Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.135019238273121 |
beta | 0.0440917299700262 |
gamma | 0.0333766681540438 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 9911 | 9855.39449786325 | 55.6055021367483 |
14 | 8915 | 8868.50505030804 | 46.4949496919617 |
15 | 9452 | 9395.41229811428 | 56.5877018857173 |
16 | 9112 | 9059.56080800653 | 52.4391919934733 |
17 | 8472 | 8427.54470525155 | 44.4552947484517 |
18 | 8230 | 8162.79860877957 | 67.2013912204302 |
19 | 8384 | 8503.52373838579 | -119.523738385786 |
20 | 8625 | 8434.15916403987 | 190.840835960125 |
21 | 8221 | 7985.6692311748 | 235.330768825194 |
22 | 8649 | 8814.04560710458 | -165.045607104577 |
23 | 8625 | 8488.4642483113 | 136.5357516887 |
24 | 10443 | 9897.66500383773 | 545.334996162268 |
25 | 10357 | 10207.5800348888 | 149.419965111239 |
26 | 8586 | 9240.47675450445 | -654.476754504447 |
27 | 8892 | 9676.24010234525 | -784.240102345255 |
28 | 8329 | 9224.94465761887 | -895.944657618873 |
29 | 8101 | 8457.20578773181 | -356.205787731811 |
30 | 7922 | 8129.19198695794 | -207.19198695794 |
31 | 8120 | 8416.01698300128 | -296.01698300128 |
32 | 7838 | 8319.27103852083 | -481.271038520834 |
33 | 7735 | 7764.80460021012 | -29.8046002101173 |
34 | 8406 | 8527.73234758384 | -121.732347583844 |
35 | 8209 | 8198.87235621862 | 10.1276437813794 |
36 | 9451 | 9584.22169187039 | -133.221691870385 |
37 | 10041 | 9768.46277445654 | 272.537225543463 |
38 | 9411 | 8772.88139397185 | 638.118606028147 |
39 | 10405 | 9365.22615274824 | 1039.77384725176 |
40 | 8467 | 9153.64399041275 | -686.643990412755 |
41 | 8464 | 8427.654347122 | 36.3456528779898 |
42 | 8102 | 8157.1888010478 | -55.1888010477978 |
43 | 7627 | 8463.12187198599 | -836.12187198599 |
44 | 7513 | 8286.0368038243 | -773.036803824307 |
45 | 7510 | 7701.40708453483 | -191.407084534827 |
46 | 8291 | 8435.09615523769 | -144.096155237687 |
47 | 8064 | 8102.12504170216 | -38.1250417021565 |
48 | 9383 | 9471.63515753307 | -88.6351575330718 |
49 | 9706 | 9668.69038683757 | 37.3096131624316 |
50 | 8579 | 8645.58256306614 | -66.582563066142 |
51 | 9474 | 9143.85912583628 | 330.140874163722 |
52 | 8318 | 8771.8804255021 | -453.880425502099 |
53 | 8213 | 8084.83642706802 | 128.163572931981 |
54 | 8059 | 7811.31731168935 | 247.682688310645 |
55 | 9111 | 8124.59311036594 | 986.406889634055 |
56 | 7708 | 8195.25062554122 | -487.250625541223 |
57 | 7680 | 7667.54550318863 | 12.4544968113705 |
58 | 8014 | 8432.8855319782 | -418.885531978196 |
59 | 8007 | 8066.99593374934 | -59.9959337493392 |
60 | 8718 | 9433.08858293744 | -715.088582937438 |
61 | 9486 | 9546.4609336245 | -60.4609336244976 |
62 | 9113 | 8503.83510699378 | 609.164893006217 |
63 | 9025 | 9105.50922047261 | -80.5092204726134 |
64 | 8476 | 8653.71049770796 | -177.710497707958 |
65 | 7952 | 8020.66304206782 | -68.6630420678202 |
66 | 7759 | 7722.75190740084 | 36.2480925991576 |
67 | 7835 | 8026.28116891763 | -191.281168917627 |
68 | 7600 | 7885.84644121834 | -285.846441218339 |
69 | 7651 | 7391.42339227517 | 259.576607724832 |
70 | 8319 | 8170.81003207372 | 148.189967926277 |
71 | 8812 | 7888.35690790335 | 923.643092096655 |
72 | 8630 | 9370.71210645267 | -740.712106452673 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
73 | 9501.73645841764 | 8679.82223219945 | 10323.6506846358 |
74 | 8489.1786288639 | 7659.1375325786 | 9319.2197251492 |
75 | 8987.63864227532 | 8148.8590064294 | 9826.41827812125 |
76 | 8543.32917791797 | 7695.19001067107 | 9391.46834516488 |
77 | 7937.90741206751 | 7079.78014071188 | 8796.03468342315 |
78 | 7653.18781348538 | 6784.4379865592 | 8521.93764041155 |
79 | 7945.93018360513 | 7065.91911854136 | 8825.9412486689 |
80 | 7830.40682696975 | 6938.49318978734 | 8722.32046415216 |
81 | 7393.84156561816 | 6489.38287100986 | 8298.30026022646 |
82 | 8136.93585747923 | 7219.28987965724 | 9054.58183530122 |
83 | 7857.95073533312 | 6926.4768220809 | 8789.42464858533 |
84 | 9163.13648903983 | 8217.19677350901 | 10109.0762045706 |