Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.548527818590737 |
beta | 0.000644959083758779 |
gamma | 0.777318754607708 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 92559 | 85982.6856303419 | 6576.3143696581 |
14 | 73981 | 71586.9604668322 | 2394.03953316779 |
15 | 71107 | 70498.5715023652 | 608.428497634843 |
16 | 96942 | 97786.5237936756 | -844.523793675617 |
17 | 86270 | 87414.9842268457 | -1144.98422684574 |
18 | 69610 | 70986.2703504739 | -1376.27035047389 |
19 | 57768 | 77316.5777070669 | -19548.5777070669 |
20 | 80077 | 65669.0780938773 | 14407.9219061227 |
21 | 71454 | 81693.1770129404 | -10239.1770129404 |
22 | 70382 | 70634.7007984483 | -252.700798448277 |
23 | 69881 | 62502.4118639836 | 7378.58813601641 |
24 | 84530 | 89920.4992505915 | -5390.4992505915 |
25 | 79322 | 90255.6905370996 | -10933.6905370996 |
26 | 80181 | 64778.6985396935 | 15402.3014603065 |
27 | 82137 | 70194.8430185478 | 11942.1569814522 |
28 | 88439 | 103189.552725928 | -14750.5527259283 |
29 | 91575 | 85079.5948009386 | 6495.40519906138 |
30 | 82909 | 72758.2513081145 | 10150.7486918855 |
31 | 73282 | 79035.7491092813 | -5753.74910928126 |
32 | 94089 | 86878.245386985 | 7210.754613015 |
33 | 108112 | 90308.8827063547 | 17803.1172936453 |
34 | 95653 | 98150.921087073 | -2497.92108707299 |
35 | 85273 | 91478.2838988088 | -6205.28389880882 |
36 | 105093 | 106972.388389777 | -1879.388389777 |
37 | 102275 | 107297.752646559 | -5022.75264655927 |
38 | 99308 | 94317.0069144006 | 4990.99308559937 |
39 | 79687 | 92815.9178297424 | -13128.9178297424 |
40 | 93263 | 102690.049489015 | -9427.04948901468 |
41 | 114918 | 94957.1587042393 | 19960.8412957607 |
42 | 103374 | 91310.5113770731 | 12063.4886229269 |
43 | 65124 | 93062.119251958 | -27938.1192519581 |
44 | 104045 | 93284.1657418708 | 10760.8342581292 |
45 | 101183 | 102379.196874525 | -1196.19687452525 |
46 | 95492 | 92668.2757189951 | 2823.72428100491 |
47 | 85035 | 87608.6324510824 | -2573.63245108243 |
48 | 90692 | 106609.180934283 | -15917.1809342834 |
49 | 107486 | 98122.5958088848 | 9363.4041911152 |
50 | 98179 | 96543.6443028818 | 1635.35569711824 |
51 | 82551 | 86838.131213733 | -4287.13121373301 |
52 | 106804 | 102859.680348468 | 3944.3196515321 |
53 | 110898 | 112777.735604522 | -1879.73560452218 |
54 | 89950 | 94374.7745724244 | -4424.77457242443 |
55 | 65184 | 73033.5320266145 | -7849.5320266145 |
56 | 95357 | 97852.2563509315 | -2495.25635093151 |
57 | 98280 | 95471.6927177199 | 2808.30728228015 |
58 | 92146 | 89361.4262838443 | 2784.57371615572 |
59 | 77874 | 82379.4880579576 | -4505.48805795761 |
60 | 100039 | 95630.2377650423 | 4408.7622349577 |
61 | 104777 | 107164.734780101 | -2387.73478010108 |
62 | 102341 | 96423.5591683452 | 5917.44083165479 |
63 | 71316 | 86985.646123207 | -15669.646123207 |
64 | 88838 | 99645.4512239981 | -10807.4512239981 |
65 | 85457 | 99415.8046599267 | -13958.8046599267 |
66 | 70784 | 73477.6505399322 | -2693.65053993219 |
67 | 70522 | 51868.3759639063 | 18653.6240360937 |
68 | 88629 | 93097.4877013623 | -4468.48770136235 |
69 | 88452 | 91488.725954073 | -3036.72595407293 |
70 | 98886 | 82154.85259344 | 16731.14740656 |
71 | 79601 | 80260.4592153847 | -659.459215384675 |
72 | 108135 | 98746.3901054685 | 9388.60989453146 |
73 | 113835 | 110626.266227334 | 3208.73377266599 |
74 | 101617 | 105870.431017513 | -4253.43101751289 |
75 | 68698 | 83275.1106313527 | -14577.1106313527 |
76 | 79182 | 98238.2397860906 | -19056.2397860906 |
77 | 86003 | 92372.765956804 | -6369.76595680404 |
78 | 84165 | 74548.2556034055 | 9616.74439659451 |
79 | 68550 | 67184.9722859613 | 1365.02771403872 |
80 | 90385 | 90812.1005252403 | -427.100525240254 |
81 | 100368 | 91919.7565422856 | 8448.24345771439 |
82 | 99081 | 95824.2105580484 | 3256.78944195157 |
83 | 81288 | 80432.1772399301 | 855.822760069917 |
84 | 103491 | 103272.507087103 | 218.492912897287 |
85 | 111695 | 107947.300102278 | 3747.69989772202 |
86 | 82504 | 100862.271080889 | -18358.2710808893 |
87 | 62237 | 66896.0181375353 | -4659.01813753534 |
88 | 78249 | 85720.0439735783 | -7471.04397357826 |
89 | 92341 | 90658.0768001031 | 1682.92319989686 |
90 | 84412 | 82860.3513339137 | 1551.64866608626 |
91 | 75102 | 68173.836344098 | 6928.16365590201 |
92 | 90461 | 94222.0789336987 | -3761.07893369869 |
93 | 106451 | 96612.97425354 | 9838.02574646 |
94 | 98379 | 99455.7023418756 | -1076.70234187559 |
95 | 72615 | 80840.3224286113 | -8225.32242861128 |
96 | 98367 | 98468.7998254973 | -101.799825497321 |
97 | 116949 | 104199.393604992 | 12749.6063950084 |
98 | 95832 | 94290.4828376276 | 1541.51716237245 |
99 | 68060 | 76050.5858463905 | -7990.58584639052 |
100 | 83923 | 92062.3122483282 | -8139.31224832825 |
101 | 87653 | 99848.022238282 | -12195.022238282 |
102 | 78054 | 84388.6465854162 | -6334.6465854162 |
103 | 57566 | 67257.1697219225 | -9691.16972192255 |
104 | 78784 | 80426.1750096974 | -1642.1750096974 |
105 | 88916 | 88740.7260864393 | 175.273913560726 |
106 | 84662 | 82438.2951417569 | 2223.7048582431 |
107 | 63442 | 63111.2467866248 | 330.753213375188 |
108 | 77773 | 88273.5351006883 | -10500.5351006883 |
109 | 88102 | 92796.2129153977 | -4694.21291539774 |
110 | 87972 | 69365.4041120282 | 18606.5958879718 |
111 | 61790 | 57126.9038036889 | 4663.09619631115 |
112 | 95276 | 80017.7111681615 | 15258.2888318385 |
113 | 104418 | 99213.0099491208 | 5204.99005087925 |
114 | 95420 | 95359.4637510156 | 60.5362489844265 |
115 | 82141 | 80565.0655957316 | 1575.9344042684 |
116 | 104064 | 102750.147274705 | 1313.85272529542 |
117 | 96287 | 113336.078986117 | -17049.078986117 |
118 | 78426 | 98310.4952321351 | -19884.4952321351 |
119 | 59111 | 66190.3665165909 | -7079.36651659092 |
120 | 76837 | 83482.4587396106 | -6645.45873961064 |
121 | 76615 | 92154.3440649274 | -15539.3440649274 |
122 | 65860 | 70944.9097820315 | -5084.90978203154 |
123 | 57703 | 40802.3732135801 | 16900.6267864199 |
124 | 68656 | 74113.1041187262 | -5457.10411872623 |
125 | 77955 | 78399.0665012763 | -444.066501276335 |
126 | 65856 | 69621.1892586357 | -3765.18925863574 |
127 | 60947 | 53238.448154569 | 7708.55184543097 |
128 | 69885 | 78675.9997528165 | -8790.99975281647 |
129 | 80550 | 77251.8501785946 | 3298.14982140542 |
130 | 73694 | 72376.3892805472 | 1317.6107194528 |
131 | 67538 | 56371.6664970912 | 11166.3335029088 |
132 | 76326 | 83822.4196999445 | -7496.41969994445 |
133 | 84727 | 88904.1400319154 | -4177.14003191541 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
134 | 77597.8778022822 | 59479.768657828 | 95715.9869467364 |
135 | 57963.7412902554 | 37295.8224081766 | 78631.6601723341 |
136 | 74155.4863106948 | 51216.7114796307 | 97094.2611417589 |
137 | 83193.6678936945 | 58186.8784027714 | 108200.457384618 |
138 | 73493.6045085956 | 46574.8500283783 | 100412.358988813 |
139 | 63203.8144075576 | 34497.9449852659 | 91909.6838298492 |
140 | 78621.0380878178 | 48230.8687499474 | 109011.207425688 |
141 | 86262.9894207008 | 54275.0888296753 | 118250.890011726 |
142 | 78883.642268976 | 45372.1935242394 | 112395.091013713 |
143 | 65612.282951652 | 30641.7709050069 | 100582.794998297 |
144 | 80384.3963127775 | 44011.5436078764 | 116757.249017679 |
145 | 90741.4942934366 | 53016.6963164359 | 128466.292270437 |