Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.0725975572270489 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 100.1 | 100.3 | -0.200000000000017 |
4 | 100.2 | 100.685480488555 | -0.485480488554586 |
5 | 100.1 | 100.750235791004 | -0.65023579100415 |
6 | 100.4 | 100.603030260956 | -0.203030260955629 |
7 | 99.8 | 100.888290759967 | -1.08829075996709 |
8 | 99.7 | 100.209283509241 | -0.509283509240703 |
9 | 99.4 | 100.072310770534 | -0.672310770533812 |
10 | 100.2 | 99.7235026508956 | 0.476497349104363 |
11 | 100.5 | 100.558095194466 | -0.0580951944657784 |
12 | 100.6 | 100.853877625261 | -0.253877625260927 |
13 | 100.9 | 100.935446729832 | -0.0354467298323584 |
14 | 101.9 | 101.232873383835 | 0.667126616165135 |
15 | 102.1 | 102.28130514653 | -0.18130514652961 |
16 | 102.6 | 102.468142835779 | 0.131857164221145 |
17 | 103.5 | 102.977715343804 | 0.522284656195808 |
18 | 103.9 | 103.915631934021 | -0.0156319340211724 |
19 | 103.7 | 104.314497093797 | -0.614497093796516 |
20 | 103 | 104.069886105864 | -1.06988610586376 |
21 | 103.1 | 103.292214988067 | -0.192214988066894 |
22 | 103.2 | 103.378260649471 | -0.178260649470801 |
23 | 103.2 | 103.46531936177 | -0.265319361769528 |
24 | 103.1 | 103.44605782422 | -0.346057824220026 |
25 | 103.7 | 103.320934871522 | 0.379065128477677 |
26 | 104.2 | 103.94845407388 | 0.25154592612023 |
27 | 104.4 | 104.466715693647 | -0.0667156936465148 |
28 | 104.9 | 104.661872297259 | 0.238127702740925 |
29 | 105.4 | 105.179159786786 | 0.220840213213847 |
30 | 105.9 | 105.695192246803 | 0.204807753197031 |
31 | 105.5 | 106.210060789386 | -0.710060789386247 |
32 | 106.1 | 105.758512110594 | 0.341487889405911 |
33 | 105.4 | 106.383303297188 | -0.983303297187561 |
34 | 105.7 | 105.611917879798 | 0.0880821202015341 |
35 | 106.2 | 105.91831242656 | 0.281687573439527 |
36 | 106.7 | 106.438762256293 | 0.261237743706602 |
37 | 106.8 | 106.957727478342 | -0.157727478342011 |
38 | 106.8 | 107.046276848707 | -0.246276848706785 |
39 | 106.8 | 107.028397751089 | -0.228397751089105 |
40 | 107.3 | 107.011816632284 | 0.288183367716115 |
41 | 107.3 | 107.532738040814 | -0.23273804081353 |
42 | 107.5 | 107.515841827577 | -0.015841827576665 |
43 | 107.4 | 107.714691749593 | -0.314691749592583 |
44 | 106.9 | 107.591845897293 | -0.691845897292652 |
45 | 108.1 | 107.041619575172 | 1.05838042482833 |
46 | 108.6 | 108.318455408631 | 0.281544591368885 |
47 | 108.2 | 108.838894858215 | -0.638894858214982 |
48 | 108.3 | 108.392512652184 | -0.0925126521836575 |
49 | 108.3 | 108.485796459623 | -0.185796459622523 |
50 | 109.3 | 108.472308090512 | 0.827691909487498 |
51 | 109.2 | 109.532396501278 | -0.33239650127787 |
52 | 109.4 | 109.408265327254 | -0.00826532725429274 |
53 | 109.7 | 109.607665284686 | 0.0923347153140526 |
54 | 109.6 | 109.914368559465 | -0.314368559465009 |
55 | 109.3 | 109.791546169979 | -0.491546169978847 |
56 | 108.4 | 109.455861118774 | -1.05586111877408 |
57 | 108.7 | 108.47920818078 | 0.22079181921994 |
58 | 109.4 | 108.795237127511 | 0.604762872488863 |
59 | 109 | 109.539141434755 | -0.53914143475545 |
60 | 110.3 | 109.100001083592 | 1.19999891640768 |
61 | 109.5 | 110.487118073599 | -0.987118073598623 |
62 | 109.7 | 109.615455712761 | 0.0845442872393107 |
63 | 109.5 | 109.821593421492 | -0.32159342149177 |
64 | 110.9 | 109.598246524671 | 1.30175347532882 |
65 | 110.9 | 111.092750647092 | -0.19275064709187 |
66 | 110.4 | 111.078757420959 | -0.678757420959073 |
67 | 111.1 | 110.529481290248 | 0.570518709752278 |
68 | 110.8 | 111.270899554928 | -0.470899554928053 |
69 | 111.3 | 110.936713397541 | 0.363286602459027 |
70 | 111.7 | 111.463087117453 | 0.236912882547202 |
71 | 112.2 | 111.880286414001 | 0.319713585998642 |
72 | 111.7 | 112.403496839357 | -0.703496839357157 |
73 | 111.3 | 111.852424687303 | -0.552424687302889 |
74 | 111.9 | 111.412320004453 | 0.487679995547239 |
75 | 111.7 | 112.047724380838 | -0.347724380838002 |
76 | 111.8 | 111.822480440201 | -0.02248044020088 |
77 | 111.5 | 111.920848415157 | -0.420848415156897 |
78 | 112.9 | 111.590295848254 | 1.30970415174637 |
79 | 112 | 113.085377170361 | -1.08537717036054 |
80 | 112.4 | 112.106581439122 | 0.29341856087764 |
81 | 111.1 | 112.527882909887 | -1.42788290988716 |
82 | 111.7 | 111.124222098623 | 0.57577790137691 |
83 | 111.4 | 111.766022167768 | -0.366022167768378 |
84 | 112.2 | 111.439449852497 | 0.760550147502556 |
85 | 112.5 | 112.294663935355 | 0.205336064645195 |
86 | 113.2 | 112.609570832059 | 0.590429167941352 |
87 | 114.7 | 113.352434547367 | 1.34756545263321 |
88 | 115.2 | 114.950264507432 | 0.249735492568462 |
89 | 114.1 | 115.468394694145 | -1.36839469414491 |
90 | 113.7 | 114.269052582028 | -0.56905258202751 |
91 | 115.5 | 113.827740754639 | 1.67225924536142 |
92 | 115 | 115.749142690902 | -0.749142690902161 |
93 | 115.4 | 115.194756761528 | 0.205243238471837 |
94 | 115 | 115.609656919279 | -0.609656919278606 |
95 | 114.6 | 115.165397316192 | -0.565397316192403 |
96 | 114.6 | 114.724350852174 | -0.124350852174103 |
97 | 114.5 | 114.715323284067 | -0.215323284067154 |
98 | 115.2 | 114.59969133963 | 0.600308660370217 |
99 | 116.3 | 115.343272281955 | 0.956727718045101 |
100 | 116.5 | 116.512728377216 | -0.0127283772163764 |
101 | 118.4 | 116.711804328123 | 1.688195671877 |
102 | 118.5 | 118.734363210023 | -0.234363210022565 |
103 | 118.7 | 118.817349013471 | -0.117349013471028 |
104 | 119.2 | 119.00882976175 | 0.191170238249967 |
105 | 119.5 | 119.522708254061 | -0.0227082540614845 |
106 | 118.5 | 119.821059690288 | -1.32105969028773 |
107 | 118.6 | 118.725153983822 | -0.125153983821733 |
108 | 118.2 | 118.816068110319 | -0.61606811031902 |
109 | 118.6 | 118.371343070424 | 0.228656929575607 |
110 | 120.6 | 118.787943004955 | 1.81205699504538 |
111 | 124.5 | 120.919493916351 | 3.58050608364891 |
112 | 124.6 | 125.079429911661 | -0.479429911660603 |
113 | 126.5 | 125.144624471212 | 1.35537552878755 |
114 | 126 | 127.143021423728 | -1.14302142372775 |
115 | 126.3 | 126.560040860507 | -0.260040860506933 |
116 | 126.3 | 126.841162529255 | -0.541162529254905 |
117 | 125.1 | 126.801875451568 | -1.7018754515682 |
118 | 126.7 | 125.47832345108 | 1.22167654892036 |
119 | 123.9 | 127.167014184253 | -3.26701418425284 |
120 | 123.6 | 124.12983693505 | -0.529836935049985 |
121 | 124.9 | 123.791372067837 | 1.10862793216333 |
122 | 126.2 | 125.171855747585 | 1.02814425241459 |
123 | 126.3 | 126.546496508788 | -0.246496508787743 |
124 | 126.4 | 126.628601464385 | -0.228601464384738 |
125 | 126.2 | 126.712005556492 | -0.5120055564919 |
126 | 125.8 | 126.474835203804 | -0.674835203803909 |
127 | 124.9 | 126.025843816477 | -1.12584381647692 |
128 | 126.2 | 125.044110305582 | 1.15588969441848 |
129 | 125.9 | 126.42802507382 | -0.528025073820217 |
130 | 124.6 | 126.089691743306 | -1.48969174330625 |
131 | 122.9 | 124.681543761721 | -1.7815437617209 |
132 | 119.9 | 122.852208036527 | -2.95220803652688 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
133 | 119.637884944649 | 117.953708581719 | 121.322061307579 |
134 | 119.375769889298 | 116.906015251751 | 121.845524526845 |
135 | 119.113654833947 | 115.980028767035 | 122.247280900859 |
136 | 118.851539778596 | 115.106393376032 | 122.59668618116 |
137 | 118.589424723245 | 114.259399988854 | 122.919449457636 |
138 | 118.327309667894 | 113.426443552484 | 123.228175783304 |
139 | 118.065194612543 | 112.600385054892 | 123.530004170193 |
140 | 117.803079557192 | 111.776805655051 | 123.829353459332 |
141 | 117.540964501841 | 110.952801776892 | 124.129127226789 |
142 | 117.27884944649 | 110.126383100936 | 124.431315792043 |
143 | 117.016734391139 | 109.296142715122 | 124.737326067156 |
144 | 116.754619335788 | 108.461063428731 | 125.048175242844 |