Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.65361082410817 |
beta | 0.0529322491866611 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 1904.92 | 2299.41713141026 | -394.497131410257 |
14 | 1644.25 | 1776.77452130964 | -132.524521309642 |
15 | 1430.79 | 1466.20883186548 | -35.4188318654815 |
16 | 1430.79 | 1416.93375024156 | 13.8562497584396 |
17 | 2250.79 | 2209.48353125984 | 41.3064687401638 |
18 | 2336 | 2272.20290618713 | 63.7970938128728 |
19 | 1686.83 | 1646.63167429723 | 40.1983257027712 |
20 | 952.46 | 1215.67261060118 | -263.212610601183 |
21 | 1340.96 | 1067.15948413939 | 273.800515860606 |
22 | 1340.96 | 1240.10415118778 | 100.85584881222 |
23 | 1644.25 | 1344.32796419542 | 299.922035804582 |
24 | 1819.29 | 1632.69252170468 | 186.597478295321 |
25 | 1776.67 | 1361.37686548707 | 415.293134512931 |
26 | 1340.96 | 1493.51819606475 | -152.558196064748 |
27 | 1559.04 | 1237.55331392062 | 321.486686079383 |
28 | 1473.42 | 1485.03046383807 | -11.6104638380698 |
29 | 2207.79 | 2315.9688766312 | -108.178876631205 |
30 | 2032.71 | 2329.12725546843 | -296.417255468427 |
31 | 1340.96 | 1487.83303403125 | -146.873034031248 |
32 | 824.25 | 850.923081670693 | -26.6730816706934 |
33 | 1298.33 | 1072.63310669722 | 225.69689330278 |
34 | 1430.79 | 1182.16913999325 | 248.620860006753 |
35 | 1559.04 | 1484.97895106714 | 74.061048932859 |
36 | 1729.46 | 1611.70060447514 | 117.759395524858 |
37 | 1383.54 | 1397.4644164662 | -13.9244164661973 |
38 | 1084.92 | 1060.37236105436 | 24.547638945641 |
39 | 1213.17 | 1098.50253809565 | 114.667461904347 |
40 | 1255.75 | 1102.39656603312 | 153.353433966881 |
41 | 2378.63 | 2020.39159490652 | 358.238405093476 |
42 | 2378.63 | 2302.02298167171 | 76.6070183282864 |
43 | 1729.46 | 1798.06887857494 | -68.6088785749371 |
44 | 1644.25 | 1298.38381561885 | 345.866184381146 |
45 | 1904.92 | 1908.33116770465 | -3.41116770464578 |
46 | 1776.67 | 1925.45723664367 | -148.787236643674 |
47 | 2122.58 | 1943.698951241 | 178.881048759003 |
48 | 2553.67 | 2193.34295864026 | 360.327041359741 |
49 | 2639.29 | 2139.7041305913 | 499.585869408698 |
50 | 2032.71 | 2217.00659016131 | -184.296590161314 |
51 | 1861.88 | 2208.05737718422 | -346.177377184215 |
52 | 1686.83 | 1966.40166867186 | -279.571668671858 |
53 | 2856.96 | 2699.68718818742 | 157.272811812576 |
54 | 2942.58 | 2772.74348647667 | 169.836513523331 |
55 | 2724.5 | 2302.98170757379 | 421.518292426207 |
56 | 2942.58 | 2307.73345046459 | 634.846549535406 |
57 | 2899.54 | 3036.08818922336 | -136.548189223364 |
58 | 2553.67 | 2961.7441956435 | -408.074195643497 |
59 | 2942.58 | 2960.94975266546 | -18.3697526654641 |
60 | 3373.67 | 3174.6309831368 | 199.039016863203 |
61 | 3548.71 | 3088.34176479991 | 460.368235200091 |
62 | 3027.79 | 2926.29631415639 | 101.493685843606 |
63 | 2681.88 | 3081.13112035937 | -399.25112035937 |
64 | 2942.58 | 2859.08329195804 | 83.4967080419583 |
65 | 4065.42 | 4024.77949829103 | 40.6405017089664 |
66 | 4411.33 | 4065.70751420787 | 345.622485792133 |
67 | 4326.13 | 3843.85480443908 | 482.27519556092 |
68 | 4496.5 | 4010.14813909159 | 486.351860908411 |
69 | 4453.92 | 4417.04049299697 | 36.8795070030337 |
70 | 4022.83 | 4410.79528186596 | -387.965281865956 |
71 | 4757.21 | 4607.62758595087 | 149.582414049132 |
72 | 4932.25 | 5061.69681393794 | -129.446813937935 |
73 | 5188.29 | 4895.16725832475 | 293.12274167525 |
74 | 4411.33 | 4537.6518205943 | -126.321820594305 |
75 | 4108.04 | 4400.40334849102 | -292.363348491021 |
76 | 4453.92 | 4449.40713651665 | 4.51286348335452 |
77 | 5278.13 | 5579.87109918968 | -301.741099189677 |
78 | 6012.5 | 5522.04922357146 | 490.450776428544 |
79 | 5837.46 | 5466.59547993164 | 370.86452006836 |
80 | 5837.46 | 5582.02982684304 | 255.430173156965 |
81 | 5923.08 | 5694.85581214125 | 228.224187858747 |
82 | 5624 | 5685.69279287713 | -61.6927928771283 |
83 | 6401.42 | 6312.44798338328 | 88.9720166167162 |
84 | 6401.42 | 6658.61890440541 | -257.198904405413 |
85 | 6268.96 | 6578.91287826765 | -309.95287826765 |
86 | 5534.17 | 5685.01512770074 | -150.845127700742 |
87 | 5666.63 | 5476.46002990073 | 190.169970099274 |
88 | 5752.25 | 5962.6188347804 | -210.368834780396 |
89 | 6315.79 | 6858.04776457266 | -542.257764572661 |
90 | 7050.17 | 6920.60413581405 | 129.565864185947 |
91 | 6529.21 | 6578.53900612129 | -49.329006121292 |
92 | 6789.92 | 6355.49791776487 | 434.422082235134 |
93 | 6571.83 | 6558.23650277268 | 13.5934972273153 |
94 | 6444 | 6283.28424868908 | 160.71575131092 |
95 | 7439.08 | 7090.21123068964 | 348.868769310365 |
96 | 7221 | 7477.94979442168 | -256.949794421679 |
97 | 6917.71 | 7371.74797426465 | -454.037974264649 |
98 | 6486.63 | 6425.41771330865 | 61.2122866913533 |
99 | 6917.71 | 6467.55601059731 | 450.153989402688 |
100 | 7135.79 | 6987.86200384758 | 147.927996152417 |
101 | 7396.04 | 8017.87204156591 | -621.832041565912 |
102 | 7741.92 | 8273.73435251396 | -531.814352513959 |
103 | 7396.04 | 7427.13899144658 | -31.098991446579 |
104 | 7609.5 | 7373.93236812307 | 235.567631876934 |
105 | 7349.21 | 7284.40026897007 | 64.809731029929 |
106 | 7306.63 | 7079.13019248745 | 227.49980751255 |
107 | 8386.88 | 7982.43779588641 | 404.442204113589 |
108 | 8476.71 | 8186.12911483016 | 290.580885169837 |
109 | 8130.83 | 8377.95137966831 | -247.12137966831 |
110 | 7524.29 | 7760.92118863067 | -236.631188630672 |
111 | 8041 | 7748.38647533972 | 292.613524660278 |
112 | 8258.67 | 8060.85957397609 | 197.81042602391 |
113 | 8519.33 | 8858.38762076955 | -339.057620769554 |
114 | 8907.83 | 9341.58953750782 | -433.759537507816 |
115 | 8519.33 | 8747.2526879703 | -227.9226879703 |
116 | 8822.63 | 8665.6873125161 | 156.942687483899 |
117 | 8690.17 | 8470.81313022177 | 219.35686977823 |
118 | 8216.04 | 8433.45441951389 | -217.414419513891 |
119 | 9211.08 | 9102.4030627976 | 108.676937202401 |
120 | 9211.08 | 9058.25691913031 | 152.823080869686 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 8953.9371739592 | 8424.26386940841 | 9483.61047850999 |
122 | 8490.76378741252 | 7847.77658062767 | 9133.75099419738 |
123 | 8813.10707842638 | 8064.77088004943 | 9561.44327680334 |
124 | 8888.25112412372 | 8039.16397586354 | 9737.3382723839 |
125 | 9350.44427101065 | 8403.38042450559 | 10297.5081175157 |
126 | 10014.1060231058 | 8970.73575301934 | 11057.4762931923 |
127 | 9781.23740053981 | 8642.5120686793 | 10919.9627324003 |
128 | 9996.50206473205 | 8762.88010693122 | 11230.1240225329 |
129 | 9729.78238335619 | 8401.37115064513 | 11058.1936160672 |
130 | 9399.28203473333 | 7975.93147730044 | 10822.6325921662 |
131 | 10332.336752172 | 8813.70382224023 | 11850.9696821038 |
132 | 10237.7371663797 | 8623.33154032756 | 11852.1427924319 |