Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.279673175984277 |
beta | 0.105814685840969 |
gamma | 0.78536497988161 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 1532 | 1461.32451923077 | 70.6754807692303 |
14 | 1333 | 1292.14960396448 | 40.8503960355224 |
15 | 1583 | 1561.42565325019 | 21.5743467498050 |
16 | 1712 | 1703.11583634011 | 8.88416365989133 |
17 | 2641 | 2632.14482937862 | 8.8551706213807 |
18 | 2267 | 2257.34443625948 | 9.65556374052358 |
19 | 2126 | 2204.84530050069 | -78.8453005006945 |
20 | 2231 | 2333.67820292190 | -102.678202921904 |
21 | 1517 | 1477.72373809470 | 39.2762619052953 |
22 | 2010 | 2046.21578582993 | -36.2157858299286 |
23 | 2628 | 2350.43964656270 | 277.560353437296 |
24 | 2115 | 2179.21560048522 | -64.2156004852159 |
25 | 1829 | 1703.57144991363 | 125.428550086370 |
26 | 1636 | 1540.23909556032 | 95.7609044396831 |
27 | 1787 | 1822.99452763994 | -35.9945276399433 |
28 | 2122 | 1948.72871381541 | 173.271286184586 |
29 | 2620 | 2935.90432526461 | -315.904325264612 |
30 | 2555 | 2473.30778251156 | 81.6922174884371 |
31 | 2337 | 2395.59809608675 | -58.59809608675 |
32 | 2524 | 2521.91943884728 | 2.08056115272302 |
33 | 1801 | 1783.97835235479 | 17.0216476452104 |
34 | 2417 | 2311.28922691044 | 105.710773089564 |
35 | 2389 | 2844.66568156603 | -455.665681566025 |
36 | 2267 | 2265.28020063706 | 1.71979936293701 |
37 | 2135 | 1907.56458843248 | 227.435411567518 |
38 | 1760 | 1751.19878443253 | 8.80121556746508 |
39 | 1905 | 1927.74539989475 | -22.7453998947549 |
40 | 2176 | 2168.61093155192 | 7.38906844808389 |
41 | 2344 | 2820.78870880933 | -476.788708809333 |
42 | 2674 | 2521.49522099752 | 152.504779002478 |
43 | 2766 | 2369.69054082385 | 396.309459176148 |
44 | 2783 | 2656.49233463977 | 126.507665360232 |
45 | 2000 | 1964.41278510354 | 35.5872148964602 |
46 | 2588 | 2550.24868591158 | 37.7513140884166 |
47 | 2736 | 2748.18552767517 | -12.1855276751658 |
48 | 2704 | 2565.85397137374 | 138.14602862626 |
49 | 2466 | 2392.29471768894 | 73.7052823110639 |
50 | 1976 | 2083.00957052961 | -107.009570529613 |
51 | 2171 | 2219.65370142218 | -48.653701422184 |
52 | 2397 | 2479.88753334324 | -82.8875333432361 |
53 | 2942 | 2839.80347393924 | 102.196526060758 |
54 | 2707 | 3082.46931401563 | -375.469314015630 |
55 | 2861 | 2929.33399331702 | -68.3339933170246 |
56 | 2765 | 2928.20941041026 | -163.209410410261 |
57 | 1814 | 2089.74860599598 | -275.748605995978 |
58 | 2611 | 2566.60328441252 | 44.3967155874766 |
59 | 2606 | 2715.21186676898 | -109.211866768981 |
60 | 2518 | 2564.98222464364 | -46.9822246436352 |
61 | 2267 | 2271.90567319405 | -4.90567319405318 |
62 | 1730 | 1804.78835867401 | -74.7883586740134 |
63 | 1901 | 1950.79760594561 | -49.7976059456057 |
64 | 2124 | 2158.65157818861 | -34.6515781886083 |
65 | 2448 | 2605.49775285329 | -157.497752853291 |
66 | 2489 | 2466.35821387092 | 22.6417861290806 |
67 | 2521 | 2571.14683632024 | -50.1468363202389 |
68 | 2466 | 2494.80458474976 | -28.8045847497588 |
69 | 1827 | 1607.61384605312 | 219.386153946877 |
70 | 2278 | 2396.05591370195 | -118.055913701951 |
71 | 2373 | 2399.52298152739 | -26.5229815273888 |
72 | 2356 | 2297.26227090758 | 58.7377290924205 |
73 | 2075 | 2050.32345397171 | 24.6765460282932 |
74 | 1606 | 1545.58811496899 | 60.4118850310088 |
75 | 1699 | 1741.19066886177 | -42.1906688617651 |
76 | 2311 | 1957.60928603307 | 353.390713966933 |
77 | 2093 | 2452.83633609464 | -359.836336094642 |
78 | 2064 | 2362.38098007643 | -298.380980076427 |
79 | 2180 | 2330.07442315643 | -150.074423156432 |
80 | 2136 | 2228.76584063650 | -92.7658406365035 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
81 | 1453.10735371171 | 1135.99658362481 | 1770.2181237986 |
82 | 1971.81721176882 | 1639.88752183333 | 2303.74690170431 |
83 | 2046.0987618704 | 1697.20886461394 | 2394.98865912686 |
84 | 1986.28981850676 | 1618.3551782775 | 2354.22445873603 |
85 | 1688.71666093899 | 1299.73250802994 | 2077.70081384805 |
86 | 1181.62796535169 | 769.683053326427 | 1593.57287737696 |
87 | 1284.8347077243 | 848.117576845865 | 1721.55183860273 |
88 | 1720.63361476536 | 1257.43329986197 | 2183.83392966875 |
89 | 1686.87486483945 | 1195.57782286799 | 2178.17190681090 |
90 | 1715.80592397974 | 1194.89063095480 | 2236.72121700469 |
91 | 1843.66192850033 | 1291.69223383100 | 2395.63162316966 |
92 | 1814.00044837101 | 1229.61844799555 | 2398.38244874647 |