Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.582325806328971 |
beta | 0.119665026828977 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 3675 | 3715 | -40 |
4 | 3680 | 3818.91960641734 | -138.919606417339 |
5 | 3735 | 3855.55529479502 | -120.555294795021 |
6 | 3860 | 3894.48421657639 | -34.4842165763862 |
7 | 3765 | 3981.13154908894 | -216.131549088941 |
8 | 3905 | 3946.94003417822 | -41.9400341782161 |
9 | 4110 | 4011.26218290788 | 98.7378170921152 |
10 | 4170 | 4164.38512413923 | 5.61487586077237 |
11 | 4110 | 4263.67144072641 | -153.67144072641 |
12 | 4025 | 4259.49277878655 | -234.492778786546 |
13 | 4145 | 4191.9093634013 | -46.9093634012979 |
14 | 4285 | 4230.2917779958 | 54.7082220042021 |
15 | 4370 | 4331.66102450927 | 38.338975490733 |
16 | 4355 | 4426.16965079017 | -71.1696507901734 |
17 | 4385 | 4451.9491896609 | -66.9491896609043 |
18 | 4525 | 4475.52112240426 | 49.4788775957413 |
19 | 4375 | 4570.3400110431 | -195.340011043101 |
20 | 4525 | 4508.98246312861 | 16.0175368713853 |
21 | 4610 | 4571.82003629887 | 38.1799637011254 |
22 | 4595 | 4650.22389640253 | -55.2238964025282 |
23 | 4500 | 4670.38805452466 | -170.388054524662 |
24 | 4370 | 4611.61582455335 | -241.615824553347 |
25 | 4390 | 4494.52906081817 | -104.529060818168 |
26 | 4530 | 4449.98745076376 | 80.0125492362395 |
27 | 4590 | 4518.48477972593 | 71.5152202740674 |
28 | 4580 | 4587.01736373514 | -7.0173637351354 |
29 | 4595 | 4609.32939923032 | -14.3293992303225 |
30 | 4685 | 4626.38491742763 | 58.6150825723716 |
31 | 4490 | 4690.00242517013 | -200.002425170132 |
32 | 4635 | 4589.08330854254 | 45.9166914574553 |
33 | 4710 | 4634.56890005051 | 75.4310999494928 |
34 | 4655 | 4702.49783655794 | -47.4978365579436 |
35 | 4665 | 4695.53224017111 | -30.5322401711082 |
36 | 4550 | 4696.31853874119 | -146.318538741189 |
37 | 4590 | 4619.48342171769 | -29.4834217176867 |
38 | 4675 | 4608.6298846835 | 66.3701153164966 |
39 | 4645 | 4658.21927321393 | -13.2192732139301 |
40 | 4665 | 4660.54053461913 | 4.45946538086991 |
41 | 4635 | 4673.46733526525 | -38.4673352652489 |
42 | 4720 | 4658.71619304281 | 61.2838069571908 |
43 | 4565 | 4706.32321798822 | -141.323217988217 |
44 | 4720 | 4626.09897194485 | 93.9010280551547 |
45 | 4830 | 4689.39527700684 | 140.604722993159 |
46 | 4830 | 4789.68625307257 | 40.3137469274343 |
47 | 4765 | 4834.38443011412 | -69.3844301141207 |
48 | 4705 | 4810.36754082289 | -105.367540822892 |
49 | 4675 | 4758.05432235709 | -83.0543223570912 |
50 | 4900 | 4712.94710666653 | 187.052893333473 |
51 | 4945 | 4838.16489318448 | 106.835106815523 |
52 | 4905 | 4924.11449362071 | -19.1144936207065 |
53 | 4955 | 4935.38841641731 | 19.6115835826868 |
54 | 5120 | 4970.58014758956 | 149.419852410439 |
55 | 4860 | 5091.77476153682 | -231.774761536818 |
56 | 5040 | 4974.83891436242 | 65.1610856375828 |
57 | 5140 | 5035.35716107919 | 104.642838920809 |
58 | 5240 | 5126.15858667733 | 113.841413322668 |
59 | 5145 | 5230.2495083609 | -85.2495083609001 |
60 | 5070 | 5212.4641189682 | -142.4641189682 |
61 | 5085 | 5151.43371091846 | -66.4337109184644 |
62 | 5215 | 5130.04840262208 | 84.9515973779235 |
63 | 5255 | 5202.73843598101 | 52.2615640189897 |
64 | 5275 | 5260.03401586943 | 14.9659841305729 |
65 | 5315 | 5296.6543072624 | 18.3456927375973 |
66 | 5450 | 5336.52109205761 | 113.478907942387 |
67 | 5205 | 5439.69407109844 | -234.69407109844 |
68 | 5370 | 5323.76250992628 | 46.2374900737241 |
69 | 5500 | 5374.64666143207 | 125.353338567933 |
70 | 5490 | 5480.33713941686 | 9.6628605831429 |
71 | 5440 | 5519.33141362261 | -79.3314136226145 |
72 | 5360 | 5500.97389247918 | -140.973892479182 |
73 | 5380 | 5436.89673572233 | -56.8967357223346 |
74 | 5460 | 5417.81508304458 | 42.1849169554189 |
75 | 5450 | 5459.37084881005 | -9.37084881005376 |
76 | 5520 | 5470.2513631653 | 49.7486368347036 |
77 | 5475 | 5519.02536533109 | -44.0253653310883 |
78 | 5600 | 5510.12448105196 | 89.8755189480362 |
79 | 5250 | 5585.46042582846 | -335.460425828462 |
80 | 5465 | 5389.73603813897 | 75.2639618610274 |
81 | 5515 | 5438.43175710965 | 76.5682428903474 |
82 | 5425 | 5493.22257656492 | -68.2225765649237 |
83 | 5325 | 5458.94394103897 | -133.94394103897 |
84 | 5275 | 5377.0603049133 | -102.060304913297 |
85 | 5160 | 5306.63135922339 | -146.631359223392 |
86 | 5360 | 5200.02967388364 | 159.970326116363 |
87 | 5435 | 5283.11743970329 | 151.882560296708 |
88 | 5285 | 5372.07928015054 | -87.0792801505386 |
89 | 5415 | 5315.81943872517 | 99.1805612748258 |
90 | 5575 | 5374.93481117294 | 200.065188827063 |
91 | 5265 | 5506.73925497416 | -241.739254974158 |
92 | 5480 | 5364.42420352067 | 115.575796479332 |
93 | 5565 | 5438.23671516163 | 126.763284838367 |
94 | 5500 | 5527.39736693605 | -27.3973669360485 |
95 | 5280 | 5524.87713383353 | -244.877133833535 |
96 | 5135 | 5378.64879377903 | -243.648793779031 |
97 | 5050 | 5216.15731719322 | -166.157317193221 |
98 | 5100 | 5087.21261517991 | 12.7873848200907 |
99 | 5070 | 5063.36310760362 | 6.63689239637915 |
100 | 5115 | 5036.39449499772 | 78.6055050022815 |
101 | 5140 | 5056.81261138116 | 83.1873886188396 |
102 | 5330 | 5085.69570958958 | 244.30429041042 |
103 | 5080 | 5225.42544584005 | -145.425445840047 |
104 | 5285 | 5128.07166757658 | 156.928332423422 |
105 | 5405 | 5217.7216961695 | 187.278303830497 |
106 | 5385 | 5338.09560388291 | 46.9043961170864 |
107 | 5255 | 5379.99465009757 | -124.994650097575 |
108 | 5100 | 5313.08231426619 | -213.082314266186 |
109 | 5040 | 5180.02582330051 | -140.025823300512 |
110 | 5235 | 5079.754448219 | 155.245551780999 |
111 | 5310 | 5162.24535090798 | 147.754649092016 |
112 | 5265 | 5250.67024752681 | 14.3297524731943 |
113 | 5380 | 5262.39693858534 | 117.603061414658 |
114 | 5465 | 5342.45739818593 | 122.542601814066 |
115 | 5225 | 5433.93354237034 | -208.933542370335 |
116 | 5445 | 5317.82324170276 | 127.176758297241 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
117 | 5406.30083233914 | 5166.19928190177 | 5646.4023827765 |
118 | 5420.72011465376 | 5134.09106806244 | 5707.34916124509 |
119 | 5435.13939696839 | 5100.20342456898 | 5770.07536936781 |
120 | 5449.55867928302 | 5064.47906495106 | 5834.63829361499 |
121 | 5463.97796159765 | 5026.90967090345 | 5901.04625229185 |
122 | 5478.39724391228 | 4987.51118915438 | 5969.28329867019 |
123 | 5492.81652622691 | 4946.31175723573 | 6039.32129521809 |
124 | 5507.23580854154 | 4903.34542847818 | 6111.1261886049 |
125 | 5521.65509085617 | 4858.64877592061 | 6184.66140579173 |
126 | 5536.0743731708 | 4812.25901056515 | 6259.88973577645 |
127 | 5550.49365548543 | 4764.21293162697 | 6336.77437934388 |
128 | 5564.91293780006 | 4714.54634895353 | 6415.27952664658 |