Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.84683402486491 |
beta | 0.0224388718805353 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 2450 | 2768 | -318 |
4 | 2842 | 2591.66414403317 | 250.335855966832 |
5 | 3440 | 2901.37131043192 | 538.628689568077 |
6 | 2678 | 3465.44967990938 | -787.449679909375 |
7 | 2981 | 2891.59664751024 | 89.4033524897559 |
8 | 2260 | 3061.99144027349 | -801.991440273491 |
9 | 2844 | 2462.28335143855 | 381.716648561454 |
10 | 2546 | 2872.23292756458 | -326.232927564584 |
11 | 2456 | 2676.46763658748 | -220.467636587481 |
12 | 2295 | 2566.07866658764 | -271.078666587639 |
13 | 2379 | 2407.67951747674 | -28.6795174767367 |
14 | 2471 | 2454.00724723476 | 16.9927527652358 |
15 | 2057 | 2539.33470571776 | -482.334705717759 |
16 | 2280 | 2192.64935863929 | 87.3506413607051 |
17 | 2351 | 2330.05278383741 | 20.9472161625899 |
18 | 2276 | 2411.62156821565 | -135.621568215649 |
19 | 2548 | 2358.02549768592 | 189.974502314076 |
20 | 2311 | 2583.76515357178 | -272.765153571777 |
21 | 2201 | 2412.45804069975 | -211.458040699753 |
22 | 2725 | 2289.04975124486 | 435.950248755144 |
23 | 2408 | 2722.17275598877 | -314.17275598877 |
24 | 2139 | 2514.09616671327 | -375.096166713266 |
25 | 1898 | 2247.29998289503 | -349.299982895026 |
26 | 2539 | 1995.71148690509 | 543.288513094905 |
27 | 2070 | 2510.32086795041 | -440.320867950413 |
28 | 2063 | 2183.60938073466 | -120.609380734658 |
29 | 2565 | 2125.34863955797 | 439.65136044203 |
30 | 2443 | 2549.89001203952 | -106.890012039517 |
31 | 2196 | 2509.57043027845 | -313.570430278452 |
32 | 2799 | 2288.26837270424 | 510.731627295763 |
33 | 2076 | 2774.71826672792 | -698.718266727924 |
34 | 2628 | 2223.68779448736 | 404.312205512645 |
35 | 2292 | 2614.42379720808 | -322.42379720808 |
36 | 2155 | 2383.60832867541 | -228.608328675407 |
37 | 2476 | 2227.89497545037 | 248.105024549629 |
38 | 2138 | 2480.59320156688 | -342.593201566881 |
39 | 1854 | 2226.5581153 | -372.558115299996 |
40 | 2081 | 1940.06837115479 | 140.931628845213 |
41 | 1795 | 2091.09719660873 | -296.097196608734 |
42 | 1756 | 1866.4087038359 | -110.408703835898 |
43 | 2237 | 1796.86955855793 | 440.130441442067 |
44 | 1960 | 2201.90905225243 | -241.909052252431 |
45 | 1829 | 2024.77754052841 | -195.777540528407 |
46 | 2524 | 1882.99159768881 | 641.00840231119 |
47 | 2077 | 2462.00490455569 | -385.004904555688 |
48 | 2366 | 2164.83936993477 | 201.160630065225 |
49 | 2185 | 2367.8812085643 | -182.881208564304 |
50 | 2098 | 2242.22824251114 | -144.228242511144 |
51 | 1836 | 2146.56729818243 | -310.567298182433 |
52 | 1863 | 1904.14338198892 | -41.1433819889198 |
53 | 2044 | 1889.09499858814 | 154.905001411863 |
54 | 2136 | 2043.01056163685 | 92.9894383631486 |
55 | 2931 | 2146.26090455251 | 784.739095447494 |
56 | 3263 | 2850.22000621506 | 412.77999378494 |
57 | 3328 | 3247.03513025109 | 80.9648697489101 |
58 | 3570 | 3364.39641175883 | 205.603588241168 |
59 | 2313 | 3591.21288032379 | -1278.21288032379 |
60 | 1623 | 2537.19447526081 | -914.194475260806 |
61 | 1316 | 1774.06771769142 | -458.06771769142 |
62 | 1507 | 1388.5004152254 | 118.499584774601 |
63 | 1419 | 1493.44165124435 | -74.4416512443499 |
64 | 1660 | 1433.57914353202 | 226.42085646798 |
65 | 1790 | 1632.79969331385 | 157.20030668615 |
66 | 1733 | 1776.38904657778 | -43.3890465777779 |
67 | 2086 | 1749.28803180094 | 336.711968199065 |
68 | 1814 | 2050.46769010583 | -236.467690105831 |
69 | 2241 | 1861.76595230585 | 379.234047694154 |
70 | 1943 | 2201.66760068893 | -258.66760068893 |
71 | 1773 | 1996.45722690688 | -223.45722690688 |
72 | 2143 | 1816.81806140398 | 326.181938596018 |
73 | 2087 | 2108.83015190582 | -21.8301519058246 |
74 | 1805 | 2105.71894655572 | -300.718946555722 |
75 | 1913 | 1860.72095926353 | 52.2790407364707 |
76 | 2296 | 1915.6470846611 | 380.352915338899 |
77 | 2500 | 2255.62479591006 | 244.375204089943 |
78 | 2210 | 2485.09557232421 | -275.095572324205 |
79 | 2526 | 2269.43345423083 | 256.566545769168 |
80 | 2249 | 2508.87618502162 | -259.876185021619 |
81 | 2024 | 2306.03947216798 | -282.039472167976 |
82 | 2091 | 2079.07481955278 | 11.9251804472187 |
83 | 2045 | 2101.27603916083 | -56.2760391608272 |
84 | 1882 | 2064.65278816078 | -182.652788160781 |
85 | 1831 | 1917.53863784079 | -86.5386378407873 |
86 | 1964 | 1850.17281307022 | 113.827186929777 |
87 | 1763 | 1954.64653036293 | -191.646530362935 |
88 | 1688 | 1796.79304274422 | -108.793042744224 |
89 | 2149 | 1707.03542210108 | 441.964577898921 |
90 | 1823 | 2092.07630506452 | -269.076305064524 |
91 | 2094 | 1869.87058726511 | 224.129412734892 |
92 | 2145 | 2069.58715969909 | 75.4128403009122 |
93 | 1791 | 2144.79847334026 | -353.798473340264 |
94 | 1996 | 1849.81616407619 | 146.183835923806 |
95 | 2097 | 1981.01367140518 | 115.986328594822 |
96 | 1796 | 2088.84287429964 | -292.842874299638 |
97 | 1963 | 1844.89699747217 | 118.103002527833 |
98 | 2042 | 1951.19826479638 | 90.8017352036175 |
99 | 1746 | 2036.10530461793 | -290.105304617932 |
100 | 2210 | 1792.93472175512 | 417.065278244876 |
101 | 2968 | 2156.54532433972 | 811.454675660282 |
102 | 3126 | 2869.55754960111 | 256.442450398885 |
103 | 3708 | 3117.43945778587 | 590.560542214131 |
104 | 3015 | 3659.4857659769 | -644.485765976903 |
105 | 1569 | 3143.40631946171 | -1574.40631946171 |
106 | 1518 | 1809.92163865593 | -291.921638655933 |
107 | 1393 | 1556.94152689188 | -163.941526891875 |
108 | 1615 | 1409.22411135081 | 205.775888649189 |
109 | 1777 | 1578.50613634984 | 198.493863650159 |
110 | 1648 | 1745.39327524418 | -97.3932752441772 |
111 | 1463 | 1659.86245036836 | -196.862450368358 |
112 | 1779 | 1486.35696325322 | 292.643036746778 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
113 | 1732.94218102454 | 977.658814066619 | 2488.22554798246 |
114 | 1731.7073181389 | 732.654971240683 | 2730.75966503711 |
115 | 1730.47245525325 | 528.501122959206 | 2932.4437875473 |
116 | 1729.23759236761 | 346.937554891354 | 3111.53762984386 |
117 | 1728.00272948196 | 179.916015032454 | 3276.08944393147 |
118 | 1726.76786659632 | 23.0647577879622 | 3430.47097540467 |
119 | 1725.53300371067 | -126.293329910616 | 3577.35933733196 |
120 | 1724.29814082503 | -269.932008883618 | 3718.52829053367 |
121 | 1723.06327793938 | -409.094220245549 | 3855.22077612431 |
122 | 1721.82841505374 | -544.688261441918 | 3988.34509154939 |
123 | 1720.59355216809 | -677.399898004132 | 4118.58700234031 |
124 | 1719.35868928245 | -807.760575322217 | 4246.47795388711 |