Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.226903627980521 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 82.6 | 83.33 | -0.730000000000004 |
4 | 82.71 | 83.1843603515742 | -0.474360351574219 |
5 | 82.98 | 83.1867262668319 | -0.206726266831907 |
6 | 83.11 | 83.4098193268889 | -0.299819326888894 |
7 | 83.22 | 83.4717892338791 | -0.251789233879123 |
8 | 83.32 | 83.5246573432255 | -0.20465734322552 |
9 | 83.39 | 83.5782198495548 | -0.188219849554784 |
10 | 83.45 | 83.6055120828329 | -0.155512082832857 |
11 | 83.52 | 83.6302258270433 | -0.11022582704328 |
12 | 83.59 | 83.67521518699 | -0.0852151869899984 |
13 | 83.97 | 83.7258795519029 | 0.244120448097064 |
14 | 84.48 | 84.1612713672404 | 0.318728632759615 |
15 | 84.8 | 84.7435920503548 | 0.0564079496451768 |
16 | 84.93 | 85.0763912187763 | -0.146391218776245 |
17 | 85.14 | 85.1731745201314 | -0.0331745201314391 |
18 | 85.22 | 85.3756471011571 | -0.155647101157101 |
19 | 85.54 | 85.4203302092199 | 0.119669790780108 |
20 | 85.5 | 85.7674837189076 | -0.267483718907584 |
21 | 85.61 | 85.6667906926617 | -0.0567906926617212 |
22 | 85.75 | 85.7639046784612 | -0.0139046784612447 |
23 | 85.89 | 85.9007496564725 | -0.010749656472484 |
24 | 85.94 | 86.0383105204193 | -0.0983105204193464 |
25 | 86.08 | 86.0660035066675 | 0.0139964933324705 |
26 | 86.3 | 86.2091793617837 | 0.0908206382163144 |
27 | 86.97 | 86.4497868940905 | 0.520213105909534 |
28 | 87.3 | 87.2378251351443 | 0.062174864855649 |
29 | 87.62 | 87.5819328375493 | 0.0380671624507016 |
30 | 87.59 | 87.9105704148163 | -0.320570414816288 |
31 | 87.78 | 87.8078318246713 | -0.027831824671253 |
32 | 87.87 | 87.99151668268 | -0.121516682680024 |
33 | 88.17 | 88.0539441065198 | 0.116055893480222 |
34 | 88.67 | 88.380277609799 | 0.28972239020105 |
35 | 88.84 | 88.9460166712428 | -0.106016671242756 |
36 | 88.9 | 89.0919611039114 | -0.191961103911353 |
37 | 88.98 | 89.1084044330027 | -0.128404433002729 |
38 | 89.27 | 89.1592690013056 | 0.110730998694365 |
39 | 89.69 | 89.4743942666393 | 0.215605733360718 |
40 | 89.72 | 89.9433159897522 | -0.223315989752237 |
41 | 89.79 | 89.9226447814914 | -0.132644781491379 |
42 | 89.82 | 89.9625471993383 | -0.142547199338324 |
43 | 89.98 | 89.96020272265 | 0.0197972773500226 |
44 | 90.09 | 90.1246947967048 | -0.0346947967048408 |
45 | 90.31 | 90.2268224214605 | 0.0831775785395337 |
46 | 90.3 | 90.4656957157977 | -0.165695715797725 |
47 | 90.48 | 90.4180987567424 | 0.0619012432576227 |
48 | 90.52 | 90.6121443734141 | -0.0921443734140581 |
49 | 90.53 | 90.6312364807884 | -0.101236480788401 |
50 | 91.38 | 90.6182655560135 | 0.761734443986455 |
51 | 91.87 | 91.6411058649118 | 0.228894135088225 |
52 | 91.9 | 92.1830427745868 | -0.283042774586775 |
53 | 92.08 | 92.1488193421594 | -0.0688193421593724 |
54 | 92.14 | 92.3132039837482 | -0.173203983748166 |
55 | 92.09 | 92.333903371455 | -0.243903371455019 |
56 | 92.32 | 92.2285608115952 | 0.0914391884047916 |
57 | 92.67 | 92.4793086951838 | 0.19069130481617 |
58 | 92.78 | 92.872577244071 | -0.0925772440709665 |
59 | 92.96 | 92.9615711315228 | -0.00157113152283728 |
60 | 93.12 | 93.1412146360802 | -0.021214636080245 |
61 | 93.32 | 93.2964009581874 | 0.0235990418126164 |
62 | 94.12 | 93.5017556663915 | 0.618244333608502 |
63 | 94.34 | 94.4420375486657 | -0.102037548665677 |
64 | 94.52 | 94.6388848586832 | -0.118884858683202 |
65 | 94.81 | 94.791909452936 | 0.0180905470639772 |
66 | 94.95 | 95.086014263697 | -0.136014263696993 |
67 | 94.99 | 95.1951521338071 | -0.205152133807061 |
68 | 95.03 | 95.1886023703583 | -0.158602370358281 |
69 | 95.16 | 95.1926149171177 | -0.0326149171176837 |
70 | 95.41 | 95.3152144740974 | 0.0947855259026085 |
71 | 95.46 | 95.5867216538047 | -0.126721653804736 |
72 | 95.62 | 95.6079680508127 | 0.0120319491872607 |
73 | 95.66 | 95.770698143735 | -0.110698143735021 |
74 | 95.96 | 95.7855803333108 | 0.174419666689161 |
75 | 96.18 | 96.1251567884737 | 0.0548432115262614 |
76 | 96.24 | 96.3576009121392 | -0.117600912139181 |
77 | 97.03 | 96.390916838521 | 0.639083161479036 |
78 | 97.11 | 97.3259271264418 | -0.215927126441827 |
79 | 97.28 | 97.3569324780728 | -0.0769324780727629 |
80 | 97.74 | 97.5094762196885 | 0.230523780311472 |
81 | 97.83 | 98.021782901777 | -0.191782901776975 |
82 | 98.14 | 98.0682666655791 | 0.0717333344208555 |
83 | 98.18 | 98.3945432194064 | -0.21454321940638 |
84 | 98.21 | 98.3858625845645 | -0.17586258456447 |
85 | 98.43 | 98.3759587261007 | 0.0540412738992728 |
86 | 98.67 | 98.6082208872092 | 0.0617791127908163 |
87 | 99.51 | 98.8622387920348 | 0.647761207965175 |
88 | 99.64 | 99.8492181601872 | -0.209218160187177 |
89 | 99.83 | 99.9317458006013 | -0.101745800601293 |
90 | 99.84 | 100.098659309313 | -0.258659309313074 |
91 | 99.94 | 100.049968573619 | -0.109968573619014 |
92 | 100.17 | 100.125016305301 | 0.044983694698999 |
93 | 100.56 | 100.365223268828 | 0.194776731171828 |
94 | 101.05 | 100.799418815777 | 0.250581184222739 |
95 | 101.17 | 101.346276595581 | -0.176276595581044 |
96 | 101.21 | 101.426278796516 | -0.216278796515667 |
97 | 101.01 | 101.417204352931 | -0.407204352930975 |
98 | 101.92 | 101.124808207921 | 0.795191792078512 |
99 | 102.33 | 102.215240110484 | 0.114759889515568 |
100 | 102.41 | 102.651279545762 | -0.241279545762168 |
101 | 102.5 | 102.676532341471 | -0.17653234147123 |
102 | 102.69 | 102.726476512736 | -0.0364765127355184 |
103 | 102.98 | 102.90819985966 | 0.0718001403402582 |
104 | 103.11 | 103.214491571992 | -0.104491571992469 |
105 | 103.36 | 103.320782055214 | 0.0392179447860173 |
106 | 103.8 | 103.579680749168 | 0.220319250832119 |
107 | 104.07 | 104.069671986496 | 0.000328013504358182 |
108 | 104.15 | 104.33974641395 | -0.189746413949791 |
109 | 104.19 | 104.376692264228 | -0.186692264228313 |
110 | 104.64 | 104.374331112159 | 0.265668887841002 |
111 | 104.98 | 104.884612346652 | 0.0953876533483253 |
112 | 105.25 | 105.246256151261 | 0.00374384873903466 |
113 | 105.43 | 105.517105644122 | -0.0871056441224454 |
114 | 105.59 | 105.677341057454 | -0.0873410574535001 |
115 | 105.84 | 105.817523054646 | 0.0224769453543558 |
116 | 105.87 | 106.072623155092 | -0.202623155092468 |
117 | 106 | 106.056647226089 | -0.056647226089126 |
118 | 106.14 | 106.173793764974 | -0.0337937649744617 |
119 | 106.24 | 106.306125837099 | -0.0661258370986388 |
120 | 106.31 | 106.391121644758 | -0.081121644757701 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 106.442714849254 | 105.995341005967 | 106.890088692541 |
122 | 106.575429698509 | 105.867321196706 | 107.283538200312 |
123 | 106.708144547763 | 105.74667081023 | 107.669618285296 |
124 | 106.840859397018 | 105.62028800929 | 108.061430784746 |
125 | 106.973574246272 | 105.484240567068 | 108.462907925476 |
126 | 107.106289095527 | 105.337108070775 | 108.875470120278 |
127 | 107.239003944781 | 105.178406107383 | 109.299601782179 |
128 | 107.371718794036 | 105.008054367891 | 109.73538322018 |
129 | 107.50443364329 | 104.826160211003 | 110.182707075577 |
130 | 107.637148492544 | 104.632919891477 | 110.641377093612 |
131 | 107.769863341799 | 104.428570012634 | 111.111156670963 |
132 | 107.902578191053 | 104.213362513677 | 111.591793868429 |