Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.0374406816921577 |
beta | 0.180510709878271 |
gamma | 0.605025766097544 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 57.9 | 57.948705144157 | -0.0487051441569477 |
14 | 63.7 | 63.6303585893703 | 0.0696414106296857 |
15 | 85 | 84.8545462246734 | 0.145453775326558 |
16 | 66.1 | 65.8779920277422 | 0.222007972257813 |
17 | 80.2 | 79.6525466332378 | 0.547453366762184 |
18 | 83.4 | 82.46783772939 | 0.932162270610036 |
19 | 85.7 | 83.1417637867953 | 2.55823621320472 |
20 | 81.8 | 79.7373757660508 | 2.06262423394917 |
21 | 69.4 | 69.232372482659 | 0.167627517340946 |
22 | 76.4 | 72.4089070088284 | 3.99109299117163 |
23 | 90.3 | 87.6567424581175 | 2.64325754188252 |
24 | 157.3 | 154.236840917238 | 3.06315908276193 |
25 | 65.3 | 59.8489963661493 | 5.45100363385067 |
26 | 68.4 | 66.1363154238624 | 2.26368457613756 |
27 | 72.7 | 88.5151219120917 | -15.8151219120917 |
28 | 86.6 | 68.3761346092784 | 18.2238653907216 |
29 | 82.6 | 83.8688571282422 | -1.26885712824222 |
30 | 84.8 | 87.190333725817 | -2.39033372581697 |
31 | 93.4 | 88.9485453591528 | 4.45145464084719 |
32 | 82.2 | 85.3169164453911 | -3.11691644539114 |
33 | 75.2 | 73.0406181827983 | 2.15938181720171 |
34 | 83.9 | 78.9614774890216 | 4.9385225109784 |
35 | 85.4 | 94.4595676702692 | -9.05956767026915 |
36 | 166.3 | 164.636529290357 | 1.66347070964289 |
37 | 70.4 | 66.5391221657777 | 3.86087783422234 |
38 | 73.9 | 71.199106351561 | 2.70089364843899 |
39 | 82.4 | 83.7262544660784 | -1.32625446607841 |
40 | 92.3 | 84.02053133728 | 8.27946866272 |
41 | 82.7 | 88.061233125874 | -5.36123312587405 |
42 | 95.8 | 90.7759365885815 | 5.02406341141847 |
43 | 105.8 | 97.2490467691875 | 8.55095323081251 |
44 | 84.2 | 88.948820865085 | -4.74882086508491 |
45 | 82.7 | 79.1865430283325 | 3.51345697166754 |
46 | 88.4 | 87.3722185013752 | 1.02778149862480 |
47 | 90.2 | 95.1061723789435 | -4.90617237894347 |
48 | 176.6 | 177.141954535683 | -0.541954535683431 |
49 | 69.5 | 73.6173444021006 | -4.11734440210057 |
50 | 77.3 | 77.5777153804241 | -0.277715380424141 |
51 | 98.6 | 88.3006424286072 | 10.2993575713928 |
52 | 86.4 | 95.1056862137858 | -8.70568621378584 |
53 | 90.8 | 90.2617561817642 | 0.538243818235756 |
54 | 101.5 | 99.8349820018806 | 1.66501799811938 |
55 | 112.2 | 108.735304844972 | 3.46469515502804 |
56 | 93.6 | 91.4377308715287 | 2.16226912847132 |
57 | 93.8 | 86.4353103250508 | 7.36468967494922 |
58 | 90.8 | 93.7751873908708 | -2.97518739087077 |
59 | 98.1 | 98.1667570034802 | -0.0667570034802196 |
60 | 187.6 | 188.596943934841 | -0.996943934841454 |
61 | 75 | 75.9700538521501 | -0.970053852150102 |
62 | 83.7 | 82.7659105588678 | 0.934089441132244 |
63 | 99.7 | 100.909547260828 | -1.20954726082755 |
64 | 104.9 | 95.8752860625806 | 9.0247139374194 |
65 | 98.9 | 97.2405902209396 | 1.65940977906040 |
66 | 117.3 | 108.384529069019 | 8.91547093098099 |
67 | 115.7 | 119.549984834011 | -3.84998483401083 |
68 | 102.2 | 99.9270201497796 | 2.27297985022045 |
69 | 101.9 | 97.885708714722 | 4.01429128527796 |
70 | 96.6 | 99.2304817071666 | -2.63048170716661 |
71 | 110 | 105.895448711970 | 4.10455128803022 |
72 | 203.7 | 203.405070427754 | 0.294929572246417 |
73 | 82.3 | 81.6826445750636 | 0.617355424936434 |
74 | 93.3 | 90.419722008517 | 2.88027799148301 |
75 | 121.9 | 108.980529036398 | 12.9194709636017 |
76 | 100.9 | 110.739123801432 | -9.83912380143195 |
77 | 107.7 | 106.918078311387 | 0.781921688613053 |
78 | 130 | 123.691334570434 | 6.30866542956579 |
79 | 123.2 | 127.698680615347 | -4.49868061534676 |
80 | 116.1 | 110.272436724977 | 5.82756327502264 |
81 | 105.3 | 109.358056609725 | -4.05805660972473 |
82 | 107.7 | 106.320831923002 | 1.37916807699769 |
83 | 123.9 | 118.074712401493 | 5.82528759850682 |
84 | 205.2 | 222.200796333604 | -17.0007963336039 |
85 | 90.3 | 89.2911670951508 | 1.00883290484919 |
86 | 106.9 | 100.254417100626 | 6.64558289937432 |
87 | 122.4 | 126.991486755384 | -4.591486755384 |
88 | 111.3 | 113.733232389089 | -2.43323238908924 |
89 | 122.6 | 116.579958935404 | 6.02004106459587 |
90 | 124.8 | 138.512650576417 | -13.7126505764169 |
91 | 139.5 | 135.140282054159 | 4.35971794584052 |
92 | 118.8 | 123.056360645890 | -4.25636064588959 |
93 | 111 | 115.337491648461 | -4.33749164846083 |
94 | 121.2 | 115.357728816668 | 5.84227118333246 |
95 | 120.6 | 130.879044028428 | -10.2790440284283 |
96 | 219.1 | 227.273459470361 | -8.17345947036134 |
97 | 101.3 | 96.2495432639982 | 5.05045673600178 |
98 | 105 | 111.551212903444 | -6.5512129034437 |
99 | 113.4 | 132.327383735175 | -18.9273837351754 |
100 | 133.6 | 118.775939445074 | 14.8240605549257 |
101 | 123.9 | 127.485700584144 | -3.58570058414379 |
102 | 136.2 | 137.851549927542 | -1.65154992754162 |
103 | 151.7 | 145.698803343474 | 6.00119665652565 |
104 | 121.9 | 127.467128760491 | -5.56712876049113 |
105 | 120.2 | 119.046232978534 | 1.15376702146578 |
106 | 132.2 | 125.404730830119 | 6.79526916988065 |
107 | 125.2 | 131.746027470783 | -6.54602747078293 |
108 | 233.8 | 234.800218574158 | -1.00021857415777 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 104.720886767167 | 97.1658108821946 | 112.275962652140 |
110 | 113.405032371249 | 105.827662374376 | 120.982402368121 |
111 | 127.840307448734 | 120.223906734607 | 135.456708162860 |
112 | 135.06758713278 | 127.40340878845 | 142.731765477110 |
113 | 132.294141308603 | 124.589058638876 | 139.999223978329 |
114 | 144.532266559535 | 136.733869779740 | 152.330663339330 |
115 | 157.557334633567 | 149.629342512148 | 165.485326754985 |
116 | 130.924831635917 | 123.045170184615 | 138.80449308722 |
117 | 126.364465653528 | 118.433023114808 | 134.295908192247 |
118 | 136.453592955893 | 128.364269614092 | 144.542916297694 |
119 | 134.595071071724 | 126.417053045136 | 142.773089098312 |
120 | 246.821782631884 | 223.808026154102 | 269.835539109665 |