | 0.0149360811344381 | | 90 | 1.3683 | 1.35731340714340 | 0.0109865928566022 | | 91 | 1.3623 | 1.36823630454661 | -0.00593630454660676 | | 92 | 1.3563 | 1.36233441609373 | -0.00603441609373467 | | 93 | 1.3518 | 1.35633498490151 | -0.00453498490151349 | | 94 | 1.3494 | 1.35182629185619 | -0.00242629185619259 | | 95 | 1.3612 | 1.34941406657750 | 0.011785933422503 | | 96 | 1.369 | 1.36113167032011 | 0.00786832967989337 | | 97 | 1.3771 | 1.36895438287075 | 0.00814561712925466 | | 98 | 1.3972 | 1.37705277527956 | 0.0201472247204377 | | 99 | 1.401 | 1.39708319521530 | 0.00391680478469847 | | 100 | 1.3908 | 1.40097729208137 | -0.0101772920813694 | | 101 | 1.3901 | 1.39085900348196 | -0.000759003481962228 | | 102 | 1.3856 | 1.39010440036975 | -0.0045044003697543 | | 103 | 1.4098 | 1.38562611454047 | 0.0241738854595268 | | 104 | 1.422 | 1.40965985039996 | 0.0123401496000370 | | 105 | 1.4238 | 1.42192845721745 | 0.00187154278255086 | | 106 | 1.4207 | 1.42378914961466 | -0.00308914961465878 | | 107 | 1.4095 | 1.42071790953646 | -0.0112179095364573 | | 108 | 1.4177 | 1.40956503652619 | 0.0081349634738106 | | 109 | 1.3866 | 1.41765283704479 | -0.0310528370447902 | | 110 | 1.3959 | 1.38678003074843 | 0.00911996925156577 | | 111 | 1.4102 | 1.39584712641271 | 0.0143528735872889 | | 112 | 1.3969 | 1.41011678832532 | -0.0132167883253187 | | 113 | 1.4004 | 1.39697662514992 | 0.00342337485007671 | | 114 | 1.385 | 1.40038015277201 | -0.0153801527720143 | | 115 | 1.389 | 1.38508916738946 | 0.00391083261054104 | | 116 | 1.384 | 1.38897732670542 | -0.00497732670541962 | | 117 | 1.392 | 1.38402885636023 | 0.00797114363976847 | | 118 | 1.3932 | 1.39195378680044 | 0.00124621319956297 | | 119 | 1.3858 | 1.39319277500169 | -0.00739277500169466 | | 120 | 1.3978 | 1.38584286007152 | 0.0119571399284826 | | 121 | 1.4029 | 1.39773067773977 | 0.0051693222602287 | | 122 | 1.394 | 1.40287003053363 | -0.00887003053363333 | | 123 | 1.4096 | 1.39405142455207 | 0.0155485754479276 | | 124 | 1.4058 | 1.40950985616963 | -0.00370985616963315 | | 125 | 1.4134 | 1.4058215081212 | 0.00757849187879889 | | 126 | 1.4096 | 1.41335606322337 | -0.00375606322337085 | | 127 | 1.4049 | 1.40962177600946 | -0.00472177600946067 | | 128 | 1.4009 | 1.40492737478922 | -0.00402737478922433 | | 129 | 1.3897 | 1.40092334895509 | -0.0112233489550886 | | 130 | 1.4019 | 1.38976506806156 | 0.0121349319384438 | | 131 | 1.3901 | 1.40182964697957 | -0.0117296469795682 | | 132 | 1.399 | 1.39016800335575 | 0.00883199664425027 | | 133 | 1.3901 | 1.39894879595176 | -0.00884879595176002 | | 134 | 1.3975 | 1.39015130144327 | 0.00734869855673304 | | 135 | 1.3991 | 1.39745739546441 | 0.00164260453559462 | | 136 | 1.4089 | 1.39909047689834 | 0.00980952310165728 | | 137 | 1.413 | 1.40884312868150 | 0.00415687131849585 | | 138 | 1.409 | 1.41297590028075 | -0.00397590028075268 | | 139 | 1.4217 | 1.40902305052843 | 0.0126769494715664 | | 140 | 1.4223 | 1.42162650459931 | 0.000673495400691948 | | 141 | 1.4191 | 1.42229609536865 | -0.00319609536864918 | | 142 | 1.4229 | 1.41911852956110 | 0.00378147043890209 | | 143 | 1.4227 | 1.42287807669063 | -0.000178076690631634 | | 144 | 1.4269 | 1.42270103241066 | 0.00419896758934302 | | 145 | 1.4229 | 1.42687565622501 | -0.00397565622501195 | | 146 | 1.4104 | 1.42292304911351 | -0.0125230491135053 | | 147 | 1.4053 | 1.41047260315382 | -0.0051726031538224 | | 148 | 1.4138 | 1.40532998848755 | 0.0084700115124492 | | 149 | 1.4303 | 1.41375089458301 | 0.0165491054169908 | | 150 | 1.4384 | 1.43020405553509 | 0.00819594446490801 | | 151 | 1.441 | 1.43835248350371 | 0.00264751649628714 | | 152 | 1.437 | 1.44098465085893 | -0.0039846508589334 | | 153 | 1.4357 | 1.43702310126045 | -0.00132310126045332 | | 154 | 1.4202 | 1.43570767076161 | -0.0155076707616064 | | 155 | 1.4166 | 1.42028990668291 | -0.00368990668291125 | | 156 | 1.417 | 1.41662139246282 | 0.000378607537184994 | | 157 | 1.4293 | 1.41699780499932 | 0.0123021950006752 | | 158 | 1.4294 | 1.42922867726159 | 0.000171322738407476 | | 159 | 1.4072 | 1.4293990067458 | -0.0221990067458 | | 160 | 1.4101 | 1.40732870011823 | 0.00277129988177305 | | 161 | 1.4112 | 1.41008393321708 | 0.0011160667829202 | | 162 | 1.4243 | 1.41119352953362 | 0.0131064704663841 | | 163 | 1.433 | 1.42422401442470 | 0.00877598557529535 | | 164 | 1.4323 | 1.43294912067941 | -0.000649120679405701 | | 165 | 1.4324 | 1.43230376331739 | 9.62366826073868e-05 | | 166 | 1.427 | 1.43239944206186 | -0.0053994420618646 | | 167 | 1.4268 | 1.42703130360019 | -0.000231303600187083 | | 168 | 1.4364 | 1.42680134099697 | 0.00959865900303392 | | 169 | 1.4272 | 1.43634435117919 | -0.00914435117919199 | | 170 | 1.4314 | 1.42725301494303 | 0.00414698505697375 | | 171 | 1.422 | 1.43137595759697 | -0.00937595759696697 | | 172 | 1.4335 | 1.42205435769560 | 0.0114456423044043 | | 173 | 1.4262 | 1.43343364317897 | -0.00723364317896635 | | 174 | 1.433 | 1.42624193749491 | 0.00675806250509314 | | 175 | 1.4473 | 1.43296081971354 | 0.0143391802864583 | | 176 | 1.4522 | 1.44721686771308 | 0.00498313228692049 | | 177 | 1.4545 | 1.45217110998155 | 0.00232889001845038 | | 178 | 1.4594 | 1.45448649811570 | 0.00491350188430251 | | 179 | 1.4561 | 1.45937151366813 | -0.00327151366812695 | | 180 | 1.4611 | 1.45611896680337 | 0.00498103319663401 | | 181 | 1.4671 | 1.46107112215116 | 0.0060288778488442 | | 182 | 1.4712 | 1.46706504720680 | 0.00413495279319509 | | 183 | 1.4705 | 1.47117602735476 | -0.000676027354762354 | | 184 | 1.4658 | 1.47050391931051 | -0.00470391931051140 | | 185 | 1.478 | 1.46582727126390 | 0.0121727287360951 | | 186 | 1.4783 | 1.47792942785029 | 0.000370572149710036 | | 187 | 1.4768 | 1.47829785158498 | -0.00149785158498195 | | 188 | 1.467 | 1.47680868388745 | -0.00980868388744938 | | 189 | 1.465 | 1.4670568664531 | -0.00205686645309933 | | 190 | 1.4549 | 1.46501192481081 | -0.0101119248108135 | | 191 | 1.4643 | 1.45495862451116 | 0.0093413754888425 | | 192 | 1.4539 | 1.46424584279632 | -0.0103458427963206 | | 193 | 1.4537 | 1.45395998066518 | -0.000259980665184179 | | 194 | 1.4616 | 1.45370150725403 | 0.00789849274597154 | | 195 | 1.4722 | 1.4615542079985 | 0.0106457920015008 | | 196 | 1.4694 | 1.47213828036070 | -0.00273828036069812 | | 197 | 1.4763 | 1.4694158753502 | 0.00688412464980082 | | 198 | 1.475 | 1.47626008886044 | -0.00126008886044016 | | 199 | 1.4765 | 1.47500730544331 | 0.00149269455668999 | | 200 | 1.4864 | 1.47649134601074 | 0.00990865398925833 | | 201 | 1.4881 | 1.48634255396404 | 0.00175744603596417 | | 202 | 1.4864 | 1.48808981109762 | -0.00168981109762267 | | 203 | 1.4869 | 1.48640979678463 | 0.000490203215372187 | | 204 | 1.4918 | 1.48689715801646 | 0.00490284198353974 | | 205 | 1.4971 | 1.49177157546956 | 0.00532842453043769 | | 206 | 1.4921 | 1.49706910812836 | -0.00496910812835538 | | 207 | 1.5 | 1.49212880871252 | 0.00787119128747849 | | 208 | 1.502 | 1.49995436628040 | 0.00204563371960220 | | 209 | 1.5019 | 1.50198814031166 | -8.81403116554935e-05 | | 210 | 1.4874 | 1.50190051099892 | -0.0145005109989227 | | 211 | 1.4785 | 1.48748406761173 | -0.00898406761173076 | | 212 | 1.4788 | 1.47855208568910 | 0.000247914310895547 | | 213 | 1.48 | 1.47879856270141 | 0.00120143729859135 | | 214 | 1.4772 | 1.47999303459276 | -0.00279303459275715 | | 215 | 1.4658 | 1.47721619279125 | -0.0114161927912548 | | 216 | 1.4761 | 1.46586618608565 | 0.0102338139143450 | | 217 | 1.4867 | 1.47604066882921 | 0.0106593311707937 | | 218 | 1.4862 | 1.48663820186652 | -0.000438201866524546 | | 219 | 1.4984 | 1.48620254050250 | 0.0121974594975047 | | 220 | 1.4966 | 1.49832928447217 | -0.00172928447216703 | | 221 | 1.5037 | 1.49661002563396 | 0.00708997436603531 | | 222 | 1.4922 | 1.50365889543395 | -0.0114588954339452 | | 223 | 1.4868 | 1.49226643365687 | -0.00546643365687416 | | 224 | 1.4965 | 1.48683169198811 | 0.00966830801188667 | | 225 | 1.4875 | 1.49644394738474 | -0.00894394738474413 | | 226 | 1.4957 | 1.4875518530896 | 0.00814814691039945 | | 227 | 1.4863 | 1.495652760613 | -0.00935276061299928 | | 228 | 1.4815 | 1.48635422320964 | -0.00485422320964268 | | 229 | 1.4968 | 1.48152814266008 | 0.0152718573399191 | | 230 | 1.4969 | 1.49671146046002 | 0.000188539539975663 | | 231 | 1.5083 | 1.49689890693033 | 0.0114010930696749 | | 232 | 1.5071 | 1.50823390145592 | -0.00113390145591707 | | 233 | 1.4918 | 1.50710657386401 | -0.0153065738640070 | | 234 | 1.5023 | 1.49188874081118 | 0.0104112591888230 | | 235 | 1.5074 | 1.50223964007922 | 0.00516035992077657 | | 236 | 1.509 | 1.50737008249335 | 0.00162991750664787 | | 237 | 1.512 | 1.50899055045218 | 0.00300944954782034 | | 238 | 1.5068 | 1.51198255252962 | -0.00518255252962274 | | 239 | 1.4787 | 1.50683004616967 | -0.0281300461696741 | | 240 | 1.4774 | 1.47886308568709 | -0.00146308568708564 | | 241 | 1.4768 | 1.47740848233 | -0.00060848233000077 | | 242 | 1.473 | 1.47680352771404 | -0.00380352771404158 | | 243 | 1.4757 | 1.47302205118779 | 0.00267794881221106 | | 244 | 1.4647 | 1.47568447442569 | -0.0109844744256948 | | 245 | 1.4541 | 1.46476368317166 | -0.0106636831716587 | | 246 | 1.456 | 1.45416182336447 | 0.00183817663552976 | | 247 | 1.4343 | 1.45598934305697 | -0.0216893430569656 | | 248 | 1.4337 | 1.43442574531139 | -0.00072574531138514 | | 249 | 1.4368 | 1.43370420755345 | 0.00309579244655200 | | 250 | 1.4279 | 1.43678205195131 | -0.00888205195131309 | | 251 | 1.4276 | 1.42795149424699 | -0.000351494246986883 | | 252 | 1.4398 | 1.42760203780969 | 0.0121979621903061 | | 253 | 1.4405 | 1.43972928155777 | 0.000770718442225427 | | 254 | 1.4433 | 1.44049553171204 | 0.0028044682879631 | | 255 | 1.4338 | 1.44328374092119 | -0.00948374092118831 | | 256 | 1.4406 | 1.43385498257610 | 0.0067450174238981 | | 257 | 1.4389 | 1.44056089534321 | -0.0016608953432089 | | 258 | 1.4442 | 1.43890962914375 | 0.00529037085625128 | | 259 | 1.435 | 1.44416932874689 | -0.00916932874689103 | | 260 | 1.4304 | 1.43505315975202 | -0.00465315975202407 | | 261 | 1.4273 | 1.43042697698222 | -0.00312697698221664 | | 262 | 1.4528 | 1.42731812884297 | 0.0254818711570337 | | 263 | 1.4481 | 1.45265226727177 | -0.00455226727177038 | | 264 | 1.4563 | 1.44812639205181 | 0.008173607948194 | | 265 | 1.4486 | 1.45625261300105 | -0.00765261300105347 | | 266 | 1.4374 | 1.44864436649843 | -0.0112443664984321 | | 267 | 1.4369 | 1.43746518991207 | -0.000565189912066888 | | 268 | 1.4279 | 1.43690327672356 | -0.00900327672356416 | | 269 | 1.4132 | 1.42795219705512 | -0.0147521970551214 | | 270 | 1.4064 | 1.41328552677725 | -0.00688552677724896 | | 271 | 1.4135 | 1.40643991926848 | 0.00706008073151931 | | 272 | 1.4151 | 1.41345906874415 | 0.00164093125585496 | | 273 | 1.4085 | 1.41509048659929 | -0.00659048659928563 | | 274 | 1.4072 | 1.40853820875475 | -0.00133820875475266 | | 275 | 1.3999 | 1.40720775834824 | -0.00730775834824149 | | 276 | 1.3966 | 1.39994236718220 | -0.00334236718219683 | | 277 | 1.3913 | 1.39661937758101 | -0.00531937758100764 | | 278 | 1.3937 | 1.39133083942139 | 0.00236916057860559 | | 279 | 1.3984 | 1.39368626464463 | 0.00471373535537234 | | 280 | 1.3847 | 1.39837267182697 | -0.0136726718269664 | | 281 | 1.3691 | 1.38477926816279 | -0.0156792681627949 | | 282 | 1.3675 | 1.36919090152949 | -0.00169090152948592 | | 283 | 1.376 | 1.36750980310647 | 0.0084901968935256 | | 284 | 1.374 | 1.37595077755701 | -0.00195077755701045 | | 285 | 1.3718 | 1.37401130975386 | -0.00221130975385986 | | 286 | 1.3572 | 1.37181282020543 | -0.0146128202054270 | | 287 | 1.3607 | 1.35728471873132 | 0.00341528126868029 | | 288 | 1.3649 | 1.36068019969505 | 0.00421980030494562 | | 289 | 1.3726 | 1.36487553544605 | 0.0077244645539487 | | 290 | 1.3567 | 1.37255521693773 | -0.0158552169377344 | | 291 | 1.3519 | 1.35679192160342 | -0.00489192160341956 | | 292 | 1.3626 | 1.35192836121886 | 0.0106716387811434 | | 293 | 1.3577 | 1.36253813051239 | -0.00483813051239035 | | 294 | 1.3547 | 1.35772804936167 | -0.00302804936167056 | | 295 | 1.3489 | 1.35471755530395 | -0.00581755530395145 | | 296 | 1.357 | 1.34893372763764 | 0.00806627236236368 | | 297 | 1.3525 | 1.35695323528577 | -0.00445323528576869 | | 298 | 1.3548 | 1.35252581790773 | 0.00227418209227404 | | 299 | 1.3641 | 1.35478681528829 | 0.00931318471170806 | | 300 | 1.3668 | 1.3640460062341 | 0.00275399376590091 | | 301 | 1.3582 | 1.36678403355036 | -0.00858403355035975 | | 302 | 1.3662 | 1.35824976646683 | 0.00795023353317359 | | 303 | 1.3557 | 1.36615390802808 | -0.010453908028077 | | 304 | 1.361 | 1.35576060718007 | 0.00523939281993324 | | 305 | 1.3657 | 1.36096962429522 | 0.00473037570478185 | | 306 | 1.3765 | 1.36567257535351 | 0.0108274246464914 | | 307 | 1.3705 | 1.37643722733418 | -0.00593722733417534 | | 308 | 1.3723 | 1.37053442144365 | 0.00176557855634729 | | 309 | 1.3756 | 1.37228976394883 | 0.00331023605116831 | | 310 | 1.366 | 1.37558080870122 | -0.0095808087012168 | | 311 | 1.3548 | 1.36605554533258 | -0.0112555453325762 | | 312 | 1.3471 | 1.35486525472205 | -0.00776525472205125 | | 313 | 1.3519 | 1.34714501954579 | 0.00475498045420553 | | 314 | 1.3338 | 1.35187243270595 | -0.0180724327059480 | | 315 | 1.3356 | 1.33390477604933 | 0.00169522395066868 | | 316 | 1.3353 | 1.33559017183402 | -0.000290171834020692 | | 317 | 1.3471 | 1.33530168228920 | 0.0117983177107981 | | 318 | 1.3482 | 1.34703159852143 | 0.00116840147857267 | | 319 | 1.3479 | 1.34819322611997 | -0.000293226119972401 | | 320 | 1.3468 | 1.34790169999661 | -0.00110169999661425 | | 321 | 1.3396 | 1.34680638717405 | -0.00720638717404976 | | 322 | 1.334 | 1.33964177947653 | -0.00564177947652822 | | 323 | 1.3296 | 1.33403270856638 | -0.00443270856637668 | | 324 | 1.3384 | 1.32962569890280 | 0.00877430109720279 | | 325 | 1.3585 | 1.33834913044527 | 0.0201508695547281 | | 326 | 1.3583 | 1.35838317408415 | -8.31740841487072e-05 | | 327 | 1.3615 | 1.35830048220691 | 0.00319951779308925 | | 328 | 1.3544 | 1.36148145059718 | -0.00708145059718412 | | 329 | 1.3535 | 1.35444105514898 | -0.000941055148976355 | | 330 | 1.3432 | 1.35350545582558 | -0.0103054558255835 | | 331 | 1.3486 | 1.34325974651922 | 0.00534025348078315 | | 332 | 1.3373 | 1.34856903954928 | -0.0112690395492823 | | 333 | 1.3339 | 1.33736533295561 | -0.00346533295560914 | | 334 | 1.3311 | 1.33392009048270 | -0.00282009048270448 | | 335 | 1.3321 | 1.33111634964945 | 0.000983650350545595 | | 336 | 1.329 | 1.33209429722609 | -0.00309429722609411 | | 337 | 1.3245 | 1.32901793938005 | -0.00451793938005363 | | 338 | 1.3256 | 1.32452619303373 | 0.00107380696627479 | | 339 | 1.3315 | 1.32559377453752 | 0.00590622546247666 | | 340 | 1.3238 | 1.33146575829162 | -0.00766575829162064 | | 341 | 1.3089 | 1.32384444270907 | -0.0149444427090695 | | 342 | 1.2924 | 1.30898664133335 | -0.0165866413333495 | | 343 | 1.2727 | 1.29249616208171 | -0.0197961620817109 | | 344 | 1.2746 | 1.27281476947728 | 0.00178523052271995 | | 345 | 1.2969 | 1.27458965001534 | 0.0223103499846622 | | 346 | 1.2698 | 1.29677065436244 | -0.0269706543624411 | | 347 | 1.2686 | 1.26995636404119 | -0.00135636404118666 | | 348 | 1.2587 | 1.26860786360464 | -0.00990786360464035 | | 349 | 1.2492 | 1.25875744145366 | -0.0095574414536601 | | 350 | 1.2349 | 1.24925540985951 | -0.0143554098595093 | | 351 | 1.2428 | 1.23498322637888 | 0.00781677362112299 | | 352 | 1.227 | 1.24275468177019 | -0.015754681770193 | | 353 | 1.2334 | 1.22709133874455 | 0.0063086612554486 | | 354 | 1.2497 | 1.23336342514516 | 0.0163365748548450 | | 355 | 1.236 | 1.24960528769421 | -0.0136052876942057 | | 356 | 1.2223 | 1.23607887749911 | -0.0137788774991063 | | 357 | 1.2309 | 1.22237988389676 | 0.00852011610323511 | | 358 | 1.2255 | 1.23085060409854 | -0.00535060409853716 | | 359 | 1.2384 | 1.22553102045907 | 0.0128689795409338 | | 360 | 1.2307 | 1.23832539129307 | -0.0076253912930726 | | 361 | 1.2155 | 1.23074420867889 | -0.0152442086788918 | | 362 | 1.2218 | 1.21558837924515 | 0.00621162075485127 | | 363 | 1.2268 | 1.22176398774347 | 0.00503601225652495 | | 364 | 1.206 | 1.22677080340665 | -0.0207708034066465 | | 365 | 1.1959 | 1.20612042002080 | -0.0102204200208014 | | 366 | 1.1942 | 1.19595925351887 | -0.0017592535188653 | | 367 | 1.201 | 1.19421019938137 | 0.00678980061862866 | | 368 | 1.2045 | 1.20096063570986 | 0.00353936429013957 | | 369 | 1.2127 | 1.20447948031604 | 0.00822051968395732 | | 370 | 1.2249 | 1.21265234102736 | 0.0122476589726437 | | 371 | 1.2258 | 1.22482899343760 | 0.000971006562402899 | | 372 | 1.2277 | 1.22579437052924 | 0.00190562947076023 | | 373 | 1.2363 | 1.22768895199497 | 0.00861104800502965 | | 374 | 1.2372 | 1.23625007691520 | 0.000949923084802684 | | 375 | 1.2391 | 1.23719449276201 | 0.00190550723799143 | | 376 | 1.2258 | 1.23908895270362 | -0.0132889527036224 | | 377 | 1.2271 | 1.22587704352738 | 0.00122295647261850 | | 378 | 1.2262 | 1.22709290983401 | -0.000892909834011357 | | 379 | 1.2294 | 1.22620517670013 | 0.00319482329986576 | | 380 | 1.2339 | 1.2293814778138 | 0.0045185221862003 | | 381 | 1.2198 | 1.23387380358742 | -0.0140738035874202 | | 382 | 1.2271 | 1.21988159374905 | 0.00721840625094905 | | 383 | 1.2328 | 1.22705815084213 | 0.00574184915787179 | | 384 | 1.2548 | 1.23276671127344 | 0.0220332887265597 | | 385 | 1.2531 | 1.25467226064227 | -0.00157226064226612 | | 386 | 1.2579 | 1.25310911527857 | 0.00479088472142641 | | 387 | 1.2567 | 1.25787222454873 | -0.00117222454873245 | | 388 | 1.266 | 1.25670679604451 | 0.00929320395548605 | | 389 | 1.2637 | 1.26594612207377 | -0.00224612207377239 | | 390 | 1.2572 | 1.26371302203201 | -0.00651302203201043 | | 391 | 1.2569 | 1.25723775964912 | -0.000337759649120084 | | 392 | 1.2703 | 1.25690195818251 | 0.0133980418174890 | | 393 | 1.2828 | 1.27022232402172 | 0.0125776759782841 | | 394 | 1.3 | 1.28272708014354 | 0.0172729198564585 | | 395 | 1.2957 | 1.29989985917599 | -0.00419985917599353 | | 396 | 1.2844 | 1.29572434894402 | -0.0113243489440171 | | 397 | 1.2817 | 1.28446565361526 | -0.00276565361525516 | | 398 | 1.285 | 1.28171603404834 | 0.00328396595166014 | | 399 | 1.2897 | 1.28498096100375 | 0.00471903899625215 | | 400 | 1.2931 | 1.28967264107878 | 0.00342735892122037 | | 401 | 1.3033 | 1.29308012967411 | 0.0102198703258851 | | 402 | 1.2992 | 1.30324074966802 | -0.00404074966802503 | | 403 | 1.3069 | 1.29922342649678 | 0.00767657350322226 | | 404 | 1.3028 | 1.30685549458907 | -0.00405549458907073 | | 405 | 1.3073 | 1.30282351198137 | 0.0044764880186281 | | 406 | 1.3221 | 1.30727404728311 | 0.0148259527168868 | | 407 | 1.3206 | 1.32201404561973 | -0.00141404561972802 | | 408 | 1.3184 | 1.32060819801717 | -0.00220819801716909 | | 409 | 1.3176 | 1.31841280216494 | -0.000812802164940507 | | 410 | 1.3253 | 1.31760471227096 | 0.0076952877290446 | | 411 | 1.3133 | 1.32525538609219 | -0.0119553860921862 | | 412 | 1.3016 | 1.31336931209225 | -0.0117693120922537 | | 413 | 1.279 | 1.3016682333167 | -0.0226682333167005 | | 414 | 1.2799 | 1.27913142048837 | 0.000768579511630563 | | 415 | 1.282 | 1.27989554411262 | 0.00210445588738017 | | 416 | 1.286 | 1.28198779928649 | 0.00401220071350994 | | 417 | 1.288 | 1.28597673901756 | 0.00202326098244354 | | 418 | 1.2836 | 1.28798827001899 | -0.00438827001898656 | | 419 | 1.2711 | 1.28362544126756 | -0.0125254412675633 | | 420 | 1.2704 | 1.27117261702248 | -0.000772617022483768 | | 421 | 1.2611 | 1.2704044792951 | -0.00930447929509981 | | 422 | 1.2613 | 1.26115394329571 | 0.000146056704291686 | | 423 | 1.2693 | 1.2612991532272 | 0.00800084677280055 | | 424 | 1.2713 | 1.26925361459468 | 0.00204638540531854 | | 425 | 1.27 | 1.27128813595371 | -0.00128813595371113 | | 426 | 1.268 | 1.27000746804807 | -0.00200746804807239 | | 427 | 1.28 | 1.26801163842050 | 0.0119883615795031 | | 428 | 1.2818 | 1.27993049673031 | 0.00186950326968649 | | 429 | 1.2834 | 1.28178916143886 | 0.00161083856113886 | | 430 | 1.2874 | 1.28339066106355 | 0.00400933893645039 | | 431 | 1.2744 | 1.28737675560889 | -0.0129767556088864 | | 432 | 1.2697 | 1.27447523354536 | -0.0047752335453648 | | 433 | 1.2715 | 1.26972768471260 | 0.00177231528739608 | | 434 | 1.2725 | 1.27148972489222 | 0.00101027510778451 | | 435 | 1.2801 | 1.27249414286741 | 0.00760585713258721 | | 436 | 1.285 | 1.28005590457161 | 0.00494409542838503 | | 437 | 1.2989 | 1.28497133630016 | 0.0139286636998424 | | 438 | 1.3078 | 1.29881924770845 | 0.0089807522915526 | | 439 | 1.306 | 1.30774793353167 | -0.00174793353166991 | | 440 | 1.3074 | 1.30601013375304 | 0.00138986624695603 | | 441 | 1.312 | 1.30739194216424 | 0.00460805783575613 | | 442 | 1.3364 | 1.31197328449894 | 0.0244267155010605 | | 443 | 1.3323 | 1.33625838460212 | -0.0039583846021185 | | 444 | 1.3412 | 1.3323229489802 | 0.00887705101979952 | | 445 | 1.3477 | 1.34114853474622 | 0.00655146525377615 | | 446 | 1.346 | 1.34766201747392 | -0.0016620174739177 | | 447 | 1.3611 | 1.34600963564937 | 0.0150903643506288 | | 448 | 1.3648 | 1.36101251267688 | 0.0037874873231154 | | 449 | 1.3726 | 1.36477804180737 | 0.00782195819262776 | | 450 | 1.3705 | 1.37255465171232 | -0.00205465171231833 | | 451 | 1.378 | 1.37051191197072 | 0.00748808802928336 | | 452 | 1.3856 | 1.37795658734529 | 0.00764341265470558 | | 453 | 1.397 | 1.38555568684115 | 0.0114443131588535 | | 454 | 1.3874 | 1.39693365088477 | -0.0095336508847701 | | 455 | 1.3936 | 1.38745527193221 | 0.0061447280677891 | | 456 | 1.3833 | 1.39356437555798 | -0.0102643755579765 | | 457 | 1.3958 | 1.38335950835382 | 0.012440491646182 | | 458 | 1.4101 | 1.39572787547821 | 0.0143721245217858 | | 459 | 1.4089 | 1.41001667671683 | -0.00111667671683202 | | 460 | 1.3896 | 1.40890647400251 | -0.0193064740025140 | | 461 | 1.3859 | 1.38971193048027 | -0.00381193048027417 | | 462 | 1.3861 | 1.38592209990335 | 0.000177900096653083 | | 463 | 1.4016 | 1.38609896861316 | 0.0155010313868422 | | 464 | 1.3934 | 1.40151013180928 | -0.00811013180927556 | | 465 | 1.4031 | 1.39344701899209 | 0.00965298100790535 | | 466 | 1.3912 | 1.403044036244 | -0.0118440362440002 | | 467 | 1.3803 | 1.39126866653460 | -0.0109686665346038 | | 468 | 1.3857 | 1.38036359152443 | 0.00533640847557004 | | 469 | 1.3857 | 1.38566906184094 | 3.09381590617441e-05 | | 470 | 1.3926 | 1.38569982063410 | 0.00690017936589582 | | 471 | 1.4018 | 1.39255999578223 | 0.0092400042177716 | | 472 | 1.4014 | 1.40174643050255 | -0.000346430502550898 | | 473 | 1.4244 | 1.40140200845232 | 0.0229979915476786 | | 474 | 1.4084 | 1.42426666771784 | -0.0158666677178372 | | 475 | 1.3917 | 1.40849198799003 | -0.0167919879900276 | | 476 | 1.3945 | 1.39179735259169 | 0.00270264740831316 | | 477 | 1.377 | 1.39448433123405 | -0.0174843312340522 | | 478 | 1.37 | 1.37710136649458 | -0.00710136649457804 | | 479 | 1.3711 | 1.37004117061263 | 0.00105882938737345 | | 480 | 1.3626 | 1.37109386137097 | -0.00849386137096597 | | 481 | 1.3612 | 1.36264924368802 | -0.00144924368802468 | | 482 | 1.3481 | 1.36120840208015 | -0.0131084020801526 | | 483 | 1.3647 | 1.34817599677395 | 0.0165240032260543 | | 484 | 1.3674 | 1.3646042010666 | 0.00279579893339932 | | 485 | 1.3647 | 1.36738379118231 | -0.00268379118230877 | | 486 | 1.3496 | 1.36471555944581 | -0.0151155594458083 | | 487 | 1.3339 | 1.34968763339324 | -0.0157876333932419 | | 488 | 1.3321 | 1.33399152978363 | -0.00189152978362950 | | 489 | 1.3225 | 1.33211096626122 | -0.00961096626121938 | | 490 | 1.3146 | 1.3225557201729 | -0.00795572017290036 | | 491 | 1.2998 | 1.31464612378106 | -0.0148461237810571 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 492 | 1.29988607132327 | 1.27970886493365 | 1.32006327771289 | | 493 | 1.29988607132327 | 1.27143378852472 | 1.32833835412182 | | 494 | 1.29988607132327 | 1.26507306893611 | 1.33469907371042 | | 495 | 1.29988607132327 | 1.25970699873607 | 1.34006514391047 | | 496 | 1.29988607132327 | 1.25497760204712 | 1.34479454059942 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/1h2cp1292336343.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/1h2cp1292336343.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/2stcs1292336343.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/2stcs1292336343.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/3stcs1292336343.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/14/t1292336278r7iwkh5a7dkf82c/3stcs1292336343.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 5 ; par2 = Single ; par3 = additive ; | | | | Parameters (R input): | | par1 = 5 ; par2 = Single ; 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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