Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.238478317886849 |
beta | 0.0332524755449531 |
gamma | 0.786856072763765 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 74 | 76.1609807081855 | -2.16098070818548 |
14 | 77.6 | 79.0715192698551 | -1.47151926985515 |
15 | 75.1 | 75.9320633301454 | -0.83206333014536 |
16 | 85 | 85.3702471707489 | -0.370247170748897 |
17 | 75.4 | 75.2330732961018 | 0.16692670389817 |
18 | 63.2 | 62.7602291643611 | 0.439770835638889 |
19 | 64.7 | 59.9747603108474 | 4.72523968915258 |
20 | 77 | 76.9857929700979 | 0.0142070299020816 |
21 | 82.6 | 80.737854397984 | 1.862145602016 |
22 | 97.6 | 98.590085292572 | -0.99008529257209 |
23 | 99 | 95.3036784097252 | 3.69632159027485 |
24 | 75.3 | 77.0443186004388 | -1.7443186004388 |
25 | 71.6 | 73.9638293823682 | -2.36382938236817 |
26 | 76.8 | 77.2147861428936 | -0.414786142893647 |
27 | 83.9 | 74.7678706727276 | 9.13212932727244 |
28 | 79.7 | 87.221791561436 | -7.52179156143598 |
29 | 77.5 | 75.7272089028127 | 1.77279109718732 |
30 | 73.1 | 63.7419643602922 | 9.35803563970784 |
31 | 65.6 | 65.7266265579438 | -0.126626557943766 |
32 | 85.2 | 79.2392222151445 | 5.96077778485555 |
33 | 98.3 | 85.923694277481 | 12.376305722519 |
34 | 98 | 106.148503406018 | -8.1485034060185 |
35 | 100.6 | 104.187778000516 | -3.58777800051568 |
36 | 84.1 | 79.9568905416234 | 4.14310945837656 |
37 | 76.7 | 77.8784201026497 | -1.17842010264968 |
38 | 82.4 | 83.1904662296599 | -0.79046622965987 |
39 | 95.5 | 86.705936204537 | 8.79406379546302 |
40 | 79.9 | 89.2371047653084 | -9.33710476530837 |
41 | 82.4 | 82.75425249186 | -0.354252491859938 |
42 | 83.6 | 74.2039821018118 | 9.3960178981882 |
43 | 73.1 | 70.2437180091495 | 2.85628199085046 |
44 | 91.1 | 89.6339225146001 | 1.46607748539991 |
45 | 118.6 | 99.6214602990688 | 18.9785397009312 |
46 | 102.9 | 109.646879399444 | -6.74687939944442 |
47 | 111.8 | 111.20817886582 | 0.59182113417981 |
48 | 93.9 | 90.9098801962 | 2.99011980379998 |
49 | 91.6 | 84.9414952417987 | 6.65850475820132 |
50 | 92 | 93.3551953110195 | -1.3551953110195 |
51 | 91.1 | 103.838593280986 | -12.7385932809861 |
52 | 97.5 | 89.578106760884 | 7.92189323911596 |
53 | 94.7 | 92.9771154747697 | 1.7228845252303 |
54 | 96.7 | 90.4818649150129 | 6.21813508498714 |
55 | 78.7 | 80.792937942156 | -2.09293794215606 |
56 | 103.5 | 100.231119765343 | 3.26888023465663 |
57 | 113.8 | 123.074772075817 | -9.27477207581728 |
58 | 106.1 | 110.425674864106 | -4.32567486410616 |
59 | 120.3 | 117.373090491436 | 2.92690950856441 |
60 | 114.2 | 98.0002142902896 | 16.1997857097104 |
61 | 106.3 | 97.0108623302688 | 9.28913766973125 |
62 | 98.8 | 101.5715103602 | -2.77151036020022 |
63 | 113.1 | 105.144676842999 | 7.95532315700119 |
64 | 97.7 | 108.537492182488 | -10.8374921824884 |
65 | 116.3 | 103.648649972666 | 12.6513500273344 |
66 | 107.2 | 106.560862008207 | 0.639137991792992 |
67 | 94.5 | 88.821026272786 | 5.67897372721407 |
68 | 123.5 | 116.807493792395 | 6.69250620760509 |
69 | 126.6 | 135.306892493306 | -8.70689249330616 |
70 | 126.5 | 124.849835511515 | 1.65016448848509 |
71 | 141.4 | 140.04766311641 | 1.35233688358954 |
72 | 124.3 | 126.053479973353 | -1.75347997335339 |
73 | 124.9 | 115.508293700746 | 9.39170629925364 |
74 | 108.9 | 112.372600800479 | -3.47260080047873 |
75 | 126.7 | 123.562341312867 | 3.13765868713308 |
76 | 107.7 | 113.357500396483 | -5.65750039648297 |
77 | 121.8 | 125.153856399775 | -3.35385639977471 |
78 | 118.3 | 116.411184433191 | 1.88881556680887 |
79 | 122.8 | 100.589716017468 | 22.2102839825317 |
80 | 149.5 | 136.795936209635 | 12.7040637903651 |
81 | 147 | 148.689573475122 | -1.68957347512176 |
82 | 139.3 | 145.99850723732 | -6.69850723732011 |
83 | 162.1 | 161.325666058821 | 0.774333941179265 |
84 | 142.2 | 143.165877883393 | -0.965877883392778 |
85 | 141.4 | 139.02279915057 | 2.37720084943001 |
86 | 124.7 | 124.864928135823 | -0.164928135823189 |
87 | 114 | 143.170115879426 | -29.1701158794258 |
88 | 126.6 | 118.590286921694 | 8.00971307830588 |
89 | 121.9 | 136.628867189686 | -14.7288671896856 |
90 | 125.1 | 127.843674456522 | -2.7436744565224 |
91 | 122.1 | 121.985461586875 | 0.114538413125246 |
92 | 135.9 | 147.364252207196 | -11.4642522071958 |
93 | 148.4 | 144.42242866009 | 3.97757133991038 |
94 | 137.5 | 139.721582528843 | -2.22158252884333 |
95 | 145.3 | 160.004715605443 | -14.7047156054434 |
96 | 139.9 | 137.327183895329 | 2.57281610467101 |
97 | 128.2 | 135.68006196386 | -7.48006196386035 |
98 | 115.4 | 118.06081079513 | -2.66081079512979 |
99 | 124.7 | 117.075888338417 | 7.62411166158346 |
100 | 111.5 | 123.266342255578 | -11.7663422555776 |
101 | 121.1 | 122.295704578738 | -1.1957045787378 |
102 | 122.5 | 123.608740001927 | -1.10874000192676 |
103 | 127.4 | 119.66695035705 | 7.73304964294964 |
104 | 143.7 | 139.486618516595 | 4.21338148340496 |
105 | 157.8 | 149.575133025594 | 8.22486697440613 |
106 | 148.8 | 141.838162915263 | 6.96183708473666 |
107 | 162.9 | 157.143153892183 | 5.75684610781713 |
108 | 153.9 | 149.151505063144 | 4.74849493685602 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 141.406617179124 | 129.050372233495 | 153.762862124753 |
110 | 127.400448551296 | 114.621471934327 | 140.179425168265 |
111 | 133.89525133318 | 120.496490331273 | 147.294012335088 |
112 | 125.967364911902 | 112.207592956421 | 139.727136867383 |
113 | 135.248587930581 | 120.678153390128 | 149.819022471035 |
114 | 137.307558410042 | 122.113058613373 | 152.502058206711 |
115 | 139.273724885247 | 123.437805739424 | 155.109644031071 |
116 | 156.957822687201 | 139.630152314849 | 174.285493059552 |
117 | 169.65855869907 | 150.976538992097 | 188.340578406043 |
118 | 158.359978394713 | 139.825673108269 | 176.894283681157 |
119 | 172.225506261968 | 152.108321390685 | 192.342691133252 |
120 | 161.598571755364 | 134.580639386293 | 188.616504124436 |