Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.859571451160984 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 23 | 20 | 3 |
3 | 27 | 22.578714353483 | 4.42128564651705 |
4 | 23 | 26.3791252726568 | -3.37912527265684 |
5 | 21 | 23.4745256583844 | -2.47452565838444 |
6 | 18 | 21.3474940472718 | -3.34749404727184 |
7 | 16 | 18.4700837313056 | -2.47008373130563 |
8 | 11 | 16.3468702738981 | -5.34687027389811 |
9 | 14 | 11.750853233394 | 2.24914676660602 |
10 | -3 | 13.6841555834396 | -16.6841555834396 |
11 | 2 | -0.657068242813222 | 2.65706824281322 |
12 | 26 | 1.62687176249551 | 24.3731282375045 |
13 | 11 | 22.57731697094 | -11.57731697094 |
14 | 11 | 12.6257858216784 | -1.62578582167841 |
15 | 11 | 11.2283067436613 | -0.228306743661348 |
16 | 3 | 11.0320607847025 | -8.03206078470252 |
17 | 8 | 4.12793064018254 | 3.87206935981746 |
18 | 8 | 7.45625091879682 | 0.543749081203182 |
19 | 7 | 7.92364210559409 | -0.923642105594089 |
20 | 3 | 7.12970572053519 | -4.12970572053519 |
21 | 4 | 3.57992858146694 | 0.420071418533062 |
22 | -7 | 3.94100998028666 | -10.9410099802867 |
23 | 0 | -5.46356984563516 | 5.46356984563516 |
24 | -5 | -0.76724118490315 | -4.23275881509685 |
25 | 5 | -4.4055998220104 | 9.4055998220104 |
26 | -1 | 3.67918526603458 | -4.67918526603458 |
27 | -4 | -0.342908803341861 | -3.65709119665814 |
28 | 4 | -3.48643999028136 | 7.48643999028136 |
29 | 7 | 2.94869009619441 | 4.05130990380559 |
30 | 6 | 6.43108042931145 | -0.43108042931145 |
31 | 13 | 6.06053599912111 | 6.93946400087889 |
32 | 20 | 12.025501140636 | 7.97449885936401 |
33 | 21 | 18.8801526974611 | 2.11984730253887 |
34 | 37 | 20.7023129195442 | 16.2976870804558 |
35 | 52 | 34.7113394538592 | 17.2886605461408 |
36 | 59 | 49.5721784881351 | 9.42782151186489 |
37 | 66 | 57.6760647063756 | 8.32393529362444 |
38 | 73 | 64.8310818460864 | 8.16891815391355 |
39 | 71 | 71.8528506780612 | -0.85285067806123 |
40 | 69 | 71.1197645830965 | -2.11976458309651 |
41 | 63 | 69.2976754642846 | -6.29767546428458 |
42 | 68 | 63.8843734265086 | 4.11562657349144 |
43 | 58 | 67.4220485327213 | -9.42204853272131 |
44 | 50 | 59.3231246025408 | -9.32312460254083 |
45 | 50 | 51.3092328585801 | -1.30923285858013 |
46 | 50 | 50.1838536704228 | -0.183853670422764 |
47 | 47 | 50.0258183041362 | -3.02581830413619 |
48 | 60 | 47.4249112735004 | 12.5750887264996 |
49 | 62 | 58.2340985386158 | 3.76590146138421 |
50 | 63 | 61.4711599227071 | 1.52884007729291 |
51 | 56 | 62.7853072065388 | -6.78530720653883 |
52 | 38 | 56.9528508444412 | -18.9528508444412 |
53 | 45 | 40.6615213404472 | 4.33847865955281 |
54 | 39 | 44.39075373767 | -5.39075373766996 |
55 | 26 | 39.7570157245295 | -13.7570157245295 |
56 | 25 | 27.9318777545512 | -2.93187775455119 |
57 | 19 | 25.411719338445 | -6.41171933844502 |
58 | 14 | 19.9003884422609 | -5.90038844226089 |
59 | 6 | 14.8285829865332 | -8.8285829865332 |
60 | 4 | 7.23978509710368 | -3.23978509710368 |
61 | 5 | 4.45495831973654 | 0.545041680263461 |
62 | -3 | 4.92346058778382 | -7.92346058778382 |
63 | -5 | -1.88731992787438 | -3.11268007212562 |
64 | 0 | -4.56289085447128 | 4.56289085447128 |
65 | -6 | -0.640760141204218 | -5.35923985879578 |
66 | 4 | -5.2474097237491 | 9.2474097237491 |
67 | -3 | 2.70139967197411 | -5.70139967197411 |
68 | 14 | -2.19936071771344 | 16.1993607177134 |
69 | 16 | 11.7251472822917 | 4.27485271770825 |
70 | 17 | 15.3996886363517 | 1.60031136364829 |
71 | 25 | 16.7752705975123 | 8.22472940248771 |
72 | 25 | 23.8450131854151 | 1.15498681458493 |
73 | 30 | 24.8378068776996 | 5.16219312230036 |
74 | 51 | 29.2750807110086 | 21.7249192889914 |
75 | 31 | 47.9492011106022 | -16.9492011106022 |
76 | 31 | 33.3801517159425 | -2.3801517159425 |
77 | 25 | 31.3342412514865 | -6.3342412514865 |
78 | 35 | 25.8895083069425 | 9.11049169305752 |
79 | 39 | 33.720626872334 | 5.27937312766597 |
80 | 48 | 38.2586252929022 | 9.74137470709783 |
81 | 41 | 46.6320328861852 | -5.63203288618516 |
82 | 47 | 41.7908982052206 | 5.20910179477941 |
83 | 61 | 46.2684933942044 | 14.7315066057956 |
84 | 55 | 58.9312759051358 | -3.93127590513576 |
85 | 63 | 55.552063370444 | 7.447936629556 |
86 | 45 | 61.9540970672665 | -16.9540970672665 |
87 | 62 | 47.380839248032 | 14.619160751968 |
88 | 55 | 59.9470524703568 | -4.94705247035684 |
89 | 50 | 55.6947073994427 | -5.69470739944268 |
90 | 52 | 50.7996994961665 | 1.20030050383346 |
91 | 45 | 51.8314435420759 | -6.83144354207593 |
92 | 36 | 45.9593297030894 | -9.95932970308939 |
93 | 40 | 37.3985742176141 | 2.60142578238585 |
94 | 32 | 39.6346855524672 | -7.63468555246715 |
95 | 29 | 33.0721278129752 | -4.07212781297516 |
96 | 24 | 29.5718429994631 | -5.57184299946309 |
97 | 28 | 24.7824458267734 | 3.21755417322657 |
98 | 27 | 27.5481635366429 | -0.548163536642875 |
99 | 33 | 27.0769778099772 | 5.92302219002278 |
100 | 33 | 32.1682385891138 | 0.831761410886187 |
101 | 24 | 32.883196952089 | -8.88319695208896 |
102 | 26 | 25.247454457033 | 0.752545542966981 |
103 | 38 | 25.8943211214659 | 12.1056788785341 |
104 | 32 | 36.3000170823763 | -4.30001708237633 |
105 | 30 | 32.6038451588611 | -2.60384515886108 |
106 | 26 | 30.3656541970604 | -4.36565419706036 |
107 | 21 | 26.6130624836261 | -5.61306248362614 |
108 | 21 | 21.7882342191183 | -0.78823421911834 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
109 | 21.110690587536 | 5.34016085114357 | 36.8812203239285 |
110 | 21.110690587536 | 0.314730518448382 | 41.9066506566237 |
111 | 21.110690587536 | -3.71337640850104 | 45.9347575835731 |
112 | 21.110690587536 | -7.17352142645484 | 49.3949026015269 |
113 | 21.110690587536 | -10.2542420009621 | 52.4756231760342 |
114 | 21.110690587536 | -13.0583208601147 | 55.2797020351867 |
115 | 21.110690587536 | -15.6491202163614 | 57.8705013914335 |
116 | 21.110690587536 | -18.0689729812975 | 60.2903541563696 |
117 | 21.110690587536 | -20.347823428232 | 62.569204603304 |
118 | 21.110690587536 | -22.5077771918837 | 64.7291583669558 |
119 | 21.110690587536 | -24.5657046123145 | 66.7870857873866 |
120 | 21.110690587536 | -26.5348278321598 | 68.7562090072319 |