Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.214229733832505 |
beta | 0.107869753887267 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 865911 | 816579.606432536 | 49331.3935674642 |
14 | 850038 | 810021.753278465 | 40016.2467215352 |
15 | 874569 | 838608.461074196 | 35960.5389258041 |
16 | 914862 | 879266.048812001 | 35595.9511879993 |
17 | 1144188 | 1100546.42786206 | 43641.5721379353 |
18 | 1144188 | 1102050.36649766 | 42137.6335023411 |
19 | 1095237 | 1031186.86102386 | 64050.1389761432 |
20 | 1046175 | 968464.458406447 | 77710.5415935531 |
21 | 1086468 | 1017720.42779461 | 68747.572205389 |
22 | 1135530 | 1052115.91318225 | 83414.0868177502 |
23 | 1144188 | 1096866.83616054 | 47321.1638394594 |
24 | 1168719 | 1140751.02396739 | 27967.976032607 |
25 | 1242312 | 1281188.81344969 | -38876.8134496922 |
26 | 1193250 | 1240799.93118894 | -47549.9311889368 |
27 | 1193250 | 1256841.1211785 | -63591.1211784952 |
28 | 1266843 | 1289326.3240663 | -22483.3240663002 |
29 | 1470861 | 1591300.44340944 | -120439.44340944 |
30 | 1487400 | 1547916.18917266 | -60516.1891726558 |
31 | 1446330 | 1443555.63154729 | 2774.36845271289 |
32 | 1348206 | 1348910.81070484 | -704.810704835458 |
33 | 1421799 | 1371685.25087152 | 50113.7491284807 |
34 | 1421799 | 1411092.26427897 | 10706.7357210263 |
35 | 1429680 | 1400222.90578222 | 29457.0942177828 |
36 | 1470861 | 1418104.83610092 | 52756.1638990818 |
37 | 1503273 | 1518412.76778444 | -15139.7677844365 |
38 | 1519812 | 1457806.77296215 | 62005.2270378454 |
39 | 1519812 | 1480096.15214416 | 39715.8478558357 |
40 | 1568874 | 1581299.98878164 | -12425.988781641 |
41 | 1757130 | 1857698.24555015 | -100568.245550151 |
42 | 1806081 | 1867972.06802645 | -61891.0680264502 |
43 | 1813962 | 1798734.47737448 | 15227.5226255185 |
44 | 1691418 | 1676515.96601958 | 14902.0339804241 |
45 | 1757130 | 1754501.97219549 | 2628.02780451439 |
46 | 1732599 | 1748019.04107473 | -15420.0410747339 |
47 | 1683537 | 1741906.75662924 | -58369.756629244 |
48 | 1789542 | 1758754.69336057 | 30787.3066394278 |
49 | 1813962 | 1801115.94593536 | 12846.0540646366 |
50 | 1772892 | 1801063.83844784 | -28171.838447839 |
51 | 1781550 | 1776855.97793963 | 4694.02206037147 |
52 | 1838493 | 1829610.89759578 | 8882.10240422096 |
53 | 2051280 | 2066296.81955504 | -15016.819555037 |
54 | 2157174 | 2128583.79056245 | 28590.2094375533 |
55 | 2157174 | 2135155.98464355 | 22018.0153564466 |
56 | 2108223 | 1987088.55742878 | 121134.442571217 |
57 | 2181705 | 2088213.32439296 | 93491.6756070412 |
58 | 2108223 | 2082231.47996969 | 25991.5200303062 |
59 | 2067042 | 2043715.21077278 | 23326.7892272212 |
60 | 2222886 | 2171888.99266813 | 50997.0073318686 |
61 | 2247306 | 2211765.18665374 | 35540.8133462612 |
62 | 2189586 | 2179232.06002905 | 10353.939970952 |
63 | 2336661 | 2194502.42950116 | 142158.570498839 |
64 | 2394381 | 2300156.44319473 | 94224.5568052693 |
65 | 2565987 | 2601839.12537863 | -35852.1253786292 |
66 | 2679873 | 2728992.84608298 | -49119.8460829807 |
67 | 2664111 | 2719261.7912728 | -55150.7912727962 |
68 | 2655342 | 2616666.09771626 | 38675.9022837398 |
69 | 2721054 | 2692938.51476204 | 28115.4852379584 |
70 | 2713062 | 2601504.78412663 | 111557.215873365 |
71 | 2615049 | 2569744.87620987 | 45304.1237901291 |
72 | 2762124 | 2762357.69684806 | -233.69684805721 |
73 | 2811186 | 2784050.94886098 | 27135.0511390241 |
74 | 2762124 | 2716033.49828219 | 46090.5017178087 |
75 | 2966142 | 2870475.78828826 | 95666.2117117424 |
76 | 3064266 | 2936102.46677908 | 128163.533220921 |
77 | 3292704 | 3184994.35709175 | 107709.642908255 |
78 | 3382836 | 3366127.4281403 | 16708.571859695 |
79 | 3358416 | 3368630.07491094 | -10214.0749109411 |
80 | 3309354 | 3349881.37232018 | -40527.372320184 |
81 | 3350424 | 3419510.1049249 | -69086.1049248991 |
82 | 3399486 | 3364908.86693014 | 34577.1330698631 |
83 | 3235761 | 3237228.68938609 | -1467.68938608794 |
84 | 3366297 | 3416769.6837878 | -50472.6837878013 |
85 | 3448548 | 3456014.68548473 | -7466.68548472598 |
86 | 3415359 | 3377990.58210024 | 37368.4178997567 |
87 | 3628035 | 3605929.28182528 | 22105.7181747244 |
88 | 3701517 | 3689249.38251578 | 12267.6174842203 |
89 | 4012317 | 3928998.69823718 | 83318.3017628156 |
90 | 4069260 | 4040100.27340544 | 29159.7265945645 |
91 | 3995778 | 4009852.92578276 | -14074.925782762 |
92 | 4036848 | 3949064.54197323 | 87783.4580267677 |
93 | 4061379 | 4027896.07075888 | 33482.9292411185 |
94 | 4085910 | 4080881.23311858 | 5028.76688142167 |
95 | 3930066 | 3881098.78116699 | 48967.2188330111 |
96 | 4077141 | 4057770.50292639 | 19370.4970736117 |
97 | 4158615 | 4161051.16612882 | -2436.16612881748 |
98 | 4077141 | 4108911.68779596 | -31770.6877959576 |
99 | 4314459 | 4348316.6558885 | -33857.655888495 |
100 | 4387941 | 4421129.15211169 | -33188.1521116905 |
101 | 4706622 | 4757044.26975436 | -50422.2697543632 |
102 | 4755684 | 4797267.50519041 | -41583.5051904116 |
103 | 4771446 | 4695442.27506637 | 76003.724933628 |
104 | 4853697 | 4729672.28919557 | 124024.710804425 |
105 | 4853697 | 4769278.07634154 | 84418.9236584622 |
106 | 4886109 | 4808702.04818739 | 77406.9518126138 |
107 | 4739034 | 4624206.7425048 | 114827.257495199 |
108 | 4812627 | 4814454.20382262 | -1827.20382261928 |
109 | 4861578 | 4907005.27840535 | -45427.278405345 |
110 | 4771446 | 4804761.64980539 | -33315.6498053931 |
111 | 5033184 | 5080766.55700692 | -47582.5570069188 |
112 | 5082246 | 5160514.92226235 | -78268.9222623538 |
113 | 5408808 | 5524070.48694524 | -115262.486945244 |
114 | 5466528 | 5560147.36810164 | -93619.3681016443 |
115 | 5548002 | 5531594.82100758 | 16407.1789924214 |
116 | 5621595 | 5590018.50486931 | 31576.4951306935 |
117 | 5629476 | 5564531.37830576 | 64944.6216942389 |
118 | 5638134 | 5584852.55347606 | 53281.4465239421 |
119 | 5491059 | 5387528.53655974 | 103530.463440265 |
120 | 5638134 | 5482104.10179898 | 156029.898201019 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 5574020.31269337 | 5462684.66450545 | 5685355.9608813 |
122 | 5471521.17213525 | 5357269.93283676 | 5585772.41143374 |
123 | 5776552.31448532 | 5658146.73444295 | 5894957.89452768 |
124 | 5846349.10362535 | 5723717.88190237 | 5968980.32534832 |
125 | 6246108.95722367 | 6116995.77295983 | 6375222.1414875 |
126 | 6334523.36135735 | 6199784.86007234 | 6469261.86264235 |
127 | 6425996.08835047 | 6285051.94760985 | 6566940.22909109 |
128 | 6504101.79232213 | 6356536.26108899 | 6651667.32355527 |
129 | 6496938.56920526 | 6343218.19971718 | 6650658.93869334 |
130 | 6492061.5633806 | 6331887.49741555 | 6652235.62934565 |
131 | 6294036.04691511 | 6129893.70770016 | 6458178.38613006 |
132 | 6418171.56786756 | 6285850.77308905 | 6550492.36264608 |