Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.447201661696798 |
beta | 0 |
gamma | 0.474929455987073 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 17.848 | 16.0586436237374 | 1.78935637626262 |
14 | 19.592 | 18.5204301019031 | 1.07156989809688 |
15 | 21.092 | 20.3506796076230 | 0.74132039237702 |
16 | 20.899 | 20.3169493189437 | 0.582050681056295 |
17 | 25.89 | 25.4484933507038 | 0.441506649296159 |
18 | 24.965 | 24.5786025245859 | 0.386397475414068 |
19 | 22.225 | 23.4831084509999 | -1.25810845099988 |
20 | 20.977 | 20.9673135944513 | 0.00968640554871314 |
21 | 22.897 | 21.2221453711085 | 1.67485462889146 |
22 | 22.785 | 22.4188931442494 | 0.36610685575063 |
23 | 22.769 | 22.9049917384996 | -0.135991738499648 |
24 | 19.637 | 18.3173010070656 | 1.31969899293444 |
25 | 20.203 | 19.6536672624031 | 0.549332737596895 |
26 | 20.45 | 21.3724652931722 | -0.922465293172213 |
27 | 23.083 | 22.2242751719428 | 0.858724828057163 |
28 | 21.738 | 22.2012336378836 | -0.463233637883551 |
29 | 26.766 | 26.8284263250821 | -0.0624263250820825 |
30 | 25.28 | 25.7187074611296 | -0.438707461129585 |
31 | 22.574 | 23.8224761508690 | -1.24847615086896 |
32 | 22.729 | 21.6438360079938 | 1.08516399200619 |
33 | 21.378 | 22.8167967702696 | -1.43879677026962 |
34 | 22.902 | 22.2775155432228 | 0.624484456777235 |
35 | 24.989 | 22.7473399575732 | 2.24166004242681 |
36 | 21.116 | 19.6051164097721 | 1.51088359022795 |
37 | 15.169 | 20.8247286131131 | -5.65572861311307 |
38 | 15.846 | 19.3822067268321 | -3.53620672683214 |
39 | 20.927 | 19.5327811289706 | 1.39421887102939 |
40 | 18.273 | 19.4021461621031 | -1.12914616210312 |
41 | 22.538 | 23.8367696996340 | -1.29876969963403 |
42 | 15.596 | 22.0753670941416 | -6.47936709414157 |
43 | 14.034 | 17.2651459130930 | -3.23114591309303 |
44 | 11.366 | 14.8125269406535 | -3.44652694065349 |
45 | 14.861 | 13.2962667886879 | 1.56473321131210 |
46 | 15.149 | 14.6418634554185 | 0.507136544581474 |
47 | 13.577 | 15.4837833129012 | -1.90678331290119 |
48 | 13.026 | 10.2945107969368 | 2.73148920306324 |
49 | 13.19 | 10.1784559565142 | 3.01154404348576 |
50 | 13.196 | 13.1684125344169 | 0.0275874655831316 |
51 | 15.826 | 16.2071566133214 | -0.381156613321352 |
52 | 14.733 | 14.6200859837136 | 0.112914016286412 |
53 | 16.307 | 19.5656278970912 | -3.2586278970912 |
54 | 15.703 | 15.5676582999848 | 0.135341700015152 |
55 | 14.589 | 14.5683345675782 | 0.0206654324217919 |
56 | 12.043 | 13.5133848512927 | -1.47038485129271 |
57 | 15.057 | 14.1965160385504 | 0.860483961449637 |
58 | 14.053 | 14.9495096151991 | -0.896509615199067 |
59 | 12.698 | 14.5299655414359 | -1.83196554143592 |
60 | 10.888 | 10.5918847165021 | 0.296115283497945 |
61 | 10.045 | 9.4602522701558 | 0.584747729844194 |
62 | 11.549 | 10.5815329052276 | 0.967467094772395 |
63 | 13.767 | 13.9332809581206 | -0.166280958120614 |
64 | 12.434 | 12.5720164874451 | -0.138016487445114 |
65 | 13.116 | 16.5201765268627 | -3.40417652686269 |
66 | 14.211 | 13.3481708452732 | 0.862829154726803 |
67 | 12.266 | 12.6440735796332 | -0.378073579633224 |
68 | 12.602 | 11.0193464538816 | 1.58265354611840 |
69 | 15.714 | 13.6797482827775 | 2.03425171722251 |
70 | 13.742 | 14.4963712805018 | -0.754371280501832 |
71 | 12.745 | 13.8947969070686 | -1.14979690706864 |
72 | 10.491 | 10.8204898243408 | -0.329489824340847 |
73 | 10.057 | 9.48486335845752 | 0.572136641542476 |
74 | 10.9 | 10.7009835178861 | 0.199016482113857 |
75 | 11.771 | 13.411424723346 | -1.640424723346 |
76 | 11.992 | 11.3983412714638 | 0.593658728536237 |
77 | 11.933 | 14.8162093273194 | -2.8832093273194 |
78 | 14.504 | 12.9974416281841 | 1.50655837181589 |
79 | 11.727 | 12.2554342685767 | -0.528434268576699 |
80 | 11.477 | 11.0782353122247 | 0.398764687775271 |
81 | 13.578 | 13.3277627569255 | 0.250237243074533 |
82 | 11.555 | 12.6144458385062 | -1.05944583850623 |
83 | 11.846 | 11.7726264871401 | 0.0733735128598703 |
84 | 11.397 | 9.46068684585417 | 1.93631315414583 |
85 | 10.066 | 9.37504444240165 | 0.690955557598347 |
86 | 10.269 | 10.5463415719972 | -0.277341571997182 |
87 | 14.279 | 12.5608273762253 | 1.71817262377473 |
88 | 13.87 | 12.6362509866776 | 1.23374901332236 |
89 | 13.695 | 15.4275507978102 | -1.73255079781023 |
90 | 14.42 | 15.2758500566134 | -0.855850056613422 |
91 | 11.424 | 12.9431023187442 | -1.51910231874418 |
92 | 9.704 | 11.5663019766636 | -1.86230197666362 |
93 | 12.464 | 12.7656822246914 | -0.301682224691426 |
94 | 14.301 | 11.4617015265481 | 2.83929847345190 |
95 | 13.464 | 12.6608177450433 | 0.803182254956747 |
96 | 9.893 | 11.1643463581869 | -1.27134635818687 |
97 | 11.572 | 9.31727684065678 | 2.25472315934321 |
98 | 12.38 | 10.9336765045623 | 1.44632349543769 |
99 | 16.692 | 14.2428909153154 | 2.44910908468457 |
100 | 16.052 | 14.5180098472874 | 1.53399015271255 |
101 | 16.459 | 16.6648050074222 | -0.205805007422200 |
102 | 14.761 | 17.4260367209542 | -2.6650367209542 |
103 | 13.654 | 14.1100873095826 | -0.456087309582628 |
104 | 13.48 | 13.1185653343451 | 0.361434665654912 |
105 | 18.068 | 15.7221297477755 | 2.34587025222454 |
106 | 16.56 | 16.4267726616529 | 0.133227338347059 |
107 | 14.53 | 15.8811669839622 | -1.35116698396216 |
108 | 10.65 | 12.8766198513743 | -2.22661985137434 |
109 | 11.651 | 11.5280854863124 | 0.122914513687613 |
110 | 13.735 | 11.9788993606364 | 1.75610063936356 |
111 | 13.36 | 15.689918168187 | -2.32991816818701 |
112 | 17.818 | 13.5875926510712 | 4.23040734892884 |
113 | 20.613 | 16.4834638681830 | 4.12953613181703 |
114 | 16.231 | 18.5378201226600 | -2.30682012266002 |
115 | 13.862 | 15.9620038206483 | -2.10000382064834 |
116 | 12.004 | 14.4499520443661 | -2.44595204436612 |
117 | 17.734 | 16.3190425997773 | 1.41495740022269 |
118 | 15.034 | 16.0264719950507 | -0.992471995050687 |
119 | 12.609 | 14.5877385017339 | -1.97873850173393 |
120 | 12.32 | 11.0726987603369 | 1.24730123966314 |
121 | 10.833 | 11.8945549349842 | -1.06155493498421 |
122 | 11.35 | 12.2444491387021 | -0.894449138702052 |
123 | 13.648 | 13.6973934286187 | -0.0493934286186999 |
124 | 14.89 | 14.3372716302824 | 0.552728369717578 |
125 | 16.325 | 15.5619959457684 | 0.763004054231564 |
126 | 18.045 | 14.4210311120424 | 3.62396888795764 |
127 | 15.616 | 14.5517711069576 | 1.06422889304242 |
128 | 11.926 | 14.3639441375175 | -2.43794413751746 |
129 | 16.855 | 17.2502598343074 | -0.395259834307392 |
130 | 15.083 | 15.516110045447 | -0.433110045447014 |
131 | 12.52 | 14.0685895256775 | -1.54858952567754 |
132 | 12.355 | 11.5928782854899 | 0.762121714510064 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
133 | 11.5915937758937 | 8.10705777593714 | 15.0761297758502 |
134 | 12.4600891020489 | 8.64298813913186 | 16.2771900649660 |
135 | 14.534893640132 | 10.4119664776403 | 18.6578208026237 |
136 | 15.3549418509889 | 10.9473578173802 | 19.7625258845975 |
137 | 16.3876909442985 | 11.7127507693411 | 21.062631119256 |
138 | 15.6566277495631 | 10.7288154291169 | 20.5844400700092 |
139 | 13.4946881495897 | 8.32636125477636 | 18.6630150444030 |
140 | 11.9114749935637 | 6.51333906365603 | 17.3096109234714 |
141 | 16.4243301340399 | 10.8057769266857 | 22.0428833413940 |
142 | 14.8570039973481 | 9.02636005606865 | 20.6876479386276 |
143 | 13.3103127880576 | 7.27502676367656 | 19.3455988124386 |
144 | 12.1337879807172 | 5.90057484284054 | 18.3670011185939 |