Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.840013960810943 |
beta | 0.212264917034862 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 101.4 | 104.4 | -3 |
4 | 101.5 | 105.045041636468 | -3.54504163646818 |
5 | 101.8 | 104.600140289904 | -2.80014028990354 |
6 | 101.5 | 104.281686077061 | -2.78168607706051 |
7 | 102.2 | 103.482743751354 | -1.28274375135366 |
8 | 101.8 | 103.714213647816 | -1.91421364781573 |
9 | 98.5 | 103.073925205897 | -4.5739252058974 |
10 | 98.4 | 99.3838859314774 | -0.983885931477374 |
11 | 97.5 | 98.5340975006736 | -1.03409750067355 |
12 | 97.7 | 97.4577453853595 | 0.242254614640473 |
13 | 98.3 | 97.4967421944844 | 0.803257805515642 |
14 | 99.6 | 98.1502147955844 | 1.44978520441560 |
15 | 99.4 | 99.605284104439 | -0.205284104438945 |
16 | 96.7 | 99.6334688041553 | -2.93346880415530 |
17 | 96.9 | 96.8468866650616 | 0.0531133349383737 |
18 | 96.1 | 96.5785456173235 | -0.478545617323505 |
19 | 97.9 | 95.7782763147406 | 2.12172368525943 |
20 | 99.2 | 97.5405845173899 | 1.6594154826101 |
21 | 97.8 | 99.210430272496 | -1.41043027249603 |
22 | 94.9 | 98.0500752697104 | -3.15007526971044 |
23 | 93.3 | 94.866718456253 | -1.56671845625304 |
24 | 91.5 | 92.7340489632144 | -1.23404896321439 |
25 | 89.1 | 90.6607887790286 | -1.56078877902863 |
26 | 92.3 | 88.0347653742005 | 4.26523462579949 |
27 | 91.8 | 91.0631977311374 | 0.736802268862618 |
28 | 92.1 | 91.2590735407788 | 0.840926459221194 |
29 | 94.4 | 91.6923569314561 | 2.7076430685439 |
30 | 92.8 | 94.1764959689413 | -1.37649596894133 |
31 | 92.6 | 92.9844644037283 | -0.384464403728316 |
32 | 92.3 | 92.5572010875426 | -0.25720108754264 |
33 | 92.1 | 92.1909803667577 | -0.0909803667576625 |
34 | 89.8 | 91.9481650727964 | -2.14816507279642 |
35 | 87.4 | 89.5942562719425 | -2.19425627194252 |
36 | 87.7 | 86.8103822724631 | 0.889617727536887 |
37 | 86.3 | 86.7756292140407 | -0.475629214040708 |
38 | 89.1 | 85.5092423629112 | 3.59075763708883 |
39 | 90.4 | 88.2989290500254 | 2.10107094997457 |
40 | 87.1 | 90.2118906157628 | -3.11189061576276 |
41 | 86.7 | 87.191024496527 | -0.491024496526919 |
42 | 84.4 | 86.2841701415937 | -1.88417014159373 |
43 | 88.4 | 83.8710961080504 | 4.52890389194957 |
44 | 88.9 | 87.65262223877 | 1.24737776122997 |
45 | 88.5 | 88.9000349144654 | -0.400034914465351 |
46 | 87.2 | 88.6922695204388 | -1.49226952043884 |
47 | 86.2 | 87.300931955339 | -1.10093195533895 |
48 | 83.4 | 86.0420211924863 | -2.64202119248627 |
49 | 87.5 | 83.0174870624831 | 4.48251293751686 |
50 | 85.7 | 86.7769177482957 | -1.07691774829574 |
51 | 87.4 | 85.6743286930812 | 1.72567130691880 |
52 | 86.8 | 87.2336502450063 | -0.433650245006334 |
53 | 87.9 | 86.9017893264056 | 0.998210673594443 |
54 | 85.9 | 87.9506980163406 | -2.05069801634055 |
55 | 87.7 | 86.0728301192598 | 1.62716988074017 |
56 | 87 | 87.5745559306639 | -0.574555930663905 |
57 | 86.8 | 87.1243548437356 | -0.324354843735634 |
58 | 86.2 | 86.826491912291 | -0.62649191229103 |
59 | 86.1 | 86.1631226754615 | -0.0631226754615142 |
60 | 87.5 | 85.9617363428484 | 1.53826365715162 |
61 | 85.7 | 87.3798177471108 | -1.67981774711079 |
62 | 88.9 | 85.7951451120427 | 3.10485488795734 |
63 | 89.8 | 88.7832769720049 | 1.01672302799513 |
64 | 91.4 | 90.1986362190472 | 1.20136378095282 |
65 | 95.2 | 91.9833060383843 | 3.21669396161570 |
66 | 94.1 | 96.0344355500285 | -1.93443555002848 |
67 | 96.8 | 95.4136238721683 | 1.38637612783172 |
68 | 96.1 | 97.8295388448611 | -1.72953884486112 |
69 | 96.6 | 97.3196554621864 | -0.719655462186424 |
70 | 94.2 | 97.5297696972706 | -3.32976969727063 |
71 | 93.9 | 94.9536353057947 | -1.05363530579473 |
72 | 96.5 | 94.1016166164614 | 2.3983833835386 |
73 | 93.4 | 96.5769867524313 | -3.17698675243125 |
74 | 95 | 93.8024939461285 | 1.19750605387151 |
75 | 95.2 | 94.916158076731 | 0.283841923269023 |
76 | 94 | 95.3129421563963 | -1.31294215639633 |
77 | 97 | 94.1343005173468 | 2.86569948265321 |
78 | 96.9 | 96.9767461533741 | -0.076746153374117 |
79 | 96.3 | 97.3338121154443 | -1.03381211544435 |
80 | 96.3 | 96.7025949283216 | -0.402594928321633 |
81 | 97.3 | 96.5298241032304 | 0.770175896769558 |
82 | 95.7 | 97.4795237375567 | -1.77952373755669 |
83 | 96.4 | 95.970141224599 | 0.429858775400987 |
84 | 95.1 | 96.3933170484664 | -1.29331704846638 |
85 | 94.6 | 95.1383955885162 | -0.538395588516252 |
86 | 95.9 | 94.421619803024 | 1.47838019697609 |
87 | 96.2 | 95.6625671440682 | 0.537432855931783 |
88 | 94.3 | 96.2089328129547 | -1.90893281295470 |
89 | 98.3 | 94.3599439590746 | 3.94005604092544 |
90 | 95.9 | 98.1267210366629 | -2.22672103666287 |
91 | 92.1 | 96.3162826820945 | -4.21628268209452 |
92 | 94.6 | 92.0827984042614 | 2.51720159573861 |
93 | 94.7 | 93.9543657979788 | 0.745634202021193 |
94 | 96.7 | 94.4707425229669 | 2.22925747703312 |
95 | 97.5 | 96.630872366575 | 0.86912763342491 |
96 | 96.2 | 97.8034443848026 | -1.60344438480264 |
97 | 97.1 | 96.6131184459564 | 0.48688155404362 |
98 | 95.9 | 97.2655091342532 | -1.36550913425320 |
99 | 94.5 | 96.1183880031701 | -1.61838800317011 |
100 | 99.4 | 94.4702776198999 | 4.92972238010013 |
101 | 101.3 | 99.2016679582938 | 2.09833204170624 |
102 | 101.4 | 101.928795014574 | -0.528795014573788 |
103 | 100.9 | 102.354811610615 | -1.45481161061495 |
104 | 101.4 | 101.743560435568 | -0.343560435568207 |
105 | 103.1 | 102.004517048449 | 1.09548295155136 |
106 | 102.4 | 103.669620825238 | -1.26962082523809 |
107 | 101.1 | 103.121624042702 | -2.02162404270229 |
108 | 102 | 101.581467385913 | 0.41853261408734 |
109 | 103.9 | 102.165703051776 | 1.73429694822367 |
110 | 101.7 | 104.164433801026 | -2.46443380102647 |
111 | 101.2 | 102.196750017638 | -0.99675001763815 |
112 | 101.9 | 101.284215098362 | 0.615784901638278 |
113 | 101.1 | 101.836029854472 | -0.736029854472065 |
114 | 103.1 | 101.121063176440 | 1.97893682355986 |
115 | 103.3 | 103.039561718417 | 0.260438281583177 |
116 | 101.4 | 103.560935069876 | -2.16093506987580 |
117 | 102.8 | 101.663014407287 | 1.13698559271344 |
118 | 103 | 102.738123920357 | 0.261876079642676 |
119 | 102.6 | 103.124823168879 | -0.524823168878996 |
120 | 102.2 | 102.757105211451 | -0.557105211450988 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 102.262934967809 | 98.4513573182622 | 106.074512617355 |
122 | 102.236740879426 | 96.7967575475938 | 107.676724211257 |
123 | 102.210546791043 | 95.1115043664934 | 109.309589215592 |
124 | 102.184352702660 | 93.3604726500812 | 111.008232755238 |
125 | 102.158158614277 | 91.532220204904 | 112.784097023649 |
126 | 102.131964525893 | 89.6231952835992 | 114.640733768188 |
127 | 102.105770437510 | 87.6330076489895 | 116.578533226031 |
128 | 102.079576349127 | 85.5626452683782 | 118.596507429877 |
129 | 102.053382260744 | 83.4137058242774 | 120.693058697211 |
130 | 102.027188172361 | 81.1880370466166 | 122.866339298106 |
131 | 102.000994083978 | 78.8875599124513 | 125.114428255505 |
132 | 101.974799995595 | 76.514179868529 | 127.435420122662 |