Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.230182393893731 |
beta | 0 |
gamma | 0.28444699539051 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 22228 | 21149.8295975033 | 1078.17040249674 |
14 | 13971 | 13588.7596295972 | 382.240370402844 |
15 | 36845 | 36445.3424185781 | 399.657581421903 |
16 | 35338 | 35450.8049382778 | -112.804938277804 |
17 | 35022 | 35304.5430264437 | -282.543026443716 |
18 | 34777 | 35144.8728998077 | -367.872899807655 |
19 | 26887 | 29732.5753717209 | -2845.57537172092 |
20 | 23970 | 27435.850287071 | -3465.85028707102 |
21 | 22780 | 24233.9575488456 | -1453.95754884561 |
22 | 17351 | 20598.4935099989 | -3247.49350999893 |
23 | 21382 | 17937.4847989449 | 3444.51520105514 |
24 | 24561 | 26008.0581728100 | -1447.05817281004 |
25 | 17409 | 19964.8424926678 | -2555.84249266784 |
26 | 11514 | 12243.8474802573 | -729.847480257307 |
27 | 31514 | 32055.8959657687 | -541.895965768697 |
28 | 27071 | 30881.6624255383 | -3810.66242553825 |
29 | 29462 | 29865.7841584855 | -403.784158485501 |
30 | 26105 | 29671.5674365729 | -3566.56743657292 |
31 | 22397 | 23992.4787650306 | -1595.47876503061 |
32 | 23843 | 22126.0073240852 | 1716.99267591479 |
33 | 21705 | 20805.3919757416 | 899.60802425836 |
34 | 18089 | 17695.1369369274 | 393.863063072622 |
35 | 20764 | 17338.2804380436 | 3425.71956195636 |
36 | 25316 | 23895.2288282854 | 1420.77117171457 |
37 | 17704 | 18518.8460800047 | -814.846080004656 |
38 | 15548 | 11769.6859606657 | 3778.31403933433 |
39 | 28029 | 33877.5975507525 | -5848.59755075249 |
40 | 29383 | 30701.9994781931 | -1318.99947819307 |
41 | 36438 | 31032.3782502449 | 5405.6217497551 |
42 | 32034 | 31392.211465989 | 641.788534010993 |
43 | 22679 | 26563.4959835361 | -3884.49598353610 |
44 | 24319 | 24811.3793141501 | -492.379314150086 |
45 | 18004 | 22654.0412966401 | -4650.04129664013 |
46 | 17537 | 18095.0421221875 | -558.042122187544 |
47 | 20366 | 18151.4172882810 | 2214.58271171902 |
48 | 22782 | 23925.1751122384 | -1143.17511223840 |
49 | 19169 | 17686.5555439228 | 1482.44445607718 |
50 | 13807 | 12453.6112013796 | 1353.38879862038 |
51 | 29743 | 30846.6773732998 | -1103.67737329980 |
52 | 25591 | 29769.2538182288 | -4178.25381822879 |
53 | 29096 | 30777.7198476437 | -1681.71984764368 |
54 | 26482 | 28636.2333948486 | -2154.23339484863 |
55 | 22405 | 22810.3158587468 | -405.315858746832 |
56 | 27044 | 22608.8620358893 | 4435.13796411073 |
57 | 17970 | 20741.2948231539 | -2771.29482315392 |
58 | 18730 | 17567.7188372411 | 1162.28116275894 |
59 | 19684 | 18613.5536989637 | 1070.44630103632 |
60 | 19785 | 23317.8696718011 | -3532.86967180106 |
61 | 18479 | 17306.6578088608 | 1172.34219113921 |
62 | 10698 | 12203.4019613282 | -1505.40196132819 |
63 | 31956 | 27777.5295804939 | 4178.47041950614 |
64 | 29506 | 27291.5773317793 | 2214.42266822073 |
65 | 34506 | 30305.1720737296 | 4200.8279262704 |
66 | 27165 | 29329.6346858415 | -2164.63468584151 |
67 | 26736 | 23677.1389526525 | 3058.86104734754 |
68 | 23691 | 25363.6832163915 | -1672.68321639146 |
69 | 18157 | 20424.4120690273 | -2267.41206902729 |
70 | 17328 | 18189.8409635505 | -861.840963550465 |
71 | 18205 | 18742.3652604285 | -537.365260428542 |
72 | 20995 | 21954.7512370020 | -959.75123700203 |
73 | 17382 | 17561.6668823415 | -179.666882341469 |
74 | 9367 | 11655.7105238571 | -2288.71052385711 |
75 | 31124 | 27670.2016298888 | 3453.79837011123 |
76 | 26551 | 26652.8408876847 | -101.840887684688 |
77 | 30651 | 29367.2392659885 | 1283.76073401151 |
78 | 25859 | 26578.4534003276 | -719.45340032757 |
79 | 25100 | 22657.518093347 | 2442.48190665300 |
80 | 25778 | 23162.7872603926 | 2615.21273960745 |
81 | 20418 | 19228.2768087773 | 1189.7231912227 |
82 | 18688 | 18088.3098553626 | 599.6901446374 |
83 | 20424 | 19067.5760774308 | 1356.42392256924 |
84 | 24776 | 22776.4285230624 | 1999.57147693764 |
85 | 19814 | 18918.4361508756 | 895.56384912437 |
86 | 12738 | 12178.6161757851 | 559.38382421489 |
87 | 31566 | 32900.2593318825 | -1334.25933188250 |
88 | 30111 | 29706.9363832271 | 404.063616772899 |
89 | 30019 | 33207.3254338703 | -3188.32543387033 |
90 | 31934 | 28654.5017233966 | 3279.49827660344 |
91 | 25826 | 25967.3458825070 | -141.345882507041 |
92 | 26835 | 25900.6731709862 | 934.32682901384 |
93 | 20205 | 20910.5442576052 | -705.544257605234 |
94 | 17789 | 19128.1665817947 | -1339.16658179469 |
95 | 20520 | 19847.8475332951 | 672.15246670493 |
96 | 22518 | 23590.1985439608 | -1072.19854396078 |
97 | 15572 | 18844.7977293402 | -3272.79772934022 |
98 | 11509 | 11516.4325405584 | -7.43254055842954 |
99 | 25447 | 30202.2039985014 | -4755.20399850137 |
100 | 24090 | 26846.3398832316 | -2756.33988323155 |
101 | 27786 | 28492.0808521020 | -706.080852102026 |
102 | 26195 | 26167.4788079740 | 27.5211920259644 |
103 | 20516 | 22528.9946074653 | -2012.99460746532 |
104 | 22759 | 22231.5700946494 | 527.429905350604 |
105 | 19028 | 17623.021208704 | 1404.97879129598 |
106 | 16971 | 16406.9627957891 | 564.037204210872 |
107 | 20036 | 17844.0496883589 | 2191.95031164107 |
108 | 22485 | 21263.164670643 | 1221.83532935697 |
109 | 18730 | 16871.8810872562 | 1858.11891274379 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
110 | 11464.8978503417 | 9473.61492331017 | 13456.1807773733 |
111 | 28999.7388934272 | 25737.2725701882 | 32262.2052166662 |
112 | 27101.4466139435 | 23826.8113084822 | 30376.0819194048 |
113 | 29990.8291591272 | 26311.3368330068 | 33670.3214852476 |
114 | 27862.4977823095 | 24236.4293218185 | 31488.5662428005 |
115 | 23499.7975455901 | 20144.864914517 | 26854.7301766633 |
116 | 24286.4163462993 | 20696.8526206039 | 27875.9800719946 |
117 | 19377.3104256885 | 16164.6357435892 | 22589.9851077878 |
118 | 17547.887657666 | 14378.3324942246 | 20717.4428211074 |
119 | 19287.553675255 | 15739.3268582732 | 22835.7804922368 |
120 | 22052.6165491018 | 17974.4776577392 | 26130.7554404645 |
121 | 17459.4568282603 | 14524.2101107675 | 20394.7035457531 |