Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.137145889450086 |
beta | 0.00517785985442284 |
gamma | 0.51043125305572 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 7237 | 7055.55795940171 | 181.442040598286 |
14 | 9374 | 9209.65373173377 | 164.346268266230 |
15 | 11837 | 11732.6882617630 | 104.311738237036 |
16 | 13784 | 13700.4800435208 | 83.519956479202 |
17 | 15926 | 15742.3962939177 | 183.603706082293 |
18 | 13821 | 13555.7523335736 | 265.247666426436 |
19 | 11143 | 9946.7438650442 | 1196.25613495580 |
20 | 7975 | 8858.93553571608 | -883.93553571608 |
21 | 7610 | 7566.70976724398 | 43.2902327560214 |
22 | 10015 | 10152.0549428651 | -137.054942865141 |
23 | 12759 | 9971.90252654416 | 2787.09747345584 |
24 | 8816 | 9441.05644068983 | -625.05644068983 |
25 | 10677 | 8197.96570639205 | 2479.03429360795 |
26 | 10947 | 10663.6571207825 | 283.342879217487 |
27 | 15200 | 13180.6749394208 | 2019.32506057923 |
28 | 17010 | 15407.4098061561 | 1602.59019384390 |
29 | 20900 | 17708.2828333114 | 3191.71716668865 |
30 | 16205 | 15978.8265410794 | 226.173458920628 |
31 | 12143 | 12783.1523910586 | -640.152391058584 |
32 | 8997 | 10534.6613258750 | -1537.66132587503 |
33 | 5568 | 9568.03863235537 | -4000.03863235537 |
34 | 11474 | 11523.4405678943 | -49.4405678942767 |
35 | 12256 | 12647.2557624707 | -391.255762470704 |
36 | 10583 | 10179.5213810568 | 403.478618943216 |
37 | 10862 | 10447.1648486553 | 414.835151344701 |
38 | 10965 | 11663.7979604003 | -698.797960400292 |
39 | 14405 | 14811.0778627426 | -406.07786274265 |
40 | 20379 | 16520.2987898650 | 3858.70121013496 |
41 | 20128 | 19830.747511393 | 297.252488606988 |
42 | 17816 | 16396.4280509177 | 1419.57194908227 |
43 | 12268 | 12981.9255246590 | -713.925524658989 |
44 | 8642 | 10327.0324213861 | -1685.03242138608 |
45 | 7962 | 8254.59799501542 | -292.597995015418 |
46 | 13932 | 12459.9445412496 | 1472.05545875042 |
47 | 15936 | 13644.4937567419 | 2291.50624325811 |
48 | 12628 | 11899.2292618824 | 728.77073811762 |
49 | 12267 | 12221.2350006731 | 45.7649993269042 |
50 | 12470 | 12901.2627604665 | -431.262760466518 |
51 | 18944 | 16218.8320169917 | 2725.16798300832 |
52 | 21259 | 20242.7168271128 | 1016.2831728872 |
53 | 22015 | 21599.6599758524 | 415.340024147561 |
54 | 18581 | 18680.8012396306 | -99.801239630564 |
55 | 15175 | 14122.1575097777 | 1052.8424902223 |
56 | 10306 | 11287.0075962935 | -981.007596293519 |
57 | 10792 | 9930.0345236007 | 861.965476399306 |
58 | 14752 | 15077.387399979 | -325.387399978985 |
59 | 13754 | 16381.5175654954 | -2627.51756549536 |
60 | 11738 | 13275.0480767129 | -1537.04807671289 |
61 | 12181 | 12985.5733340186 | -804.573334018613 |
62 | 12965 | 13338.3625063755 | -373.362506375493 |
63 | 19990 | 18053.5712698969 | 1936.42873010306 |
64 | 23125 | 21215.6025948817 | 1909.39740511827 |
65 | 23541 | 22429.9539739004 | 1111.04602609963 |
66 | 21247 | 19379.7133041700 | 1867.28669582996 |
67 | 15189 | 15599.9880366453 | -410.988036645305 |
68 | 14767 | 11668.7605647262 | 3098.23943527378 |
69 | 10895 | 11686.2773256260 | -791.277325625988 |
70 | 17130 | 16086.1191114938 | 1043.88088850617 |
71 | 17697 | 16567.2567033068 | 1129.74329669315 |
72 | 16611 | 14462.1609998986 | 2148.83900010144 |
73 | 12674 | 15009.2180471533 | -2335.21804715328 |
74 | 12760 | 15349.3411978374 | -2589.34119783743 |
75 | 20249 | 20783.6984438491 | -534.698443849062 |
76 | 22135 | 23598.9294861054 | -1463.92948610542 |
77 | 20677 | 24000.6414043071 | -3323.6414043071 |
78 | 19933 | 20673.7362766254 | -740.736276625386 |
79 | 15388 | 15529.5294040313 | -141.529404031309 |
80 | 15113 | 13177.6227624109 | 1935.37723758906 |
81 | 13401 | 11318.5857238543 | 2082.41427614568 |
82 | 16135 | 16918.8166038724 | -783.81660387242 |
83 | 17562 | 17183.8308753920 | 378.169124608034 |
84 | 14720 | 15420.6858304150 | -700.68583041495 |
85 | 12225 | 13596.2037807742 | -1371.20378077415 |
86 | 11608 | 13951.4636916296 | -2343.46369162962 |
87 | 20985 | 20319.4872646026 | 665.512735397373 |
88 | 19692 | 22885.9391831898 | -3193.9391831898 |
89 | 24081 | 22225.9661544674 | 1855.03384553261 |
90 | 22114 | 20745.2029431305 | 1368.79705686955 |
91 | 14220 | 16154.0401457494 | -1934.0401457494 |
92 | 13434 | 14469.5752900437 | -1035.57529004371 |
93 | 13598 | 12264.2838112351 | 1333.71618876487 |
94 | 17187 | 16495.3749721818 | 691.625027818169 |
95 | 16119 | 17471.4670840425 | -1352.46708404247 |
96 | 13713 | 14991.5421999882 | -1278.54219998819 |
97 | 13210 | 12787.8119087772 | 422.18809122283 |
98 | 14251 | 12957.4085355135 | 1293.59146448652 |
99 | 20139 | 21148.6492016738 | -1009.64920167382 |
100 | 21725 | 21783.5337733780 | -58.5337733780252 |
101 | 26099 | 23777.4866096851 | 2321.51339031487 |
102 | 21084 | 22147.0885534734 | -1063.08855347341 |
103 | 18024 | 15766.5562523142 | 2257.44374768581 |
104 | 16722 | 15054.4360832651 | 1667.56391673492 |
105 | 14385 | 14267.0812882495 | 117.918711750523 |
106 | 21342 | 18051.4833665591 | 3290.51663344086 |
107 | 17180 | 18488.4207925968 | -1308.42079259681 |
108 | 14577 | 16051.8193322975 | -1474.81933229747 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 14574.8038861021 | 11514.7674774108 | 17634.8402947933 |
110 | 15074.5742422794 | 11985.59778837 | 18163.5506961888 |
111 | 22077.3594511678 | 18959.4168120771 | 25195.3020902585 |
112 | 23273.6941151390 | 20126.7583722407 | 26420.6298580374 |
113 | 26328.038163073 | 23152.0816481823 | 29503.9946779637 |
114 | 22891.0578994188 | 19686.052222645 | 26096.0635761926 |
115 | 18122.0094438383 | 14887.9255202497 | 21356.0933674269 |
116 | 16842.1188631964 | 13578.9269383598 | 20105.3107880330 |
117 | 15144.0018156409 | 11851.6714900932 | 18436.3321411887 |
118 | 20309.8920767217 | 16988.3923294270 | 23631.3918240164 |
119 | 18268.0727764197 | 14917.3719872643 | 21618.773565575 |
120 | 15936.5820206231 | 12556.6479919948 | 19316.5160492515 |