Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.99993997895847 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 42.1471 | 42.336 | -0.188899999999997 |
3 | 40.2564 | 42.1471113379747 | -1.89071133797475 |
4 | 39.1898 | 40.2565134824637 | -1.06671348246374 |
5 | 39.1317 | 39.1898640252542 | -0.0581640252542286 |
6 | 38.1507 | 39.1317034910654 | -0.98100349106538 |
7 | 38.2707 | 38.1507588808513 | 0.11994111914872 |
8 | 39.1335 | 38.2706928010091 | 0.862807198990893 |
9 | 40.1219 | 39.1334482134133 | 0.988451786586722 |
10 | 41.2845 | 40.1218406720943 | 1.16265932790574 |
11 | 42.5749 | 41.2844302159762 | 1.29046978402381 |
12 | 43.9019 | 42.5748225446595 | 1.3270774553405 |
13 | 43.1835 | 43.9018203474289 | -0.718320347428936 |
14 | 43.6188 | 43.1835431143354 | 0.435256885664593 |
15 | 44.7624 | 43.6187738754284 | 1.14362612457161 |
16 | 45.1972 | 44.7623313583689 | 0.43486864163112 |
17 | 44.3881 | 45.1971738987312 | -0.8090738987312 |
18 | 43.5552 | 44.3881485614581 | -0.832948561458082 |
19 | 43.5678 | 43.5552499944402 | 0.0125500055598025 |
20 | 44.2135 | 43.5677992467356 | 0.645700753264407 |
21 | 45.1451 | 44.2134612443683 | 0.931638755631724 |
22 | 45.8079 | 45.1450440820716 | 0.66285591792844 |
23 | 42.3282 | 45.8078602146974 | -3.47966021469742 |
24 | 37.8999 | 42.3284088528303 | -4.42850885283026 |
25 | 34.7964 | 37.9001658037138 | -3.10376580371377 |
26 | 35.2144 | 34.7965862912562 | 0.4178137087438 |
27 | 36.3727 | 35.214374922386 | 1.15832507761397 |
28 | 36.2502 | 36.3726304761224 | -0.122430476122418 |
29 | 36.8261 | 36.2502073484047 | 0.575892651595304 |
30 | 36.7723 | 36.8260654343232 | -0.053765434323239 |
31 | 36.9042 | 36.7723032270574 | 0.131896772942632 |
32 | 37.0494 | 36.9041920834183 | 0.145207916581683 |
33 | 36.8259 | 37.0493912844696 | -0.22349128446961 |
34 | 36.1357 | 36.8259134141797 | -0.690213414179667 |
35 | 36.03 | 36.135741427328 | -0.105741427327999 |
36 | 35.7927 | 36.0300063467106 | -0.237306346710596 |
37 | 35.9174 | 35.7927142433741 | 0.124685756625908 |
38 | 35.4008 | 35.917392516231 | -0.516592516231029 |
39 | 35.1723 | 35.4008310064209 | -0.228531006420866 |
40 | 34.9211 | 35.172313716669 | -0.251213716669021 |
41 | 35.0292 | 34.9211150781089 | 0.108084921891077 |
42 | 34.7739 | 35.0291935126304 | -0.255293512630416 |
43 | 34.8999 | 34.7739153229825 | 0.125984677017478 |
44 | 34.9054 | 34.8998924382685 | 0.00550756173152678 |
45 | 34.568 | 34.9053996694304 | -0.337399669430411 |
46 | 34.406 | 34.5680202510796 | -0.162020251079568 |
47 | 34.4578 | 34.4060097246242 | 0.0517902753757795 |
48 | 34.7316 | 34.4577968914937 | 0.273803108506272 |
49 | 34.2602 | 34.7315835660523 | -0.471383566052253 |
50 | 33.8849 | 34.2602282929326 | -0.375328292932593 |
51 | 34.0549 | 33.8849225275951 | 0.169977472404945 |
52 | 34.2755 | 34.0548897977751 | 0.220610202224925 |
53 | 34.1393 | 34.2754867587459 | -0.136186758745893 |
54 | 34.1587 | 34.1393081740711 | 0.0193918259288992 |
55 | 34.5386 | 34.1586988360824 | 0.379901163917587 |
56 | 33.7987 | 34.5385771979365 | -0.739877197936472 |
57 | 33.4973 | 33.7987444082 | -0.30144440820002 |
58 | 33.6802 | 33.4973180930073 | 0.182881906992655 |
59 | 34.3284 | 33.6801890232375 | 0.648210976762535 |
60 | 34.1538 | 34.328361093702 | -0.174561093702046 |
61 | 33.9184 | 34.1538104773387 | -0.235410477338654 |
62 | 34.3262 | 33.918414129582 | 0.407785870417968 |
63 | 34.775 | 34.3261755242673 | 0.448824475732664 |
64 | 35.0119 | 34.7749730610875 | 0.236926938912497 |
65 | 34.5513 | 35.0118857793984 | -0.460585779398357 |
66 | 34.6951 | 34.5513276448382 | 0.143772355161808 |
67 | 35.473 | 34.6950913706335 | 0.7779086293665 |
68 | 35.9794 | 35.4729533091138 | 0.50644669088615 |
69 | 36.4789 | 35.9793696025421 | 0.499530397457868 |
70 | 36.391 | 36.4788700176653 | -0.0878700176652742 |
71 | 36.6704 | 36.39100527405 | 0.27939472595002 |
72 | 37.4162 | 36.6703832304376 | 0.745816769562452 |
73 | 37.1185 | 37.4161552353007 | -0.297655235300709 |
74 | 36.3001 | 37.1185178655772 | -0.818417865577239 |
75 | 35.7002 | 36.3001491222927 | -0.599949122292699 |
76 | 35.5859 | 35.7002360095712 | -0.114336009571183 |
77 | 35.6777 | 35.5859068625664 | 0.0917931374336192 |
78 | 35.2408 | 35.6776944904803 | -0.436894490480285 |
79 | 34.8016 | 35.2408262228624 | -0.439226222862359 |
80 | 34.4389 | 34.8016263628154 | -0.362726362815366 |
81 | 34.9881 | 34.4389217712141 | 0.549178228785919 |
82 | 36.068 | 34.9880670377507 | 1.07993296224927 |
83 | 36.3566 | 36.0679351812988 | 0.288664818701179 |
84 | 36.1254 | 36.3565826740369 | -0.23118267403693 |
85 | 34.871 | 36.1254138758249 | -1.25441387582487 |
86 | 35.2199 | 34.8710752912273 | 0.348824708772668 |
87 | 34.339 | 35.2198790631777 | -0.880879063177673 |
88 | 33.8234 | 34.3390528712788 | -0.515652871278832 |
89 | 34.5199 | 33.8234309500224 | 0.696469049977601 |
90 | 35.53 | 34.5198581972022 | 1.01014180279778 |
91 | 35.7966 | 35.5299393702369 | 0.266660629763095 |
92 | 33.8484 | 35.7965839947513 | -1.94818399475127 |
93 | 33.9871 | 33.8485169320325 | 0.138583067967545 |
94 | 34.1161 | 33.9870916820999 | 0.12900831790008 |
95 | 33.8235 | 34.1160922567864 | -0.292592256786392 |
96 | 32.454 | 33.823517561692 | -1.369517561692 |
97 | 31.8774 | 32.4540821998704 | -0.576682199870447 |
98 | 31.115 | 31.8774346130663 | -0.762434613066272 |
99 | 31.0436 | 31.1150457621196 | -0.0714457621195699 |
100 | 30.8868 | 31.0436042882491 | -0.156804288249056 |
101 | 31.3001 | 30.8868094115567 | 0.413290588443303 |
102 | 30.0507 | 31.3000751938684 | -1.24937519386843 |
103 | 28.6799 | 30.0507749888004 | -1.3708749888004 |
104 | 27.6438 | 28.6799822813446 | -1.03618228134464 |
105 | 27.2394 | 27.6438621927397 | -0.404462192739739 |
106 | 26.8549 | 27.2394242762421 | -0.384524276242068 |
107 | 27.0158 | 26.8549230795476 | 0.160876920452445 |
108 | 26.9188 | 27.0157903439997 | -0.096990343999675 |
109 | 26.4966 | 26.9188058214615 | -0.422205821461464 |
110 | 26.785 | 26.4966253412331 | 0.288374658766855 |
111 | 26.8398 | 26.7849826914526 | 0.0548173085473707 |
112 | 26.4478 | 26.839796709808 | -0.391996709808048 |
113 | 25.1728 | 26.4478235280508 | -1.2750235280508 |
114 | 24.8784 | 25.1728765282401 | -0.294476528240128 |
115 | 25.4015 | 24.8784176747879 | 0.523082325212069 |
116 | 25.7716 | 25.401468604054 | 0.370131395945965 |
117 | 26.1181 | 25.7715777843281 | 0.346522215671886 |
118 | 26.3969 | 26.1180792013757 | 0.278820798624299 |
119 | 26.6571 | 26.3968832648853 | 0.260216735114735 |
120 | 25.1839 | 26.6570843815205 | -1.47318438152053 |
121 | 23.8394 | 25.1839884220609 | -1.34458842206094 |
122 | 23.8619 | 23.8394807035975 | 0.0224192964024752 |
123 | 24.2581 | 23.8618986543705 | 0.396201345629521 |
124 | 25.1098 | 24.2580762195826 | 0.85172378041742 |
125 | 26.1617 | 25.1097488786516 | 1.0519511213484 |
126 | 26.8087 | 26.1616368607981 | 0.647063139201943 |
127 | 25.6577 | 26.8086611625965 | -1.15096116259645 |
128 | 27.0982 | 25.6577690818877 | 1.44043091811226 |
129 | 27.4665 | 27.098113543836 | 0.368386456163957 |
130 | 28.289 | 27.4664778890612 | 0.822522110938785 |
131 | 28.6933 | 28.2889506313662 | 0.404349368633778 |
132 | 27.2401 | 28.6932757305298 | -1.45317573052975 |
133 | 27.2798 | 27.2401872211209 | 0.0396127788791283 |
134 | 27.6404 | 27.2797976223998 | 0.360602377600244 |
135 | 26.831 | 27.6403783562697 | -0.809378356269718 |
136 | 26.2467 | 26.8310485797319 | -0.584348579731934 |
137 | 25.2212 | 26.2467350732104 | -1.02553507321037 |
138 | 25.3653 | 25.2212615536832 | 0.144038446316781 |
139 | 26.2592 | 25.3652913546624 | 0.893908645337568 |
140 | 27.2279 | 26.2591463466721 | 0.968753653327926 |
141 | 26.3315 | 27.2278418543967 | -0.896341854396745 |
142 | 25.8981 | 26.3315537993717 | -0.433453799371666 |
143 | 26.6898 | 25.8981260163485 | 0.79167398365151 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
144 | 26.6897524829029 | 24.9975380500968 | 28.3819669157091 |
145 | 26.6897524829029 | 24.2966717002631 | 29.0828332655428 |
146 | 26.6897524829029 | 23.7588683879782 | 29.6206365778277 |
147 | 26.6897524829029 | 23.3054759688566 | 30.0740289969493 |
148 | 26.6897524829029 | 22.906027668759 | 30.4734772970469 |