Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.815582747009687 |
beta | 0 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 127.3 | 130.810637626263 | -3.51063762626266 |
14 | 127.7 | 128.847422147280 | -1.14742214727978 |
15 | 127 | 127.699104440422 | -0.699104440421593 |
16 | 123.9 | 124.495593587123 | -0.595593587122551 |
17 | 125.4 | 125.934837733236 | -0.534837733235804 |
18 | 124.6 | 125.177799972226 | -0.577799972225591 |
19 | 124.5 | 126.031556283656 | -1.53155628365568 |
20 | 124.8 | 124.111612069299 | 0.688387930701452 |
21 | 124.1 | 125.456382722162 | -1.35638272216170 |
22 | 124.2 | 123.345973708958 | 0.85402629104209 |
23 | 122.8 | 123.775836150758 | -0.975836150757843 |
24 | 122.3 | 123.688294355625 | -1.38829435562475 |
25 | 121.1 | 121.375269950793 | -0.275269950793131 |
26 | 121.7 | 122.486582235014 | -0.786582235014251 |
27 | 122.2 | 121.715236854998 | 0.484763145001978 |
28 | 122.2 | 119.496357166335 | 2.70364283366544 |
29 | 122.7 | 123.637606043225 | -0.937606043225358 |
30 | 121.7 | 122.544154419449 | -0.8441544194486 |
31 | 121 | 123.004787520158 | -2.00478752015819 |
32 | 119.8 | 121.108280087767 | -1.30828008776702 |
33 | 120.2 | 120.447511766465 | -0.247511766465024 |
34 | 116.6 | 119.649116331588 | -3.04911633158767 |
35 | 116 | 116.558184786386 | -0.558184786385723 |
36 | 118 | 116.735207829185 | 1.26479217081528 |
37 | 117.1 | 116.791255924892 | 0.308744075108322 |
38 | 116.2 | 118.284585165773 | -2.08458516577342 |
39 | 113.3 | 116.689069012447 | -3.38906901244653 |
40 | 114.3 | 111.719958348256 | 2.58004165174394 |
41 | 113.6 | 115.088891118331 | -1.48889111833141 |
42 | 113 | 113.563054990359 | -0.563054990358609 |
43 | 112.9 | 114.038907167466 | -1.13890716746577 |
44 | 112.7 | 112.977044799074 | -0.277044799074119 |
45 | 112.5 | 113.352958167211 | -0.85295816721127 |
46 | 113 | 111.544106875781 | 1.45589312421889 |
47 | 111.9 | 112.586754070804 | -0.686754070803559 |
48 | 110.9 | 112.995106626148 | -2.09510662614763 |
49 | 109.8 | 110.134567467816 | -0.334567467816143 |
50 | 108.3 | 110.661851709232 | -2.36185170923171 |
51 | 109.2 | 108.599632419164 | 0.600367580836476 |
52 | 109.2 | 107.985044402229 | 1.21495559777104 |
53 | 108.7 | 109.490255134441 | -0.790255134440912 |
54 | 109.8 | 108.704954616809 | 1.09504538319072 |
55 | 110.8 | 110.426927774763 | 0.373072225236996 |
56 | 110 | 110.757152003328 | -0.757152003328429 |
57 | 109.6 | 110.635289857648 | -1.03528985764846 |
58 | 109.5 | 109.103523997993 | 0.396476002006708 |
59 | 110.8 | 108.886987756419 | 1.91301224358060 |
60 | 111.6 | 111.155940354534 | 0.444059645466282 |
61 | 113.1 | 110.690975194481 | 2.40902480551919 |
62 | 114.3 | 113.082019768025 | 1.21798023197465 |
63 | 114.1 | 114.485733990629 | -0.385733990628566 |
64 | 113.8 | 113.180239179012 | 0.619760820988191 |
65 | 112.6 | 113.830223865268 | -1.23022386526817 |
66 | 112.7 | 113.033774384073 | -0.333774384072896 |
67 | 111.5 | 113.457282484737 | -1.95728248473745 |
68 | 110.7 | 111.678476769940 | -0.978476769939817 |
69 | 110.4 | 111.324812544079 | -0.92481254407933 |
70 | 109.7 | 110.14719240207 | -0.447192402070058 |
71 | 110 | 109.522250213665 | 0.477749786334726 |
72 | 111.3 | 110.349727311302 | 0.950272688698092 |
73 | 109 | 110.659994252659 | -1.65999425265876 |
74 | 108.2 | 109.512767916658 | -1.31276791665766 |
75 | 107.2 | 108.556695040696 | -1.35669504069567 |
76 | 108.7 | 106.644731739680 | 2.05526826031985 |
77 | 110.3 | 108.124322432746 | 2.17567756725407 |
78 | 110.3 | 110.270988148698 | 0.0290118513019877 |
79 | 109.5 | 110.690975539655 | -1.19097553965483 |
80 | 109.5 | 109.717665209314 | -0.217665209314490 |
81 | 109.4 | 109.994402375143 | -0.594402375142565 |
82 | 109.6 | 109.174340460917 | 0.425659539083128 |
83 | 111.3 | 109.431856553971 | 1.86814344602901 |
84 | 110 | 111.480456107635 | -1.48045610763479 |
85 | 109.5 | 109.326884321146 | 0.173115678853534 |
86 | 110.693 | 109.738745345710 | 0.95425465428987 |
87 | 109.195 | 110.623516046148 | -1.42851604614764 |
88 | 108.095 | 109.282201671490 | -1.18720167148965 |
89 | 108.199 | 108.139495384093 | 0.0595046159068033 |
90 | 106.87 | 108.164364756814 | -1.29436475681351 |
91 | 105.278 | 107.280042295072 | -2.00204229507204 |
92 | 108.711 | 105.824735129769 | 2.88626487023123 |
93 | 111.192 | 108.563507283177 | 2.62849271682262 |
94 | 109.641 | 110.560100017482 | -0.919100017482208 |
95 | 109.42 | 109.986872336927 | -0.566872336926934 |
96 | 109.935 | 109.431975498264 | 0.50302450173568 |
97 | 111.126 | 109.201043442293 | 1.92495655770674 |
98 | 110.733 | 111.185731167210 | -0.452731167209521 |
99 | 110.34 | 110.483564479264 | -0.14356447926437 |
100 | 111.766 | 110.234736967381 | 1.53126303261907 |
101 | 111.294 | 111.539077739818 | -0.245077739817759 |
102 | 111.54 | 111.065858127541 | 0.474141872459242 |
103 | 112.008 | 111.493391212998 | 0.514608787002174 |
104 | 111.007 | 112.992109429676 | -1.98510942967562 |
105 | 114.963 | 111.710335117425 | 3.25266488257519 |
106 | 112.045 | 113.561754594492 | -1.51675459449223 |
107 | 110.703 | 112.566047013531 | -1.86304701353136 |
108 | 108.894 | 111.151319907488 | -2.25731990748849 |
109 | 107.51 | 108.931327379251 | -1.42132737925061 |
110 | 111.35 | 107.748357019891 | 3.60164298010902 |
111 | 112.964 | 110.409883607728 | 2.55411639227209 |
112 | 115.203 | 112.670105160582 | 2.53289483941819 |
113 | 115.182 | 114.463771667873 | 0.718228332127353 |
114 | 115.191 | 114.908844373157 | 0.282155626843348 |
115 | 112.346 | 115.187259586243 | -2.84125958624323 |
116 | 110.774 | 113.487998289697 | -2.71399828969705 |
117 | 113.07 | 112.577690749174 | 0.492309250826281 |
118 | 111.138 | 111.298248559056 | -0.160248559056427 |
119 | 109.092 | 111.345021600161 | -2.25302160016095 |
120 | 107.971 | 109.539527225459 | -1.56852722545864 |
121 | 107.051 | 108.035473570529 | -0.984473570528891 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
122 | 108.135116036053 | 105.193744413258 | 111.076487658848 |
123 | 107.666022772661 | 103.870427758045 | 111.461617787277 |
124 | 107.839237441642 | 103.349090895417 | 112.329383987867 |
125 | 107.232462805545 | 102.141658301524 | 112.323267309567 |
126 | 107.011341544320 | 101.383627533306 | 112.639055555334 |
127 | 106.483623842636 | 100.365941317255 | 112.601306368017 |
128 | 107.125114023127 | 100.553895416738 | 113.696332629516 |
129 | 109.019595091960 | 102.024183133787 | 116.015007050132 |
130 | 107.218291051959 | 99.8229774713097 | 114.613604632609 |
131 | 107.009816597691 | 99.235143778354 | 114.784489417027 |
132 | 107.168080340990 | 99.0317167835196 | 115.304443898460 |
133 | 107.051 | 98.5683538072768 | 115.533646192723 |