Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.441210707478227 |
beta | 0 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 14483 | 13934.6017628205 | 548.398237179485 |
14 | 14011 | 13700.065161968 | 310.934838031986 |
15 | 15057 | 14874.7571667775 | 182.242833222539 |
16 | 14884 | 14775.1272144315 | 108.872785568528 |
17 | 15414 | 15368.5006114523 | 45.4993885476542 |
18 | 14440 | 14429.1213204717 | 10.8786795283268 |
19 | 14900 | 14650.1753353045 | 249.824664695479 |
20 | 15074 | 15288.8215439687 | -214.821543968716 |
21 | 14442 | 14114.5442035144 | 327.455796485563 |
22 | 15307 | 15602.3170987581 | -295.317098758071 |
23 | 14938 | 15141.315924293 | -203.315924292994 |
24 | 17193 | 17250.6149864358 | -57.6149864358158 |
25 | 15528 | 15827.5545920912 | -299.554592091223 |
26 | 14765 | 15086.2001187186 | -321.200118718582 |
27 | 15838 | 15910.0756977177 | -72.0756977177134 |
28 | 15723 | 15657.2392893899 | 65.7607106101223 |
29 | 16150 | 16196.1788016315 | -46.178801631504 |
30 | 15486 | 15197.004430002 | 288.995569997951 |
31 | 15986 | 15674.2870528431 | 311.712947156884 |
32 | 15983 | 16080.5997081843 | -97.5997081843307 |
33 | 15692 | 15261.0606682514 | 430.939331748588 |
34 | 16490 | 16446.4927817659 | 43.5072182341319 |
35 | 15686 | 16186.3937951023 | -500.393795102264 |
36 | 18897 | 18246.0350436742 | 650.964956325828 |
37 | 16316 | 17000.4144461031 | -684.414446103146 |
38 | 15636 | 16077.1603957516 | -441.160395751573 |
39 | 17163 | 16987.3162750127 | 175.683724987332 |
40 | 16534 | 16920.8154859542 | -386.815485954176 |
41 | 16518 | 17197.5229334711 | -679.522933471133 |
42 | 16375 | 16106.2021993498 | 268.797800650216 |
43 | 16290 | 16587.267577198 | -297.267577198043 |
44 | 16352 | 16496.1719754498 | -144.171975449834 |
45 | 15943 | 15951.4267087221 | -8.42670872209055 |
46 | 16362 | 16726.5129040676 | -364.512904067615 |
47 | 16393 | 15982.4650081338 | 410.534991866214 |
48 | 19051 | 19087.3847334156 | -36.3847334155944 |
49 | 16747 | 16792.3023814174 | -45.302381417383 |
50 | 16320 | 16286.9591759827 | 33.0408240173056 |
51 | 17910 | 17751.023600729 | 158.97639927104 |
52 | 16961 | 17362.8328245451 | -401.832824545054 |
53 | 17480 | 17469.352673964 | 10.6473260359635 |
54 | 17049 | 17212.4539204236 | -163.453920423646 |
55 | 16879 | 17186.4939385993 | -307.493938599328 |
56 | 17473 | 17176.4345396914 | 296.565460308593 |
57 | 16998 | 16902.0003503648 | 95.9996496352469 |
58 | 17307 | 17524.1834199866 | -217.183419986595 |
59 | 17418 | 17278.2273353959 | 139.77266460409 |
60 | 20169 | 20013.9498656037 | 155.050134396304 |
61 | 17871 | 17798.3475408509 | 72.6524591491034 |
62 | 17226 | 17388.8246184118 | -162.824618411767 |
63 | 19062 | 18836.8425637327 | 225.157436267276 |
64 | 17804 | 18164.4773802877 | -360.477380287688 |
65 | 19100 | 18519.733186048 | 580.266813952021 |
66 | 18522 | 18416.8707374281 | 105.129262571907 |
67 | 18060 | 18428.9245119388 | -368.924511938782 |
68 | 18869 | 18729.3032104639 | 139.696789536149 |
69 | 18127 | 18273.5828564743 | -146.582856474306 |
70 | 18871 | 18613.7325810499 | 257.267418950076 |
71 | 18890 | 18776.5725247399 | 113.427475260101 |
72 | 21263 | 21509.2081618553 | -246.208161855287 |
73 | 19547 | 19070.523441675 | 476.476558325005 |
74 | 18450 | 18707.5899661547 | -257.589966154686 |
75 | 20254 | 20330.5966431988 | -76.5966431988163 |
76 | 19240 | 19197.8478640492 | 42.1521359507606 |
77 | 20216 | 20256.4259062639 | -40.4259062638885 |
78 | 19420 | 19614.2054072447 | -194.205407244735 |
79 | 19415 | 19229.2933470368 | 185.706652963243 |
80 | 20018 | 20058.5933914304 | -40.5933914304005 |
81 | 18652 | 19363.3570782877 | -711.35707828766 |
82 | 19978 | 19679.9895785807 | 298.010421419345 |
83 | 19509 | 19780.429550844 | -271.429550843994 |
84 | 21971 | 22142.3016039647 | -171.301603964701 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
85 | 20140.4949426919 | 19558.6626343113 | 20722.3272510725 |
86 | 19157.1463938983 | 18521.1989196277 | 19793.0938681689 |
87 | 20994.9416530345 | 20309.1358897263 | 21680.7474163427 |
88 | 19962.34367931 | 19230.0664777378 | 20694.6208808821 |
89 | 20956.1800220131 | 20180.2094975098 | 21732.1505465164 |
90 | 20245.8655271396 | 19428.534131772 | 21063.1969225072 |
91 | 20158.9297634023 | 19302.2320542837 | 21015.627472521 |
92 | 20779.8400023543 | 19885.5071114435 | 21674.172893265 |
93 | 19727.6983621352 | 18797.2513326272 | 20658.1453916433 |
94 | 20922.2129732649 | 19957.0021000999 | 21887.4238464299 |
95 | 20572.9705974233 | 19574.2051671887 | 21571.7360276578 |
96 | 23110.5506993007 | 22079.3219469925 | 24141.7794516089 |