Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.147614153124017 |
beta | 0.0992579523464149 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 5714.75 | 6824.38533687058 | -1109.63533687058 |
14 | 4932.75 | 5792.71745825933 | -859.967458259334 |
15 | 4292.38 | 4950.41740023966 | -658.037400239665 |
16 | 4292.38 | 4820.82644577925 | -528.446445779246 |
17 | 6752.38 | 7342.28263272652 | -589.902632726518 |
18 | 7008 | 7323.8704467915 | -315.870446791499 |
19 | 5060.5 | 5106.41006426273 | -45.9100642627263 |
20 | 2857.38 | 4065.15552806932 | -1207.77552806932 |
21 | 4022.88 | 3839.91638289028 | 182.963617109717 |
22 | 4022.88 | 3738.35807475984 | 284.521925240158 |
23 | 4932.75 | 3721.92776623339 | 1210.82223376661 |
24 | 5457.88 | 3934.46853532285 | 1523.41146467715 |
25 | 5330 | 3045.70537433659 | 2284.29462566341 |
26 | 4022.88 | 2934.78513215116 | 1088.09486784884 |
27 | 4677.13 | 2727.12562457479 | 1950.00437542521 |
28 | 4420.25 | 3092.00072681104 | 1328.24927318896 |
29 | 6623.38 | 5339.93850064654 | 1283.44149935346 |
30 | 6098.13 | 5936.11922856946 | 162.010771430537 |
31 | 4022.88 | 4444.46520186095 | -421.585201860952 |
32 | 2472.75 | 2671.00808121079 | -198.258081210794 |
33 | 3895 | 3844.98818709534 | 50.0118129046591 |
34 | 4292.38 | 3977.06730729867 | 315.312692701335 |
35 | 4677.13 | 4932.5709835357 | -255.440983535703 |
36 | 5188.38 | 5342.71676027703 | -154.336760277028 |
37 | 4150.63 | 4848.08525046331 | -697.455250463315 |
38 | 3254.75 | 3461.55750879847 | -206.807508798473 |
39 | 3639.5 | 3650.1060373171 | -10.6060373171008 |
40 | 3767.25 | 3236.84830610918 | 530.401693890819 |
41 | 7135.88 | 4765.57627089928 | 2370.30372910072 |
42 | 7135.88 | 4680.62645446514 | 2455.25354553486 |
43 | 5188.38 | 3394.74464078451 | 1793.6353592155 |
44 | 4932.75 | 2311.60663167205 | 2621.14336832795 |
45 | 5714.75 | 4385.04890698812 | 1329.70109301188 |
46 | 5330 | 5178.85058447146 | 151.149415528545 |
47 | 6367.75 | 5922.67354805177 | 445.076451948231 |
48 | 7661 | 6934.22856328567 | 726.771436714333 |
49 | 7917.88 | 5995.43222638827 | 1922.44777361173 |
50 | 6098.13 | 5211.1152110356 | 887.014788964399 |
51 | 5585.63 | 6291.7667218379 | -706.136721837905 |
52 | 5060.5 | 6579.41197296741 | -1518.91197296741 |
53 | 8570.88 | 11736.8227694721 | -3165.94276947215 |
54 | 8827.75 | 10817.7486370406 | -1989.99863704055 |
55 | 8173.5 | 7261.38688466237 | 912.113115337625 |
56 | 8827.75 | 6121.86153716656 | 2705.88846283344 |
57 | 8698.63 | 7278.58768535501 | 1420.04231464499 |
58 | 7661 | 6987.75578333179 | 673.244216668209 |
59 | 8827.75 | 8419.7446890197 | 408.005310980299 |
60 | 10121 | 10096.0645175591 | 24.9354824409293 |
61 | 10646.13 | 10001.45930936 | 644.670690640032 |
62 | 9083.38 | 7588.43508541551 | 1494.94491458449 |
63 | 8045.63 | 7278.05868980464 | 767.571310195355 |
64 | 8827.75 | 6954.30724649774 | 1873.44275350226 |
65 | 12196.25 | 12865.9662785895 | -669.716278589547 |
66 | 13234 | 13669.2151888686 | -435.215188868617 |
67 | 12978.38 | 12527.8520497556 | 450.52795024439 |
68 | 13489.5 | 12914.1143405367 | 575.385659463269 |
69 | 13361.75 | 12526.053132711 | 835.696867288985 |
70 | 12068.5 | 11031.4217911742 | 1037.07820882578 |
71 | 14271.63 | 12847.9673922988 | 1423.66260770118 |
72 | 14796.75 | 15033.2339776797 | -236.483977679685 |
73 | 15564.88 | 15692.2968617263 | -127.416861726302 |
74 | 13234 | 13035.4170035875 | 198.58299641255 |
75 | 12324.13 | 11405.4080869746 | 918.72191302538 |
76 | 13361.75 | 12186.0864003463 | 1175.6635996537 |
77 | 15834.38 | 17186.3802012865 | -1352.00020128648 |
78 | 18037.5 | 18491.2190135937 | -453.719013593673 |
79 | 17512.38 | 17948.3260472042 | -435.946047204186 |
80 | 17512.38 | 18430.1067587108 | -917.72675871076 |
81 | 17769.25 | 17891.2693907475 | -122.019390747511 |
82 | 16872 | 15863.9466608106 | 1008.0533391894 |
83 | 19204.25 | 18560.0124537456 | 644.237546254448 |
84 | 19204.25 | 19300.0251190641 | -95.7751190640665 |
85 | 18806.88 | 20226.8391459482 | -1419.95914594816 |
86 | 16602.5 | 16901.0583964132 | -298.558396413173 |
87 | 16999.88 | 15437.1277182043 | 1562.75228179567 |
88 | 17256.75 | 16674.0489047927 | 582.701095207289 |
89 | 18947.38 | 19996.1998284085 | -1048.81982840852 |
90 | 21150.5 | 22582.9471696451 | -1432.44716964507 |
91 | 19587.63 | 21694.1510131128 | -2106.52101311283 |
92 | 20369.75 | 21422.6152799655 | -1052.86527996548 |
93 | 19715.5 | 21484.9226586186 | -1769.42265861861 |
94 | 19332 | 19841.9838832845 | -509.983883284505 |
95 | 22317.25 | 22227.2953142736 | 89.9546857263849 |
96 | 21663 | 22097.6760010012 | -434.676001001179 |
97 | 20753.13 | 21648.1259374425 | -894.995937442509 |
98 | 19459.88 | 18917.6365688197 | 542.243431180315 |
99 | 20753.13 | 19053.6113093015 | 1699.51869069852 |
100 | 21407.38 | 19383.3079115339 | 2024.07208846615 |
101 | 22188.13 | 21676.5919239223 | 511.538076077672 |
102 | 23225.75 | 24421.5902440631 | -1195.84024406313 |
103 | 22188.13 | 22702.9294488657 | -514.799448865739 |
104 | 22828.5 | 23645.7946831253 | -817.294683125325 |
105 | 22047.63 | 23000.0867419895 | -952.45674198951 |
106 | 21919.88 | 22464.274805578 | -544.394805578006 |
107 | 25160.63 | 25785.0578278594 | -624.427827859377 |
108 | 25430.13 | 24965.3074124172 | 464.822587582767 |
109 | 24392.5 | 24097.263338261 | 295.236661738989 |
110 | 22572.88 | 22527.0140722289 | 45.8659277711085 |
111 | 24123 | 23696.3912007905 | 426.608799209462 |
112 | 24776 | 24092.1481037308 | 683.851896269174 |
113 | 25558 | 24920.2514756844 | 637.748524315648 |
114 | 26723.5 | 26305.5281776866 | 417.97182231339 |
115 | 25558 | 25229.7682378388 | 328.231762161209 |
116 | 26467.88 | 26108.4815415011 | 359.398458498854 |
117 | 26070.5 | 25406.7230504603 | 663.776949539657 |
118 | 24648.13 | 25455.0549364964 | -806.924936496351 |
119 | 27633.25 | 29191.237528921 | -1557.987528921 |
120 | 27633.25 | 29185.1693455721 | -1551.91934557206 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 27692.6785169409 | 25513.4060517958 | 29871.9509820859 |
122 | 25586.3094486277 | 23383.1147158314 | 27789.5041814239 |
123 | 27235.8569217585 | 24993.7338578353 | 29477.9799856817 |
124 | 27814.7883196043 | 25531.4751234085 | 30098.1015158001 |
125 | 28532.3428606714 | 26199.7136784226 | 30864.9720429202 |
126 | 29700.3684301822 | 27304.5142927773 | 32096.2225675872 |
127 | 28285.6639667758 | 25860.2730117845 | 30711.054921767 |
128 | 29162.7011061711 | 26664.4190548726 | 31660.9831574696 |
129 | 28541.7246776207 | 25997.2689957511 | 31086.1803594903 |
130 | 27034.6887070931 | 24467.3185969871 | 29602.0588171991 |
131 | 30477.2471121983 | 27736.1159114106 | 33218.378312986 |
132 | 30668.4026071447 | 28870.699835079 | 32466.1053792103 |