Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.243472330170413 |
beta | 0.0205562664353707 |
gamma | 0.397243808484191 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 2074 | 2141.93536324786 | -67.9353632478637 |
14 | 2049 | 2102.77000853926 | -53.7700085392644 |
15 | 2406 | 2458.45107986328 | -52.4510798632814 |
16 | 2558 | 2585.14909568857 | -27.1490956885655 |
17 | 2251 | 2265.28823320274 | -14.2882332027352 |
18 | 2059 | 2076.19545728523 | -17.1954572852301 |
19 | 2397 | 2224.14212484319 | 172.857875156807 |
20 | 1747 | 2037.68498672405 | -290.684986724054 |
21 | 1707 | 1761.91314380543 | -54.9131438054333 |
22 | 2319 | 1947.31205372759 | 371.687946272413 |
23 | 1631 | 1889.56177944909 | -258.561779449087 |
24 | 1627 | 1588.36073130781 | 38.6392686921906 |
25 | 1791 | 1907.75529479443 | -116.755294794434 |
26 | 2034 | 1859.44629684248 | 174.553703157516 |
27 | 1997 | 2270.74258262418 | -273.742582624177 |
28 | 2169 | 2349.68694120936 | -180.686941209358 |
29 | 2028 | 1994.0612437758 | 33.9387562241989 |
30 | 2253 | 1813.83043889310 | 439.169561106896 |
31 | 2218 | 2130.28309877620 | 87.7169012237955 |
32 | 1855 | 1783.64150072934 | 71.3584992706608 |
33 | 2187 | 1668.53642928732 | 518.463570712676 |
34 | 1852 | 2126.27472463116 | -274.274724631161 |
35 | 1570 | 1723.14439010108 | -153.144390101079 |
36 | 1851 | 1538.75414635396 | 312.245853646036 |
37 | 1954 | 1881.26157993508 | 72.7384200649212 |
38 | 1828 | 1970.7806937783 | -142.780693778301 |
39 | 2251 | 2172.64768095312 | 78.3523190468832 |
40 | 2277 | 2369.6027385011 | -92.6027385011012 |
41 | 2085 | 2104.68424549635 | -19.6842454963517 |
42 | 2282 | 2037.67226268747 | 244.327737312528 |
43 | 2266 | 2204.58270454306 | 61.4172954569367 |
44 | 1878 | 1850.00714303399 | 27.9928569660087 |
45 | 2267 | 1861.87875317538 | 405.121246824616 |
46 | 2069 | 2056.38399510040 | 12.616004899603 |
47 | 1746 | 1763.54335798965 | -17.5433579896455 |
48 | 2299 | 1756.74565401575 | 542.254345984248 |
49 | 2360 | 2089.14236508221 | 270.857634917789 |
50 | 2214 | 2168.98727518902 | 45.0127248109839 |
51 | 2825 | 2490.83118453767 | 334.168815462334 |
52 | 2355 | 2707.77259984061 | -352.772599840605 |
53 | 2333 | 2409.20027051493 | -76.200270514933 |
54 | 3016 | 2415.26421869386 | 600.73578130614 |
55 | 2155 | 2623.25817848311 | -468.258178483112 |
56 | 2172 | 2136.30277337822 | 35.6972266217767 |
57 | 2150 | 2270.05199379037 | -120.051993790372 |
58 | 2533 | 2222.77059727665 | 310.229402723346 |
59 | 2058 | 1998.8529550737 | 59.1470449263002 |
60 | 2160 | 2184.87083389630 | -24.8708338962956 |
61 | 2260 | 2300.69797605381 | -40.6979760538079 |
62 | 2498 | 2238.32763409113 | 259.672365908869 |
63 | 2695 | 2701.92064729472 | -6.92064729471576 |
64 | 2799 | 2630.25191113638 | 168.748088863620 |
65 | 2945 | 2545.2621503655 | 399.737849634501 |
66 | 2930 | 2876.51226824777 | 53.487731752226 |
67 | 2318 | 2633.13871952370 | -315.138719523695 |
68 | 2540 | 2338.81433512761 | 201.185664872394 |
69 | 2570 | 2470.77598263163 | 99.2240173683713 |
70 | 2669 | 2612.01764729391 | 56.982352706093 |
71 | 2450 | 2255.54182604720 | 194.458173952797 |
72 | 2842 | 2454.48911570999 | 387.510884290008 |
73 | 3440 | 2673.26169729084 | 766.738302709157 |
74 | 2678 | 2909.08831638889 | -231.088316388890 |
75 | 2981 | 3181.9598610077 | -200.959861007702 |
76 | 2259 | 3123.75310501022 | -864.753105010216 |
77 | 2844 | 2859.29241091157 | -15.2924109115679 |
78 | 2546 | 2986.09942425485 | -440.099424254849 |
79 | 2456 | 2509.96132662118 | -53.9613266211827 |
80 | 2295 | 2433.89451418500 | -138.894514185003 |
81 | 2379 | 2450.21110390858 | -71.2111039085758 |
82 | 2479 | 2534.20598417388 | -55.2059841738787 |
83 | 2057 | 2188.11313454535 | -131.113134545352 |
84 | 2280 | 2360.56339693259 | -80.563396932594 |
85 | 2351 | 2571.75109163386 | -220.751091633858 |
86 | 2275 | 2254.74689883006 | 20.2531011699407 |
87 | 2543 | 2586.59374778731 | -43.5937477873131 |
88 | 2305 | 2356.72804265566 | -51.7280426556558 |
89 | 2188 | 2539.08435742891 | -351.084357428911 |
90 | 2720 | 2448.37213505697 | 271.627864943031 |
91 | 2398 | 2257.02889800291 | 140.971101997091 |
92 | 2147 | 2199.33817364837 | -52.3381736483684 |
93 | 1898 | 2253.94272245668 | -355.942722456683 |
94 | 2538 | 2268.87150259653 | 269.128497403467 |
95 | 2081 | 1976.00453059727 | 104.995469402734 |
96 | 2057 | 2219.38538054769 | -162.385380547686 |
97 | 2497 | 2366.36530768190 | 130.634692318104 |
98 | 2460 | 2206.94414390802 | 253.055856091976 |
99 | 2195 | 2577.05184215065 | -382.051842150655 |
100 | 2823 | 2261.40990062501 | 561.590099374991 |
101 | 2100 | 2505.27097288365 | -405.27097288365 |
102 | 2640 | 2590.37887889006 | 49.621121109943 |
103 | 2342 | 2306.47817788752 | 35.5218221124765 |
104 | 2171 | 2165.25204089819 | 5.7479591018132 |
105 | 2482 | 2143.28164944744 | 338.718350552561 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
106 | 2519.19172175873 | 2006.53626811179 | 3031.84717540566 |
107 | 2114.12665028470 | 1585.88230031074 | 2642.37100025866 |
108 | 2253.71711360180 | 1709.72370354922 | 2797.71052365438 |
109 | 2531.23422242952 | 1971.33334610173 | 3091.13509875732 |
110 | 2379.08475290284 | 1803.11969916223 | 2955.04980664345 |
111 | 2497.73439679447 | 1905.55009094956 | 3089.91870263938 |
112 | 2561.63288466798 | 1953.07583340372 | 3170.18993593224 |
113 | 2378.31729143701 | 1753.23553098585 | 3003.39905188818 |
114 | 2700.95448008141 | 2059.19752736499 | 3342.71143279784 |
115 | 2402.63699990829 | 1744.05580640828 | 3061.2181934083 |
116 | 2245.53847742671 | 1569.98538556802 | 2921.09156928539 |
117 | 2323.9300998666 | 1631.25880171814 | 3016.60139801507 |