Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.105286354127589 |
beta | 0.0235096656309281 |
gamma | 0.357989297961511 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 9016 | 8341.80493621812 | 674.195063781877 |
14 | 8201 | 7692.67196296991 | 508.32803703009 |
15 | 7630 | 7185.70804867018 | 444.291951329816 |
16 | 7107 | 6705.98981801135 | 401.010181988650 |
17 | 6820 | 6491.20256411012 | 328.797435889876 |
18 | 6082 | 5880.20373488518 | 201.796265114823 |
19 | 6019 | 6305.59531317355 | -286.595313173545 |
20 | 6576 | 6256.22444562094 | 319.775554379063 |
21 | 8086 | 6996.025613229 | 1089.974386771 |
22 | 8323 | 7952.29768025301 | 370.702319746989 |
23 | 7842 | 8221.85319754435 | -379.853197544355 |
24 | 9077 | 10443.1061170463 | -1366.10611704635 |
25 | 10737 | 10364.0481378173 | 372.951862182706 |
26 | 10176 | 9455.23607663357 | 720.763923366427 |
27 | 10416 | 8816.91207146927 | 1599.08792853073 |
28 | 9807 | 8315.3003014662 | 1491.69969853380 |
29 | 9565 | 8117.62542442932 | 1447.37457557068 |
30 | 10439 | 7407.05881203012 | 3031.94118796988 |
31 | 9115 | 8042.87377444761 | 1072.12622555239 |
32 | 9535 | 8383.90963683335 | 1151.09036316665 |
33 | 10790 | 9764.1128927004 | 1025.8871072996 |
34 | 11340 | 10678.1728122877 | 661.827187712335 |
35 | 11196 | 10732.2865452781 | 463.713454721888 |
36 | 12132 | 13374.3400349670 | -1242.34003496704 |
37 | 12013 | 14077.9301818921 | -2064.93018189214 |
38 | 12692 | 12753.1348944739 | -61.1348944738565 |
39 | 13330 | 12165.0146536831 | 1164.98534631695 |
40 | 11926 | 11360.2052048910 | 565.794795109046 |
41 | 11356 | 10932.0496986903 | 423.950301309724 |
42 | 11221 | 10472.1212611640 | 748.878738836045 |
43 | 9999 | 10156.8138772920 | -157.813877291954 |
44 | 11772 | 10423.5120677162 | 1348.48793228377 |
45 | 12543 | 11998.1757629573 | 544.824237042711 |
46 | 14176 | 12852.9223447867 | 1323.07765521327 |
47 | 2924 | 12883.0602369135 | -9959.06023691351 |
48 | 2322 | 14014.7344942861 | -11692.7344942861 |
49 | 15557 | 13296.0255295119 | 2260.97447048808 |
50 | 13381 | 13018.8754885759 | 362.124511424125 |
51 | 13145 | 12823.4629621890 | 321.537037811015 |
52 | 12448 | 11686.6052026555 | 761.394797344487 |
53 | 12178 | 11194.8802035217 | 983.119796478302 |
54 | 11836 | 10861.2585869274 | 974.741413072567 |
55 | 9815 | 10242.7440794549 | -427.744079454931 |
56 | 12382 | 10938.6180691959 | 1443.38193080409 |
57 | 12662 | 12245.5709638898 | 416.429036110152 |
58 | 12767 | 13305.1729213711 | -538.172921371066 |
59 | 13136 | 9269.7971729448 | 3866.20282705521 |
60 | 13533 | 11083.9330286545 | 2449.06697134546 |
61 | 17808 | 17593.1192915399 | 214.880708460139 |
62 | 15892 | 16238.0010641410 | -346.001064141023 |
63 | 16830 | 15907.0315156117 | 922.968484388324 |
64 | 14444 | 14739.3692059401 | -295.369205940066 |
65 | 15550 | 14097.8873554808 | 1452.11264451923 |
66 | 15092 | 13713.9697094146 | 1378.03029058543 |
67 | 16364 | 12425.7833247484 | 3938.21667525159 |
68 | 14314 | 14557.304094364 | -243.304094364014 |
69 | 15874 | 15581.7613180096 | 292.238681990364 |
70 | 17846 | 16515.6012963439 | 1330.39870365611 |
71 | 18504 | 13330.026761958 | 5173.97323804201 |
72 | 15130 | 15075.5598112572 | 54.4401887427684 |
73 | 19845 | 21975.8139573879 | -2130.81395738792 |
74 | 18137 | 19841.2262186486 | -1704.22621864859 |
75 | 18898 | 19799.9595923961 | -901.959592396102 |
76 | 19573 | 17704.3634348958 | 1868.63656510418 |
77 | 17368 | 17836.6883887206 | -468.688388720642 |
78 | 18938 | 17104.4607627744 | 1833.5392372256 |
79 | 16713 | 16506.8408255114 | 206.15917448861 |
80 | 16379 | 16963.8004058771 | -584.800405877104 |
81 | 19139 | 18322.5238356449 | 816.476164355106 |
82 | 21461 | 19844.7150301905 | 1616.28496980948 |
83 | 19796 | 17477.8112814679 | 2318.18871853211 |
84 | 16668 | 17208.5259236055 | -540.52592360555 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
85 | 24162.0083177812 | 22257.2556144068 | 26066.7610211557 |
86 | 22108.8640359726 | 20154.5370681269 | 24063.1910038183 |
87 | 22553.6358618585 | 20536.0683544835 | 24571.2033692335 |
88 | 21244.5166677715 | 19186.7492919231 | 23302.2840436198 |
89 | 20299.3047869967 | 18200.3665643361 | 22398.2430096573 |
90 | 20344.4408574057 | 18185.7774399637 | 22503.1042748476 |
91 | 18839.8377761620 | 16664.3611282453 | 21015.3144240787 |
92 | 19033.1548437592 | 16792.8837328223 | 21273.4259546961 |
93 | 21147.6467967923 | 18765.9439363072 | 23529.3496572775 |
94 | 23044.7500183862 | 20516.7890570771 | 25572.7109796953 |
95 | 20422.6134113410 | 17966.3847046378 | 22878.8421180443 |
96 | 18823.6559072776 | 17310.6323952597 | 20336.6794192954 |