Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.142162268610765 |
beta | 0.0318938520417184 |
gamma | 0.336498485279104 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 7237 | 7082.00026709402 | 154.999732905980 |
14 | 9374 | 9172.19518755744 | 201.804812442559 |
15 | 11837 | 11641.1256946535 | 195.874305346493 |
16 | 13784 | 13938.0178882238 | -154.017888223778 |
17 | 15926 | 16261.3869475829 | -335.386947582942 |
18 | 13821 | 13940.0348245903 | -119.034824590261 |
19 | 11143 | 9465.15009414176 | 1677.84990585824 |
20 | 7975 | 8395.98878329206 | -420.988783292065 |
21 | 7610 | 7108.04299670844 | 501.957003291564 |
22 | 1015 | 9703.95620138403 | -8688.95620138403 |
23 | 12759 | 8213.20505078443 | 4545.79494921557 |
24 | 8816 | 7870.83891453146 | 945.161085468536 |
25 | 10677 | 6741.87634985126 | 3935.12365014874 |
26 | 10947 | 9393.33431250438 | 1553.66568749562 |
27 | 15200 | 12069.2272422138 | 3130.77275778624 |
28 | 17010 | 14712.1488438752 | 2297.85115612476 |
29 | 20900 | 17372.6418529181 | 3527.3581470819 |
30 | 16205 | 15721.3077341927 | 483.692265807316 |
31 | 12143 | 11911.9605558089 | 231.039444191105 |
32 | 8997 | 10085.8661054921 | -1088.86610549210 |
33 | 5568 | 9020.96547985179 | -3452.96547985179 |
34 | 11474 | 8435.22039137308 | 3038.77960862692 |
35 | 12256 | 12518.8848619014 | -262.884861901397 |
36 | 10583 | 10518.5562304087 | 64.4437695912638 |
37 | 10862 | 10188.4947637839 | 673.505236216133 |
38 | 10965 | 11735.0708682120 | -770.07086821202 |
39 | 14405 | 14571.5610188039 | -166.561018803932 |
40 | 20379 | 16526.0390820567 | 3852.96091794326 |
41 | 20128 | 19790.3168617586 | 337.683138241431 |
42 | 17816 | 16820.2770636948 | 995.72293630516 |
43 | 12268 | 13026.4455747268 | -758.445574726766 |
44 | 8642 | 10689.8471672001 | -2047.84716720013 |
45 | 7962 | 8813.01284266297 | -851.01284266297 |
46 | 13932 | 10489.6997674117 | 3442.30023258830 |
47 | 15936 | 13698.1154236907 | 2237.88457630928 |
48 | 12628 | 12179.5755024990 | 448.424497500981 |
49 | 12267 | 12113.4415781884 | 153.558421811591 |
50 | 12470 | 13200.5667293058 | -730.566729305845 |
51 | 18944 | 16248.2319366495 | 2695.76806335050 |
52 | 21259 | 19814.2321448011 | 1444.76785519889 |
53 | 22015 | 21754.8401371267 | 260.159862873283 |
54 | 18581 | 18996.7867886545 | -415.786788654485 |
55 | 15175 | 14522.5885824860 | 652.41141751396 |
56 | 10306 | 12047.4146118136 | -1741.41461181356 |
57 | 10792 | 10594.0662250223 | 197.933774977661 |
58 | 14752 | 13698.3855561416 | 1053.61444385844 |
59 | 13754 | 16247.9210434732 | -2493.9210434732 |
60 | 11738 | 13547.0636665582 | -1809.06366655816 |
61 | 12181 | 13071.5623317288 | -890.562331728797 |
62 | 12965 | 13746.9848144270 | -781.98481442695 |
63 | 19990 | 17768.1011788146 | 2221.89882118542 |
64 | 23125 | 20895.1827040629 | 2229.81729593707 |
65 | 23541 | 22598.5670938337 | 942.432906166276 |
66 | 21247 | 19738.6034535547 | 1508.3965464453 |
67 | 15189 | 15851.2389526231 | -662.238952623136 |
68 | 14767 | 12497.1462662036 | 2269.85373379635 |
69 | 10895 | 12191.0302334449 | -1296.03023344493 |
70 | 17130 | 15340.3590996979 | 1789.64090030212 |
71 | 17697 | 16984.2246379397 | 712.77536206026 |
72 | 16611 | 14965.2000147216 | 1645.79998527843 |
73 | 12674 | 15289.9200790113 | -2615.92007901128 |
74 | 12760 | 15787.5154883498 | -3027.51548834982 |
75 | 20249 | 20382.4365910482 | -133.436591048157 |
76 | 22135 | 23192.2148414611 | -1057.21484146108 |
77 | 20677 | 24057.0365499997 | -3380.03654999974 |
78 | 19933 | 20726.7010671808 | -793.701067180846 |
79 | 15388 | 15855.7977118205 | -467.797711820498 |
80 | 15113 | 13346.9205315596 | 1766.07946844040 |
81 | 13401 | 11908.7628699328 | 1492.23713006716 |
82 | 16135 | 16326.7416969967 | -191.741696996733 |
83 | 17562 | 17350.6467426419 | 211.353257358052 |
84 | 14720 | 15499.9597680745 | -779.959768074492 |
85 | 12225 | 14208.9299309708 | -1983.92993097075 |
86 | 11608 | 14639.7188171264 | -3031.71881712642 |
87 | 20985 | 20031.5912028116 | 953.40879718843 |
88 | 19692 | 22696.2877319095 | -3004.28773190954 |
89 | 24081 | 22572.0413663742 | 1508.95863362576 |
90 | 22114 | 20663.718661195 | 1450.28133880498 |
91 | 14220 | 16196.4826943046 | -1976.48269430459 |
92 | 13434 | 14101.7024788636 | -667.702478863637 |
93 | 13598 | 12211.2118145913 | 1386.78818540866 |
94 | 17187 | 16100.3290783718 | 1086.67092162816 |
95 | 16119 | 17400.3589214253 | -1281.35892142525 |
96 | 13713 | 15022.5679092203 | -1309.56790922028 |
97 | 13210 | 13277.563949221 | -67.5639492210103 |
98 | 14251 | 13655.8764009879 | 595.123599012064 |
99 | 20139 | 20707.6892366457 | -568.689236645660 |
100 | 21725 | 22000.6554797930 | -275.655479792968 |
101 | 26099 | 23566.5758574652 | 2532.42414253480 |
102 | 21084 | 21790.9135200600 | -706.913520059981 |
103 | 18024 | 16022.1514716451 | 2001.84852835487 |
104 | 16722 | 14883.0910412963 | 1838.90895870367 |
105 | 14385 | 13965.7199679191 | 419.280032080871 |
106 | 21342 | 17649.9976110729 | 3692.00238892715 |
107 | 17180 | 18667.9977448033 | -1487.99774480328 |
108 | 14577 | 16282.8992813049 | -1705.89928130489 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 14868.4848031628 | 11028.1786658219 | 18708.7909405037 |
110 | 15476.4153788608 | 11595.0078298107 | 19357.822927911 |
111 | 22133.6992169966 | 18209.0820532435 | 26058.3163807497 |
112 | 23620.7001666745 | 19650.7576521849 | 27590.642681164 |
113 | 26066.2426564914 | 22048.8551969541 | 30083.6301160287 |
114 | 23013.8630825377 | 18946.9107154253 | 27080.8154496501 |
115 | 18149.0855957455 | 14030.4512812501 | 22267.7199102409 |
116 | 16690.9008429696 | 12518.4735446422 | 20863.3281412969 |
117 | 15106.4741759242 | 10878.1517230507 | 19334.7966287976 |
118 | 19678.1121056847 | 15391.8038325054 | 23964.4203788639 |
119 | 18661.5028257995 | 14315.1319855666 | 23007.8736660325 |
120 | 16417.3070788170 | 12008.8130333374 | 20825.8011242965 |