Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.912866565535159 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 139871 | 178421 | -38550 |
3 | 118159 | 143229.99389862 | -25070.9938986196 |
4 | 109763 | 120343.521803834 | -10580.5218038338 |
5 | 97415 | 110684.917203198 | -13269.9172031982 |
6 | 119190 | 98571.2534609787 | 20618.7465390213 |
7 | 97903 | 117393.417799695 | -19490.417799695 |
8 | 96953 | 99601.2670420421 | -2648.26704204209 |
9 | 87888 | 97183.7526027532 | -9295.75260275317 |
10 | 84637 | 88697.9708502134 | -4060.97085021337 |
11 | 90549 | 84990.8463374407 | 5558.1536625593 |
12 | 95680 | 90064.6989820979 | 5615.30101790212 |
13 | 99371 | 95190.7195367563 | 4180.28046324373 |
14 | 79984 | 99006.7578062113 | -19022.7578062113 |
15 | 86752 | 81641.5182206481 | 5110.48177935195 |
16 | 85733 | 86306.7061707951 | -573.706170795078 |
17 | 84906 | 85782.988989035 | -876.988989035046 |
18 | 78356 | 84982.4150626025 | -6626.41506260248 |
19 | 108895 | 78933.3823025941 | 29961.6176974059 |
20 | 101768 | 106284.341347902 | -4516.34134790246 |
21 | 73285 | 102161.524332858 | -28876.5243328583 |
22 | 65724 | 75801.1107405295 | -10077.1107405295 |
23 | 67457 | 66602.0532683049 | 854.946731695134 |
24 | 67203 | 67382.5055549829 | -179.505554982912 |
25 | 69273 | 67218.6409355112 | 2054.35906448882 |
26 | 80807 | 69093.9966390871 | 11713.0033609129 |
27 | 75129 | 79786.4057892654 | -4657.40578926544 |
28 | 74991 | 75534.8157621151 | -543.815762115133 |
29 | 68157 | 75038.3845350692 | -6881.38453506921 |
30 | 73858 | 68756.5986684138 | 5101.40133158618 |
31 | 71349 | 73413.4973813954 | -2064.49738139538 |
32 | 85634 | 71528.8867472846 | 14105.1132527154 |
33 | 91624 | 84404.9730387754 | 7219.02696122463 |
34 | 116014 | 90994.9813873742 | 25019.0186126258 |
35 | 120033 | 113834.006981342 | 6198.99301865787 |
36 | 108651 | 119492.860448061 | -10841.8604480608 |
37 | 105378 | 109595.688536828 | -4217.68853682805 |
38 | 138939 | 105745.501687717 | 33193.4983122832 |
39 | 132974 | 136046.736490148 | -3072.73649014786 |
40 | 135277 | 133241.738083592 | 2035.26191640797 |
41 | 152741 | 135099.660639188 | 17641.3393608121 |
42 | 158417 | 151203.849512933 | 7213.15048706735 |
43 | 157460 | 157788.49342475 | -328.493424750079 |
44 | 193997 | 157488.622760298 | 36508.3772397024 |
45 | 154089 | 190815.899704367 | -36726.8997043667 |
46 | 147570 | 157289.140908487 | -9719.14090848723 |
47 | 162924 | 148416.862127404 | 14507.1378725958 |
48 | 153629 | 161659.943252906 | -8030.94325290577 |
49 | 155907 | 154328.763667618 | 1578.23633238208 |
50 | 197675 | 155769.482847962 | 41905.5171520376 |
51 | 250708 | 194023.628367518 | 56684.3716324823 |
52 | 266652 | 245768.89601918 | 20883.1039808196 |
53 | 209842 | 264832.383427865 | -54990.3834278648 |
54 | 165826 | 214633.500970608 | -48807.5009706084 |
55 | 137152 | 170078.765187215 | -32926.7651872152 |
56 | 150581 | 140021.022136579 | 10559.9778634206 |
57 | 145973 | 149660.872860887 | -3687.87286088747 |
58 | 126532 | 146294.337028239 | -19762.3370282388 |
59 | 115437 | 128253.960298322 | -12816.9602983221 |
60 | 119526 | 116553.785770192 | 2972.21422980768 |
61 | 110856 | 119267.020766192 | -8411.02076619158 |
62 | 97243 | 111588.881126713 | -14345.8811267134 |
63 | 103876 | 98493.0058929949 | 5382.99410700513 |
64 | 116370 | 103406.961235753 | 12963.0387642474 |
65 | 109616 | 115240.48591137 | -5624.48591137026 |
66 | 98365 | 110106.080774557 | -11741.0807745568 |
67 | 90440 | 99388.0406922163 | -8948.04069221625 |
68 | 88899 | 91219.673517244 | -2320.67351724395 |
69 | 92358 | 89101.2082538291 | 3256.79174617093 |
70 | 88394 | 92074.2245498194 | -3680.22454981938 |
71 | 98219 | 88714.6706046276 | 9504.32939537242 |
72 | 113546 | 97390.8551374961 | 16155.1448625039 |
73 | 107168 | 112138.346743853 | -4970.34674385301 |
74 | 77540 | 107601.083382273 | -30061.083382273 |
75 | 74944 | 80159.3254388314 | -5215.32543883141 |
76 | 75641 | 75398.4292173372 | 242.570782662762 |
77 | 75910 | 75619.8639746058 | 290.136025394226 |
78 | 87384 | 75884.7194516454 | 11499.2805483546 |
79 | 84615 | 86382.0281919471 | -1767.02819194713 |
80 | 80420 | 84768.9672351606 | -4348.96723516055 |
81 | 80784 | 80798.9404515746 | -14.9404515745991 |
82 | 79933 | 80785.3018128581 | -852.301812858146 |
83 | 82118 | 80007.2639841549 | 2110.73601584506 |
84 | 91420 | 81934.0843216908 | 9485.91567830922 |
85 | 112426 | 90593.459587905 | 21832.540412095 |
86 | 114528 | 110523.655770802 | 4004.34422919826 |
87 | 131025 | 114179.08773453 | 16845.9122654695 |
88 | 116460 | 129557.157807616 | -13097.1578076163 |
89 | 111258 | 117601.200341506 | -6343.20034150561 |
90 | 155318 | 111810.704831254 | 43507.2951687461 |
91 | 155078 | 151527.059947672 | 3550.94005232843 |
92 | 134794 | 154768.594397662 | -19974.5943976619 |
93 | 139985 | 136534.45501191 | 3450.54498808956 |
94 | 198778 | 139684.342164412 | 59093.6578355877 |
95 | 172436 | 193628.966637695 | -21192.9666376951 |
96 | 169585 | 174282.615969641 | -4697.61596964116 |
97 | 203702 | 169994.319413232 | 33707.6805867683 |
98 | 282392 | 200764.934022631 | 81627.065977369 |
99 | 220658 | 275279.553396104 | -54621.5533961037 |
100 | 194472 | 225417.363543207 | -30945.3635432072 |
101 | 269246 | 197168.375806283 | 72077.6241937173 |
102 | 215340 | 262965.629055935 | -47625.6290559353 |
103 | 218319 | 219489.784628192 | -1170.78462819217 |
104 | 195724 | 218421.014485673 | -22697.014485673 |
105 | 174614 | 197701.668824235 | -23087.6688242349 |
106 | 172085 | 176625.707878442 | -4540.70787844242 |
107 | 152347 | 172480.64747235 | -20133.6474723502 |
108 | 189615 | 154101.31385257 | 35513.6861474297 |
109 | 173804 | 186520.570555468 | -12716.570555468 |
110 | 145683 | 174912.038467112 | -29229.0384671124 |
111 | 133550 | 148229.826507744 | -14679.8265077445 |
112 | 121156 | 134829.103700968 | -13673.1037009678 |
113 | 112040 | 122347.384485259 | -10307.3844852593 |
114 | 120767 | 112938.11781055 | 7828.88218944974 |
115 | 127019 | 120084.842606813 | 6934.15739318739 |
116 | 136295 | 126414.803051212 | 9880.19694878819 |
117 | 113425 | 135434.104506663 | -22009.104506663 |
118 | 107815 | 115342.728865161 | -7527.72886516116 |
119 | 100298 | 108470.916869742 | -8172.91686974162 |
120 | 97048 | 101010.134316456 | -3962.13431645623 |
121 | 98750 | 97393.2343708038 | 1356.76562919616 |
122 | 98235 | 98631.7803509643 | -396.780350964284 |
123 | 101254 | 98269.5728347077 | 2984.42716529232 |
124 | 139589 | 100993.956611178 | 38595.0433888221 |
125 | 134921 | 136226.081316212 | -1305.08131621237 |
126 | 80355 | 135034.716217337 | -54679.7162173375 |
127 | 80396 | 85119.4314695795 | -4723.43146957947 |
128 | 82183 | 80807.5688064038 | 1375.43119359623 |
129 | 79709 | 82063.1539562319 | -2354.15395623188 |
130 | 90781 | 79914.1255194655 | 10866.8744805345 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
131 | 89834.1319046127 | 46513.2003336315 | 133155.063475594 |
132 | 89834.1319046127 | 31177.4407185927 | 148490.823090633 |
133 | 89834.1319046127 | 19091.5582335438 | 160576.705575682 |
134 | 89834.1319046127 | 8788.36681894587 | 170879.896990279 |