Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.821146945168228 |
beta | 0.0660065936452337 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 116566 | 124441.288382663 | -7875.28838266317 |
14 | 111272 | 112397.249136598 | -1125.2491365977 |
15 | 104609 | 104733.334614409 | -124.334614408843 |
16 | 101802 | 101742.528844829 | 59.4711551713262 |
17 | 94542 | 94175.4472559367 | 366.552744063301 |
18 | 93051 | 92347.8164965284 | 703.183503471577 |
19 | 124129 | 124067.158166026 | 61.8418339735654 |
20 | 130374 | 128263.368680539 | 2110.63131946069 |
21 | 123946 | 128187.116421263 | -4241.11642126295 |
22 | 114971 | 111085.722949336 | 3885.27705066354 |
23 | 105531 | 103577.837413299 | 1953.16258670064 |
24 | 104919 | 98726.7799070003 | 6192.22009299975 |
25 | 104782 | 103532.50752725 | 1249.49247274967 |
26 | 101281 | 101047.016736103 | 233.983263897433 |
27 | 94545 | 95748.905296604 | -1203.90529660399 |
28 | 93248 | 92581.9329823049 | 666.067017695124 |
29 | 84031 | 86642.6175486143 | -2611.61754861427 |
30 | 87486 | 82884.4901658529 | 4601.50983414706 |
31 | 115867 | 116252.329496446 | -385.329496445644 |
32 | 120327 | 120855.728507834 | -528.728507834167 |
33 | 117008 | 118230.419023411 | -1222.41902341071 |
34 | 108811 | 106387.847430459 | 2423.15256954117 |
35 | 104519 | 98523.2406963605 | 5995.75930363948 |
36 | 106758 | 98625.3278229988 | 8132.67217700121 |
37 | 109337 | 105089.336850723 | 4247.6631492766 |
38 | 109078 | 105879.568262519 | 3198.43173748083 |
39 | 108293 | 103615.87536402 | 4677.12463598014 |
40 | 106534 | 107018.236098763 | -484.236098763038 |
41 | 99197 | 100015.87323194 | -818.873231940292 |
42 | 103493 | 100594.435851739 | 2898.56414826095 |
43 | 130676 | 138807.358941436 | -8131.35894143625 |
44 | 137448 | 139387.766730328 | -1939.76673032757 |
45 | 134704 | 136740.350856428 | -2036.35085642833 |
46 | 123725 | 124758.596783582 | -1033.59678358184 |
47 | 118277 | 114496.871251854 | 3780.12874814586 |
48 | 121225 | 113427.210701426 | 7797.78929857432 |
49 | 120528 | 119621.682769028 | 906.317230972039 |
50 | 118240 | 117783.911506409 | 456.088493590549 |
51 | 112514 | 113540.021069217 | -1026.02106921673 |
52 | 107304 | 111385.057518834 | -4081.05751883404 |
53 | 100001 | 101198.413758781 | -1197.41375878129 |
54 | 102082 | 102041.832072794 | 40.1679272064357 |
55 | 130455 | 135075.152567257 | -4620.15256725738 |
56 | 135574 | 139526.360231213 | -3952.36023121286 |
57 | 132540 | 134952.149675754 | -2412.14967575358 |
58 | 119920 | 122707.642245043 | -2787.64224504307 |
59 | 112454 | 111741.454813604 | 712.545186396193 |
60 | 109415 | 108492.440428369 | 922.559571631384 |
61 | 109843 | 107147.959626552 | 2695.04037344808 |
62 | 106365 | 106259.694104097 | 105.305895903308 |
63 | 102304 | 101286.695614329 | 1017.30438567123 |
64 | 97968 | 99861.3861758082 | -1893.38617580822 |
65 | 92462 | 92084.7104592586 | 377.289540741389 |
66 | 92286 | 93928.5865119708 | -1642.58651197077 |
67 | 120092 | 121144.157778838 | -1052.15777883786 |
68 | 126656 | 127532.817836819 | -876.817836818518 |
69 | 124144 | 125532.011434963 | -1388.01143496261 |
70 | 114045 | 114464.016115062 | -419.016115062186 |
71 | 108120 | 106365.679797993 | 1754.32020200747 |
72 | 105698 | 104135.94950072 | 1562.05049927977 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
73 | 103698.260996815 | 97513.998454674 | 109882.523538957 |
74 | 100200.242698003 | 92088.6810621115 | 108311.804333895 |
75 | 95453.6068432366 | 85788.2198073768 | 105118.993879096 |
76 | 92672.2535607671 | 81495.7636819867 | 103848.743439547 |
77 | 87092.7060576188 | 74818.4653642676 | 99366.94675097 |
78 | 88093.74351185 | 74030.3974960928 | 102157.089527607 |
79 | 115444.175495003 | 95539.9303516807 | 135348.420638326 |
80 | 122489.75162375 | 99640.5369187965 | 145338.966328704 |
81 | 121252.994216912 | 96852.2085516222 | 145653.779882202 |
82 | 111883.464542905 | 87592.8853441453 | 136174.043741664 |
83 | 104825.661508416 | 80326.8768733909 | 129324.446143441 |
84 | 101301.711591829 | 76669.3846894037 | 125934.038494255 |