Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.225106730423627 |
beta | 0 |
gamma | 0.506246088410288 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 3395 | 3322.84775641026 | 72.1522435897436 |
14 | 3017 | 2994.83708967985 | 22.162910320149 |
15 | 3631 | 3608.94848758107 | 22.0515124189315 |
16 | 2570 | 2539.95147573163 | 30.0485242683653 |
17 | 2403 | 2409.67131173945 | -6.6713117394529 |
18 | 2465 | 2512.12526552186 | -47.1252655218586 |
19 | 1711 | 2523.5977620356 | -812.597762035598 |
20 | 1541 | 1416.59058096325 | 124.409419036747 |
21 | 1751 | 1416.9683561389 | 334.031643861104 |
22 | 2103 | 1815.11683830221 | 287.88316169779 |
23 | 1410 | 2197.79365319839 | -787.793653198393 |
24 | 823 | 671.745043967462 | 151.254956032538 |
25 | 3471 | 3179.76196144216 | 291.238038557842 |
26 | 2207 | 2881.45883178269 | -674.458831782686 |
27 | 2483 | 3338.71228706355 | -855.712287063554 |
28 | 2334 | 2075.26185750998 | 258.73814249002 |
29 | 2273 | 1982.05656295535 | 290.943437044648 |
30 | 2247 | 2135.63605227086 | 111.363947729139 |
31 | 1667 | 1882.50086800136 | -215.500868001362 |
32 | 1692 | 1277.47965892926 | 414.520341070744 |
33 | 1779 | 1425.39536325048 | 353.604636749515 |
34 | 2000 | 1809.84642268535 | 190.153577314651 |
35 | 1934 | 1748.54995674439 | 185.450043255606 |
36 | 851 | 809.9613214541 | 41.0386785459002 |
37 | 3314 | 3348.08131269641 | -34.0813126964104 |
38 | 3178 | 2597.71658195019 | 580.283418049808 |
39 | 3360 | 3266.3176451977 | 93.6823548022976 |
40 | 2787 | 2653.76640581097 | 133.233594189028 |
41 | 2474 | 2544.94290102871 | -70.942901028709 |
42 | 2563 | 2546.61269714014 | 16.3873028598609 |
43 | 2528 | 2143.87291532935 | 384.127084670647 |
44 | 1649 | 1920.98092678533 | -271.980926785332 |
45 | 1902 | 1890.46415545416 | 11.5358445458382 |
46 | 2141 | 2133.79355295957 | 7.20644704042707 |
47 | 1471 | 2029.46932289059 | -558.469322890594 |
48 | 1178 | 866.768775610509 | 311.231224389491 |
49 | 3038 | 3436.24235496624 | -398.242354966245 |
50 | 2633 | 2844.90962727128 | -211.909627271277 |
51 | 2636 | 3144.29558539635 | -508.295585396354 |
52 | 2708 | 2411.75048475661 | 296.249515243387 |
53 | 2252 | 2259.52724016738 | -7.52724016738239 |
54 | 2579 | 2309.73080468162 | 269.269195318383 |
55 | 2321 | 2108.17585942458 | 212.82414057542 |
56 | 1490 | 1589.33998731918 | -99.3399873191802 |
57 | 2076 | 1708.90570824612 | 367.094291753881 |
58 | 2333 | 2030.57534027441 | 302.424659725591 |
59 | 1566 | 1770.79964331526 | -204.799643315259 |
60 | 961 | 1028.88446733194 | -67.8844673319363 |
61 | 3683 | 3234.69951315476 | 448.300486845236 |
62 | 2904 | 2907.025125107 | -3.02512510700308 |
63 | 3097 | 3137.16412506546 | -40.1641250654566 |
64 | 3269 | 2825.61089866653 | 443.389101333467 |
65 | 2491 | 2587.34218835397 | -96.3421883539668 |
66 | 2692 | 2726.13646682477 | -34.1364668247693 |
67 | 2293 | 2434.1402214673 | -141.140221467298 |
68 | 1994 | 1713.16675771056 | 280.833242289436 |
69 | 2069 | 2101.28798923081 | -32.2879892308051 |
70 | 2540 | 2307.6849461217 | 232.3150538783 |
71 | 2091 | 1833.14976378642 | 257.850236213583 |
72 | 1109 | 1249.09019025448 | -140.090190254479 |
73 | 4761 | 3641.14372724947 | 1119.85627275053 |
74 | 3051 | 3287.59203754706 | -236.592037547056 |
75 | 3737 | 3450.58441827148 | 286.415581728524 |
76 | 3505 | 3402.23797489871 | 102.762025101288 |
77 | 2837 | 2875.56241784436 | -38.5624178443595 |
78 | 3419 | 3051.7657879291 | 367.234212070903 |
79 | 2658 | 2808.14463541701 | -150.144635417005 |
80 | 2133 | 2250.67878943161 | -117.678789431611 |
81 | 2276 | 2426.25899002115 | -150.258990021146 |
82 | 2403 | 2709.90013170035 | -306.900131700351 |
83 | 1975 | 2124.00109401622 | -149.001094016217 |
84 | 996 | 1292.24981638112 | -296.24981638112 |
85 | 4505 | 4143.41099385389 | 361.589006146105 |
86 | 3890 | 3087.05162570874 | 802.948374291259 |
87 | 4352 | 3689.22047574808 | 662.779524251919 |
88 | 3288 | 3653.55124370376 | -365.551243703757 |
89 | 3314 | 2966.01552042769 | 347.984479572307 |
90 | 2830 | 3388.42181415194 | -558.421814151937 |
91 | 2414 | 2733.46842625167 | -319.468426251671 |
92 | 2049 | 2150.62257447973 | -101.622574479726 |
93 | 1981 | 2317.03635818012 | -336.036358180122 |
94 | 2527 | 2497.40952946261 | 29.5904705373869 |
95 | 1813 | 2049.19848138617 | -236.198481386168 |
96 | 926 | 1140.05477156751 | -214.054771567514 |
97 | 4277 | 4267.78001887984 | 9.21998112016445 |
98 | 3301 | 3305.23941576388 | -4.23941576388142 |
99 | 3773 | 3670.71848779137 | 102.281512208629 |
100 | 3175 | 3105.47691109672 | 69.523088903281 |
101 | 3045 | 2795.78991302151 | 249.210086978491 |
102 | 2933 | 2840.39030444789 | 92.6096955521134 |
103 | 2544 | 2425.72672390508 | 118.273276094925 |
104 | 2324 | 2026.87750291236 | 297.122497087641 |
105 | 2229 | 2191.09407943091 | 37.9059205690901 |
106 | 2844 | 2599.07471164084 | 244.925288359157 |
107 | 2175 | 2095.0715130501 | 79.9284869499029 |
108 | 1055 | 1265.7767940274 | -210.776794027397 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 4481.82764909252 | 3843.19642183105 | 5120.45887635399 |
110 | 3511.93162396398 | 2857.31965038886 | 4166.5435975391 |
111 | 3920.1517589071 | 3249.93998083816 | 4590.36353697605 |
112 | 3319.03523207777 | 2633.57858211604 | 4004.4918820395 |
113 | 3064.18693588113 | 2363.81716890715 | 3764.5567028551 |
114 | 2991.25621075711 | 2276.28432179531 | 3706.22809971891 |
115 | 2565.81304542197 | 1836.53134846254 | 3295.0947423814 |
116 | 2210.49988226572 | 1467.1838088256 | 2953.81595570585 |
117 | 2206.14497300015 | 1449.05463720866 | 2963.23530879164 |
118 | 2686.80366923158 | 1916.18523702061 | 3457.42210144255 |
119 | 2062.94009124615 | 1279.02698408585 | 2846.85319840645 |
120 | 1101.61312038974 | 304.627078421541 | 1898.59916235794 |