Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.571865347172465 |
beta | 0 |
gamma | 0.440257094572627 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 43 | 42.8811431623932 | 0.118856837606820 |
14 | 55 | 54.8394104718922 | 0.160589528107792 |
15 | 68 | 67.821543260933 | 0.178456739066945 |
16 | 68 | 67.7305603554387 | 0.269439644561288 |
17 | 64 | 63.774940754115 | 0.225059245885021 |
18 | 65 | 64.7939415406946 | 0.20605845930541 |
19 | 57 | 55.468743102527 | 1.53125689747303 |
20 | 59 | 58.0263797292745 | 0.973620270725512 |
21 | 54 | 55.0567899595376 | -1.05678995953762 |
22 | 57 | 54.9260789385688 | 2.0739210614312 |
23 | 43 | 47.2940463958363 | -4.29404639583629 |
24 | 42 | 38.5620605990372 | 3.43793940096275 |
25 | 52 | 46.2741327885578 | 5.72586721144224 |
26 | 51 | 61.4467211984748 | -10.4467211984748 |
27 | 58 | 68.3662683347066 | -10.3662683347066 |
28 | 60 | 62.2622718698977 | -2.26227186989774 |
29 | 61 | 56.8504889533232 | 4.14951104667676 |
30 | 58 | 60.1101662861139 | -2.11016628611392 |
31 | 62 | 49.7101849300527 | 12.2898150699473 |
32 | 61 | 58.3151596135205 | 2.68484038647953 |
33 | 49 | 55.9414466891155 | -6.94144668911549 |
34 | 51 | 53.0356099907569 | -2.03560999075687 |
35 | 47 | 41.853185200919 | 5.146814799081 |
36 | 40 | 39.9774975012094 | 0.0225024987906295 |
37 | 45 | 46.1676496343313 | -1.16764963433133 |
38 | 50 | 54.3497144748269 | -4.34971447482686 |
39 | 58 | 64.7710929832406 | -6.7710929832406 |
40 | 52 | 62.250569488423 | -10.2505694884230 |
41 | 50 | 53.4791085722009 | -3.4791085722009 |
42 | 50 | 51.1963603847112 | -1.19636038471117 |
43 | 46 | 44.0331956276124 | 1.96680437238761 |
44 | 46 | 44.9243630838981 | 1.07563691610189 |
45 | 38 | 39.8159501692132 | -1.81595016921322 |
46 | 37 | 40.7659051327993 | -3.76590513279933 |
47 | 34 | 29.9477948635093 | 4.05220513649071 |
48 | 29 | 26.4802596966426 | 2.5197403033574 |
49 | 30 | 33.8741646295526 | -3.87416462955262 |
50 | 40 | 39.9086820999807 | 0.0913179000193196 |
51 | 46 | 52.4133291447466 | -6.41332914474664 |
52 | 46 | 49.4415542369943 | -3.44155423699426 |
53 | 47 | 45.8402812436958 | 1.15971875630424 |
54 | 47 | 46.6405913066959 | 0.359408693304104 |
55 | 43 | 40.9633397423783 | 2.03666025762174 |
56 | 46 | 41.7264798123636 | 4.2735201876364 |
57 | 37 | 37.9017922463409 | -0.901792246340868 |
58 | 41 | 39.0069767659813 | 1.99302323401865 |
59 | 39 | 32.9558283418862 | 6.04417165811379 |
60 | 36 | 30.3385765496866 | 5.66142345031345 |
61 | 48 | 38.3239184238033 | 9.67608157619665 |
62 | 55 | 52.8548032438416 | 2.14519675615836 |
63 | 56 | 65.3079359462154 | -9.3079359462154 |
64 | 53 | 61.2409835416346 | -8.2409835416346 |
65 | 52 | 55.76237405281 | -3.76237405281 |
66 | 53 | 53.5970599044756 | -0.597059904475628 |
67 | 52 | 47.6889810974716 | 4.31101890252843 |
68 | 56 | 50.1743722669510 | 5.82562773304895 |
69 | 51 | 46.2617901083592 | 4.73820989164075 |
70 | 48 | 51.1379382053022 | -3.13793820530225 |
71 | 42 | 42.916168941332 | -0.916168941332018 |
72 | 42 | 36.2463956070077 | 5.75360439299234 |
73 | 44 | 45.0411727414269 | -1.04117274142691 |
74 | 50 | 52.0237398541579 | -2.02373985415791 |
75 | 60 | 59.9340089986085 | 0.0659910013915308 |
76 | 66 | 61.4287897137306 | 4.57121028626941 |
77 | 58 | 64.1211999459995 | -6.12119994599954 |
78 | 59 | 61.2035829154875 | -2.20358291548752 |
79 | 55 | 55.3019096977404 | -0.301909697740356 |
80 | 57 | 55.4348144377615 | 1.56518556223854 |
81 | 57 | 48.8808663903735 | 8.11913360962652 |
82 | 56 | 54.2058778171306 | 1.79412218286937 |
83 | 53 | 49.2233627533916 | 3.7766372466084 |
84 | 51 | 46.4944236882140 | 4.50557631178595 |
85 | 45 | 53.2947539003563 | -8.29475390035628 |
86 | 58 | 55.9440459000908 | 2.05595409990919 |
87 | 74 | 66.5812425884173 | 7.41875741158266 |
88 | 65 | 73.130001331359 | -8.13000133135901 |
89 | 65 | 66.543623656313 | -1.54362365631302 |
90 | 55 | 66.9821928435083 | -11.9821928435083 |
91 | 52 | 55.8469165529275 | -3.84691655292746 |
92 | 59 | 54.3044822298070 | 4.69551777019305 |
93 | 54 | 50.7760118971721 | 3.22398810282793 |
94 | 57 | 52.1094621469038 | 4.89053785309622 |
95 | 45 | 49.2713628183717 | -4.27136281837166 |
96 | 40 | 42.0774486294968 | -2.07744862949677 |
97 | 47 | 42.7004494819375 | 4.29955051806253 |
98 | 47 | 54.5029856456102 | -7.5029856456102 |
99 | 60 | 60.6845870783719 | -0.684587078371891 |
100 | 58 | 59.6685489748219 | -1.66854897482192 |
101 | 63 | 58.0187138331827 | 4.98128616681734 |
102 | 64 | 60.221094051115 | 3.77890594888495 |
103 | 64 | 59.6324566757825 | 4.36754332421751 |
104 | 63 | 64.3977449246665 | -1.39774492466651 |
105 | 55 | 57.1073811817044 | -2.10738118170443 |
106 | 54 | 55.7061329110397 | -1.70613291103971 |
107 | 44 | 47.3687057535314 | -3.36870575353143 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
108 | 41.1045192503759 | 31.8486925493829 | 50.360345951369 |
109 | 44.1175372069331 | 33.4551222299326 | 54.7799521839336 |
110 | 51.236657424738 | 39.3327144492062 | 63.1406004002699 |
111 | 62.9941516466638 | 49.9664648378837 | 76.0218384554439 |
112 | 62.1841388632226 | 48.1222261622203 | 76.246051564225 |
113 | 62.7419119532632 | 47.7167945150014 | 77.7670293915251 |
114 | 61.86903140038 | 45.9388424731729 | 77.799220327587 |
115 | 59.230320520282 | 42.4437876894840 | 76.01685335108 |
116 | 60.4112668377074 | 42.8100041073688 | 78.0125295680461 |
117 | 53.7864661269901 | 35.4065527723152 | 72.166379481665 |
118 | 53.6659871404481 | 34.5390955961248 | 72.7928786847714 |
119 | 45.9908610506625 | 26.1450870579140 | 65.836635043411 |