Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.225679028753732 |
beta | 0.00094149628696139 |
gamma | 0.443442884267825 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 37702 | 41487.9961256583 | -3785.99612565827 |
14 | 30364 | 32384.2423306432 | -2020.24233064318 |
15 | 32609 | 34048.8239474283 | -1439.82394742829 |
16 | 30212 | 30953.0817784316 | -741.081778431551 |
17 | 29965 | 30167.1615625239 | -202.161562523925 |
18 | 28352 | 28194.2876712464 | 157.712328753587 |
19 | 25814 | 22076.5443444737 | 3737.45565552631 |
20 | 22414 | 20801.9207532692 | 1612.07924673078 |
21 | 20506 | 21128.7820231174 | -622.782023117405 |
22 | 28806 | 26754.525919159 | 2051.47408084105 |
23 | 22228 | 22076.0673310009 | 151.932668999121 |
24 | 13971 | 13470.8643970099 | 500.1356029901 |
25 | 36845 | 37059.4733194599 | -214.473319459903 |
26 | 35338 | 29795.4839704103 | 5542.51602958971 |
27 | 35022 | 33348.7244194968 | 1673.27558050316 |
28 | 34777 | 31163.7441308367 | 3613.25586916331 |
29 | 26887 | 31542.0186569803 | -4655.01865698035 |
30 | 23970 | 28668.3449958561 | -4698.34499585611 |
31 | 22780 | 22752.2259942236 | 27.7740057763804 |
32 | 17351 | 20061.35455277 | -2710.35455277003 |
33 | 21382 | 18709.0425300708 | 2672.95746992922 |
34 | 24561 | 25498.9960342699 | -937.996034269905 |
35 | 17409 | 20022.1189854628 | -2613.11898546284 |
36 | 11514 | 11945.6711210855 | -431.671121085454 |
37 | 31514 | 31811.142739522 | -297.142739522031 |
38 | 27071 | 27135.223971572 | -64.2239715719661 |
39 | 29462 | 27863.0241804403 | 1598.97581955968 |
40 | 26105 | 26585.9480635963 | -480.948063596261 |
41 | 22397 | 23768.4474504715 | -1371.44745047153 |
42 | 23843 | 21869.5638551759 | 1973.43614482408 |
43 | 21705 | 19509.1082062688 | 2195.89179373124 |
44 | 18089 | 16761.280975965 | 1327.71902403496 |
45 | 20764 | 18040.7422278936 | 2723.25777210641 |
46 | 25316 | 23196.8285072134 | 2119.17149278664 |
47 | 17704 | 18102.3007276661 | -398.300727666137 |
48 | 15548 | 11461.2235378717 | 4086.77646212826 |
49 | 28029 | 33585.8002125576 | -5556.8002125576 |
50 | 29383 | 27714.0486189868 | 1668.9513810132 |
51 | 36438 | 29460.2103780294 | 6977.78962197057 |
52 | 32034 | 28524.1330124592 | 3509.86698754081 |
53 | 22679 | 25984.1070779241 | -3305.10707792409 |
54 | 24319 | 24768.3603312277 | -449.360331227745 |
55 | 18004 | 21738.5190502831 | -3734.51905028314 |
56 | 17537 | 17326.1475284391 | 210.852471560949 |
57 | 20366 | 18790.7238567441 | 1575.27614325593 |
58 | 22782 | 23364.3485694361 | -582.348569436119 |
59 | 19169 | 17096.146729406 | 2072.85327059405 |
60 | 13807 | 12536.4463062626 | 1270.55369373736 |
61 | 29743 | 29375.0615334862 | 367.938466513806 |
62 | 25591 | 27375.1673515005 | -1784.16735150052 |
63 | 29096 | 29845.1799392579 | -749.179939257865 |
64 | 26482 | 26329.5061513023 | 152.493848697704 |
65 | 22405 | 21403.1889229465 | 1001.81107705352 |
66 | 27044 | 22062.6515825363 | 4981.3484174637 |
67 | 17970 | 19291.1739870894 | -1321.17398708937 |
68 | 18730 | 16843.7925925239 | 1886.2074074761 |
69 | 19684 | 19125.9670976035 | 558.032902396455 |
70 | 19785 | 22648.0790967245 | -2863.07909672453 |
71 | 18479 | 16985.5773885737 | 1493.42261142634 |
72 | 10698 | 12280.7803828348 | -1582.78038283481 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
73 | 26498.9818651434 | 23698.8806723008 | 29299.083057986 |
74 | 23934.8633943185 | 20956.2883634191 | 26913.4384252178 |
75 | 26836.6936186304 | 23556.4925784394 | 30116.8946588213 |
76 | 24042.233314808 | 20686.8416091529 | 27397.6250204631 |
77 | 19769.0075844722 | 16442.310680399 | 23095.7044885454 |
78 | 21288.456756201 | 17662.4973863107 | 24914.4161260914 |
79 | 16072.1766150458 | 12656.4439046935 | 19487.9093253982 |
80 | 15124.8889897849 | 11597.6008055887 | 18652.1771739811 |
81 | 16273.7807682909 | 12429.5244948342 | 20118.0370417475 |
82 | 18070.926523693 | 13805.6598493721 | 22336.193198014 |
83 | 15008.4341904266 | 11001.7108928478 | 19015.1574880055 |
84 | 9842.62588615825 | 7798.8339209939 | 11886.4178513226 |