Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.783130982224961 |
beta | 0.234826889608407 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 86.87 | 86.1685924145299 | 0.701407585470108 |
14 | 87.32 | 87.3172702435646 | 0.00272975643538587 |
15 | 87.13 | 87.282627154211 | -0.152627154211018 |
16 | 87.42 | 87.5578344220358 | -0.137834422035809 |
17 | 87.22 | 87.294695223874 | -0.0746952238740164 |
18 | 87.17 | 87.1868491537599 | -0.0168491537598925 |
19 | 87.52 | 87.850788903725 | -0.330788903724994 |
20 | 87.49 | 87.6680405591827 | -0.178040559182691 |
21 | 87.53 | 87.4455058123634 | 0.0844941876366505 |
22 | 87.93 | 87.4399419921014 | 0.490058007898568 |
23 | 88.54 | 88.1033595366499 | 0.436640463350145 |
24 | 88.96 | 88.7069090878234 | 0.253090912176575 |
25 | 89.3 | 89.4632890120717 | -0.163289012071672 |
26 | 90.01 | 89.8224248845663 | 0.18757511543366 |
27 | 90.52 | 89.9719912367303 | 0.548008763269664 |
28 | 90.64 | 91.0010867929312 | -0.361086792931161 |
29 | 91.25 | 90.7377390324986 | 0.512260967501362 |
30 | 91.59 | 91.3709772802577 | 0.219022719742256 |
31 | 92.09 | 92.4638044034828 | -0.373804403482779 |
32 | 91.81 | 92.584837718757 | -0.774837718756984 |
33 | 92.03 | 92.1464592011992 | -0.116459201199234 |
34 | 92.15 | 92.2291123349036 | -0.0791123349035701 |
35 | 91.98 | 92.4881753437127 | -0.508175343712708 |
36 | 92.11 | 92.1912173294018 | -0.0812173294018379 |
37 | 92.28 | 92.4132240265248 | -0.133224026524772 |
38 | 92.53 | 92.695259056284 | -0.165259056284029 |
39 | 91.97 | 92.4050534258347 | -0.435053425834653 |
40 | 92.05 | 92.044719015939 | 0.00528098406100241 |
41 | 91.87 | 91.9026535476405 | -0.0326535476404928 |
42 | 91.49 | 91.5903144340195 | -0.100314434019523 |
43 | 91.48 | 91.7905231007876 | -0.310523100787549 |
44 | 91.63 | 91.3718099069993 | 0.258190093000707 |
45 | 91.46 | 91.5728510544554 | -0.112851054455433 |
46 | 91.61 | 91.3547344345269 | 0.25526556547311 |
47 | 91.7 | 91.5324060472668 | 0.167593952733185 |
48 | 91.87 | 91.7313293720529 | 0.138670627947064 |
49 | 92.21 | 92.0287674430195 | 0.181232556980461 |
50 | 92.65 | 92.5224533361916 | 0.12754666380836 |
51 | 92.83 | 92.4292275069455 | 0.400772493054532 |
52 | 93.02 | 92.9988423350708 | 0.0211576649291487 |
53 | 93.33 | 93.0437964620397 | 0.286203537960318 |
54 | 93.35 | 93.207941446165 | 0.142058553835042 |
55 | 93.45 | 93.8383953909897 | -0.388395390989714 |
56 | 93.51 | 93.7537367641905 | -0.24373676419053 |
57 | 93.8 | 93.6606341523338 | 0.139365847666156 |
58 | 93.94 | 93.9456502770051 | -0.0056502770051452 |
59 | 94.02 | 94.0777756587908 | -0.0577756587907743 |
60 | 94.26 | 94.2302852713907 | 0.0297147286093065 |
61 | 94.71 | 94.5679427386567 | 0.142057261343268 |
62 | 95.26 | 95.1284178649791 | 0.131582135020878 |
63 | 95.54 | 95.2074601073233 | 0.332539892676692 |
64 | 95.69 | 95.7386187392999 | -0.0486187392998687 |
65 | 96.03 | 95.8708827069715 | 0.159117293028473 |
66 | 96.4 | 95.9653444132091 | 0.43465558679091 |
67 | 96.55 | 96.8248122695166 | -0.274812269516602 |
68 | 96.45 | 96.9962751743638 | -0.546275174363799 |
69 | 96.65 | 96.8294906651997 | -0.179490665199722 |
70 | 96.84 | 96.8548753085739 | -0.014875308573906 |
71 | 97.21 | 96.9882998540406 | 0.221700145959375 |
72 | 97.31 | 97.4498731945078 | -0.139873194507814 |
73 | 97.91 | 97.7191210765684 | 0.190878923431612 |
74 | 98.51 | 98.3645728996327 | 0.145427100367343 |
75 | 98.54 | 98.5495998377901 | -0.00959983779013385 |
76 | 98.52 | 98.7187979422303 | -0.198797942230314 |
77 | 98.66 | 98.7395266389006 | -0.0795266389005604 |
78 | 98.53 | 98.6239911440198 | -0.0939911440197676 |
79 | 98.71 | 98.7355160599592 | -0.0255160599592017 |
80 | 98.92 | 98.9091025730134 | 0.0108974269866025 |
81 | 98.96 | 99.2264294628447 | -0.266429462844712 |
82 | 99.25 | 99.1716696237415 | 0.0783303762584922 |
83 | 99.32 | 99.3987728732546 | -0.0787728732545929 |
84 | 99.41 | 99.4607459337846 | -0.0507459337845688 |
85 | 99.36 | 99.802036050161 | -0.442036050160993 |
86 | 99.58 | 99.7560962859327 | -0.176096285932687 |
87 | 99.77 | 99.4107003696953 | 0.359299630304676 |
88 | 99.77 | 99.6505971712374 | 0.11940282876256 |
89 | 100.03 | 99.827735491498 | 0.202264508501969 |
90 | 100.2 | 99.8629144144508 | 0.33708558554919 |
91 | 100.24 | 100.339326042321 | -0.0993260423207829 |
92 | 100.1 | 100.461880002148 | -0.361880002147899 |
93 | 100.03 | 100.357449252648 | -0.327449252647511 |
94 | 100.18 | 100.248768626069 | -0.0687686260691294 |
95 | 100.29 | 100.21864969695 | 0.0713503030501812 |
96 | 100.41 | 100.32392116184 | 0.0860788381604749 |
97 | 100.6 | 100.632320516735 | -0.0323205167346288 |
98 | 100.75 | 100.985078773512 | -0.235078773511603 |
99 | 100.79 | 100.71891873573 | 0.0710812642696368 |
100 | 100.44 | 100.637389308058 | -0.197389308057794 |
101 | 100.29 | 100.48246256739 | -0.192462567390095 |
102 | 100.34 | 100.063221154268 | 0.276778845731641 |
103 | 100.46 | 100.212134274413 | 0.247865725586905 |
104 | 100.12 | 100.427867414796 | -0.307867414796164 |
105 | 100.06 | 100.261357854724 | -0.201357854724222 |
106 | 100.28 | 100.218866652772 | 0.0611333472279085 |
107 | 100.28 | 100.256097969562 | 0.0239020304383644 |
108 | 100.4 | 100.25391216907 | 0.146087830929559 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 100.521171724161 | 100.014341860153 | 101.028001588168 |
110 | 100.79875539541 | 100.093706171058 | 101.503804619762 |
111 | 100.769806692007 | 99.854730679871 | 101.684882704143 |
112 | 100.54803375199 | 99.4100265594522 | 101.686040944527 |
113 | 100.558702464453 | 99.1848182054498 | 101.932586723457 |
114 | 100.43728759524 | 98.8148722260655 | 102.059702964415 |
115 | 100.357615797601 | 98.4744121042124 | 102.240819490991 |
116 | 100.207573280386 | 98.0517425169328 | 102.36340404384 |
117 | 100.310736709844 | 97.8708480277015 | 102.750625391986 |
118 | 100.525364898806 | 97.7903726841716 | 103.26035711344 |
119 | 100.537907649896 | 97.4971251945432 | 103.578690105248 |
120 | 100.570367326551 | 97.2134404398297 | 103.927294213273 |