Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.852574377903842 |
beta | 0.0116103049718575 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 123 | 123 | 0 |
4 | 121 | 122 | -1 |
5 | 141 | 120.137526973558 | 20.8624730264425 |
6 | 140 | 137.120948575210 | 2.87905142479033 |
7 | 125 | 138.800664410429 | -13.8006644104294 |
8 | 115 | 126.123073967225 | -11.1230739672251 |
9 | 116 | 115.618225130546 | 0.381774869454063 |
10 | 116 | 114.92589468893 | 1.07410531107014 |
11 | 117 | 114.834459633846 | 2.16554036615371 |
12 | 119 | 115.694990064854 | 3.30500993514612 |
13 | 114 | 117.559718186550 | -3.5597181865503 |
14 | 110 | 113.536518601187 | -3.53651860118705 |
15 | 108 | 109.498091633199 | -1.49809163319894 |
16 | 111 | 107.18274618679 | 3.81725381321003 |
17 | 124 | 109.436913731577 | 14.5630862684230 |
18 | 125 | 120.996857569535 | 4.00314243046468 |
19 | 118 | 123.593289559116 | -5.59328955911619 |
20 | 108 | 117.952683507563 | -9.952683507563 |
21 | 107 | 108.496851756317 | -1.49685175631714 |
22 | 103 | 106.235428690599 | -3.23542869059904 |
23 | 113 | 102.459713105217 | 10.5402868947825 |
24 | 116 | 110.533154260691 | 5.46684573930912 |
25 | 113 | 114.335223863793 | -1.33522386379326 |
26 | 105 | 112.324806294824 | -7.32480629482389 |
27 | 102 | 105.135318527689 | -3.13531852768861 |
28 | 107 | 101.486645271192 | 5.51335472880787 |
29 | 119 | 105.266183996776 | 13.7338160032239 |
30 | 116 | 116.190223597188 | -0.190223597188449 |
31 | 113 | 115.241100840838 | -2.24110084083844 |
32 | 102 | 112.521268824763 | -10.5212688247633 |
33 | 96 | 102.637831398577 | -6.63783139857702 |
34 | 95 | 95.9996076600766 | -0.999607660076649 |
35 | 101 | 94.1584942530072 | 6.84150574699275 |
36 | 110 | 99.0702348919082 | 10.9297651080918 |
37 | 103 | 107.575710615723 | -4.57571061572277 |
38 | 88 | 102.816321669003 | -14.8163216690034 |
39 | 79 | 89.179388563341 | -10.1793885633410 |
40 | 96 | 79.3950236258935 | 16.6049763741065 |
41 | 118 | 92.6106887876597 | 25.3893112123403 |
42 | 116 | 113.566972627762 | 2.43302737223837 |
43 | 114 | 114.975400736747 | -0.97540073674736 |
44 | 102 | 113.468235222007 | -11.4682352220072 |
45 | 98 | 102.901627843727 | -4.90162784372738 |
46 | 98 | 97.885022174631 | 0.114977825369081 |
47 | 101 | 97.1465840881363 | 3.85341591186366 |
48 | 117 | 99.6335861373517 | 17.3664138626483 |
49 | 109 | 113.813328035276 | -4.81332803527634 |
50 | 98 | 109.035544839988 | -11.0355448399877 |
51 | 93 | 98.8436220434358 | -5.84362204343577 |
52 | 98 | 93.0203556344782 | 4.97964436552184 |
53 | 114 | 96.474020600447 | 17.5259793995531 |
54 | 115 | 110.7978528634 | 4.20214713660005 |
55 | 112 | 113.803722701084 | -1.80372270108359 |
56 | 112 | 111.671287381053 | 0.328712618946582 |
57 | 103 | 111.360165588103 | -8.36016558810333 |
58 | 107 | 103.558374522214 | 3.44162547778619 |
59 | 104 | 105.852555573482 | -1.85255557348248 |
60 | 117 | 103.614715711935 | 13.3852842880648 |
61 | 123 | 114.500763915703 | 8.49923608429749 |
62 | 113 | 121.305223562580 | -8.30522356258025 |
63 | 97 | 113.70042099093 | -16.7004209909300 |
64 | 90 | 98.7727765965878 | -8.77277659658776 |
65 | 109 | 90.517200057757 | 18.482799942243 |
66 | 104 | 105.681984471569 | -1.68198447156894 |
67 | 92 | 103.638140985079 | -11.6381409850785 |
68 | 102 | 92.9907316855148 | 9.0092683144852 |
69 | 90 | 100.035954105488 | -10.0359541054881 |
70 | 97 | 90.7443654862721 | 6.25563451372788 |
71 | 99 | 95.4044902265872 | 3.59550977341283 |
72 | 108 | 97.8322514588458 | 10.1677485411542 |
73 | 106 | 105.963982039185 | 0.0360179608146325 |
74 | 86 | 105.458015252038 | -19.4580152520378 |
75 | 72 | 88.139327171366 | -16.139327171366 |
76 | 71 | 73.4903099892101 | -2.49030998921013 |
77 | 96 | 70.4534444367942 | 25.5465555632058 |
78 | 88 | 91.5729684659963 | -3.57296846599631 |
79 | 83 | 87.8305648520608 | -4.83056485206085 |
80 | 90 | 82.9681507179086 | 7.03184928209143 |
81 | 85 | 88.2889327392391 | -3.28893273923912 |
82 | 100 | 84.7779244599996 | 15.2220755400004 |
83 | 108 | 97.199605524605 | 10.8003944753951 |
84 | 118 | 105.958383915256 | 12.0416160847441 |
85 | 124 | 115.894591772799 | 8.10540822720124 |
86 | 99 | 122.555122252200 | -23.5551222522002 |
87 | 92 | 101.989531777561 | -9.98953177756073 |
88 | 86 | 92.8907332986035 | -6.8907332986035 |
89 | 112 | 86.3656820579961 | 25.6343179420039 |
90 | 104 | 107.824401248976 | -3.82440124897619 |
91 | 93 | 104.129514848028 | -11.1295148480281 |
92 | 104 | 94.096308608965 | 9.903691391035 |
93 | 96 | 102.093508254810 | -6.09350825480951 |
94 | 109 | 96.3915878678128 | 12.6084121321872 |
95 | 113 | 106.759251860694 | 6.24074813930596 |
96 | 123 | 111.759783658593 | 11.2402163414069 |
97 | 127 | 121.133996899810 | 5.86600310018953 |
98 | 96 | 125.984359133190 | -29.9843591331898 |
99 | 100 | 99.972816455102 | 0.0271835448979232 |
100 | 95 | 99.5486151860766 | -4.54861518607657 |
101 | 133 | 95.1781800175127 | 37.8218199824873 |
102 | 130 | 127.306077157401 | 2.69392284259881 |
103 | 117 | 129.511495441588 | -12.5114954415883 |
104 | 129 | 118.629316795298 | 10.3706832047024 |
105 | 122 | 127.358553121602 | -5.35855312160182 |
106 | 134 | 122.624403138078 | 11.3755968619217 |
107 | 141 | 132.269963701760 | 8.73003629823953 |
108 | 152 | 139.746402674700 | 12.2535973252996 |
109 | 161 | 150.348233551550 | 10.6517664484504 |
110 | 122 | 159.689822557451 | -37.689822557451 |
111 | 126 | 127.443533082782 | -1.44353308278231 |
112 | 119 | 126.085612281661 | -7.08561228166147 |
113 | 160 | 119.847261331815 | 40.1527386681853 |
114 | 162 | 154.280575904178 | 7.71942409582229 |
115 | 145 | 161.138489347694 | -16.1384893476941 |
116 | 161 | 147.496007845023 | 13.5039921549769 |
117 | 151 | 159.259617841229 | -8.25961784122887 |
118 | 166 | 152.386372529904 | 13.6136274700962 |
119 | 169 | 164.296452246282 | 4.70354775371754 |
120 | 185 | 168.656585057495 | 16.3434149425053 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 183.102348116508 | 159.621775068916 | 206.582921164100 |
122 | 183.614134348091 | 152.606797653314 | 214.621471042868 |
123 | 184.125920579674 | 146.963567960784 | 221.288273198564 |
124 | 184.637706811257 | 142.091238989816 | 227.184174632697 |
125 | 185.149493042840 | 137.725370612698 | 232.573615472981 |
126 | 185.661279274422 | 133.722036996830 | 237.600521552014 |
127 | 186.173065506005 | 129.992797902333 | 242.353333109678 |
128 | 186.684851737588 | 126.478804110677 | 246.890899364499 |
129 | 187.196637969171 | 123.138617077901 | 251.254658860441 |
130 | 187.708424200754 | 119.941794355282 | 255.475054046225 |
131 | 188.220210432336 | 116.865221435005 | 259.575199429668 |
132 | 188.731996663919 | 113.890877706956 | 263.573115620882 |