Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.999933893038648 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 100.1 | 98.6 | 1.5 |
3 | 98.8 | 100.099900839558 | -1.29990083955796 |
4 | 98.3 | 98.8000859324946 | -0.500085932494557 |
5 | 102.8 | 98.3000330591614 | 4.49996694083859 |
6 | 103.6 | 102.799702520859 | 0.800297479140639 |
7 | 105.2 | 103.599947094765 | 1.60005290523453 |
8 | 100.1 | 105.199894225364 | -5.09989422536444 |
9 | 98.2 | 100.100337138510 | -1.90033713851045 |
10 | 98.4 | 98.2001256255138 | 0.199874374486228 |
11 | 97.4 | 98.3999867869125 | -0.999986786912444 |
12 | 98.4 | 97.4000661060879 | 0.999933893912129 |
13 | 100.3 | 98.3999338974087 | 1.90006610259127 |
14 | 101.1 | 100.299874392404 | 0.800125607596414 |
15 | 104.1 | 101.099947106127 | 3.00005289387262 |
16 | 107.3 | 104.099801675619 | 3.20019832438071 |
17 | 110.1 | 107.299788444613 | 2.80021155538695 |
18 | 112.6 | 110.099814886523 | 2.50018511347707 |
19 | 114.3 | 112.599834720359 | 1.70016527964067 |
20 | 115.3 | 114.299887607240 | 1.00011239276043 |
21 | 109.9 | 115.299933885609 | -5.39993388560869 |
22 | 108.2 | 109.900356973221 | -1.70035697322068 |
23 | 103.2 | 108.200112405433 | -5.00011240543272 |
24 | 101.8 | 103.200330542238 | -1.40033054223754 |
25 | 105.6 | 101.800092571597 | 3.79990742840296 |
26 | 108.2 | 105.599748799666 | 2.60025120033352 |
27 | 109.8 | 108.199828105294 | 1.60017189470560 |
28 | 114.6 | 109.799894217498 | 4.8001057825016 |
29 | 117.2 | 114.599682679593 | 2.60031732040746 |
30 | 116.5 | 117.199828100923 | -0.699828100923398 |
31 | 116.1 | 116.500046263509 | -0.400046263509225 |
32 | 112.1 | 116.100026445843 | -4.00002644584288 |
33 | 106.8 | 112.100264429594 | -5.30026442959365 |
34 | 106.9 | 106.800350384376 | 0.0996496156242017 |
35 | 104.5 | 106.899993412467 | -2.39999341246671 |
36 | 103 | 104.500158656272 | -1.50015865627176 |
37 | 105.9 | 103.000099170930 | 2.89990082906969 |
38 | 107.7 | 105.899808296368 | 1.80019170363202 |
39 | 107.1 | 107.699880994797 | -0.599880994796635 |
40 | 112.5 | 107.100039656310 | 5.39996034369027 |
41 | 114.5 | 112.499643025030 | 2.00035697496975 |
42 | 114.6 | 114.499867762479 | 0.100132237521223 |
43 | 113.1 | 114.599993380562 | -1.49999338056205 |
44 | 112.8 | 113.100099160004 | -0.300099160004436 |
45 | 111.9 | 112.800019838644 | -0.900019838643559 |
46 | 112 | 111.900059497577 | 0.0999405024233084 |
47 | 112.4 | 111.999993393237 | 0.400006606762943 |
48 | 110 | 112.399973556779 | -2.39997355677872 |
49 | 112.3 | 110.000158654959 | 2.29984134504083 |
50 | 109.6 | 112.299847964477 | -2.69984796447709 |
51 | 111.9 | 109.600178478745 | 2.29982152125497 |
52 | 110.8 | 111.899847965788 | -1.09984796578759 |
53 | 110.4 | 110.800072707607 | -0.400072707606952 |
54 | 110.8 | 110.400026447591 | 0.399973552408966 |
55 | 114 | 110.799973558964 | 3.20002644103617 |
56 | 108.4 | 113.999788455976 | -5.59978845597573 |
57 | 110.5 | 108.400370184999 | 2.09962981500095 |
58 | 105.1 | 110.499861199853 | -5.39986119985298 |
59 | 102.3 | 105.100356968416 | -2.80035696841564 |
60 | 104.3 | 102.300185123090 | 1.99981487691012 |
61 | 103.4 | 104.299867798315 | -0.899867798315213 |
62 | 102.4 | 103.400059487526 | -1.00005948752576 |
63 | 104.5 | 102.400066110894 | 2.09993388910610 |
64 | 107.3 | 104.499861179752 | 2.80013882024845 |
65 | 110.1 | 107.299814891331 | 2.80018510866877 |
66 | 111.8 | 110.099814888271 | 1.70018511172876 |
67 | 111.8 | 111.799887605929 | 0.000112394071479116 |
68 | 105.7 | 111.79999999257 | -6.09999999256996 |
69 | 106 | 105.700403252464 | 0.299596747536242 |
70 | 106.4 | 105.999980194569 | 0.400019805430617 |
71 | 107.1 | 106.399973555906 | 0.700026444093808 |
72 | 111.5 | 107.099953723379 | 4.4000462766211 |
73 | 109.6 | 111.499709126311 | -1.89970912631085 |
74 | 109.9 | 109.600125583998 | 0.299874416002226 |
75 | 109.3 | 109.899980176214 | -0.599980176213577 |
76 | 111.4 | 109.300039662866 | 2.09996033713369 |
77 | 112.9 | 111.399861178003 | 1.50013882199684 |
78 | 115.5 | 112.899900830381 | 2.60009916961913 |
79 | 118.4 | 115.499828115345 | 2.90017188465532 |
80 | 116.2 | 118.399808278449 | -2.19980827844931 |
81 | 113.3 | 116.200145422641 | -2.90014542264085 |
82 | 113.8 | 113.300191719801 | 0.499808280198636 |
83 | 114.1 | 113.799966959193 | 0.300033040806653 |
84 | 117.1 | 114.099980165727 | 3.00001983427263 |
85 | 115.5 | 117.099801677805 | -1.59980167780475 |
86 | 115.2 | 115.500105758028 | -0.300105758027684 |
87 | 114.2 | 115.200019839080 | -1.00001983907974 |
88 | 115.3 | 114.200066108273 | 1.09993389172715 |
89 | 118.8 | 115.299927286713 | 3.50007271328727 |
90 | 118 | 118.799768620828 | -0.799768620828416 |
91 | 118.1 | 118.000052870273 | 0.0999471297266865 |
92 | 111.8 | 118.099993392799 | -6.29999339279895 |
93 | 112 | 111.800416473420 | 0.199583526580270 |
94 | 114.3 | 111.999986806140 | 2.30001319386048 |
95 | 115 | 114.299847953117 | 0.700152046883318 |
96 | 118.5 | 114.999953715076 | 3.50004628492431 |
97 | 117.6 | 118.499768622576 | -0.899768622575522 |
98 | 119.1 | 117.600059480970 | 1.49994051903045 |
99 | 120.6 | 119.09990084349 | 1.50009915650992 |
100 | 123.6 | 120.599900833003 | 3.00009916699696 |
101 | 122.7 | 123.599801672560 | -0.8998016725603 |
102 | 123.8 | 122.700059483154 | 1.09994051684561 |
103 | 123.1 | 123.799927286275 | -0.699927286274772 |
104 | 124.5 | 123.100046270066 | 1.39995372993394 |
105 | 120.7 | 124.499907453313 | -3.79990745331288 |
106 | 118.7 | 120.700251200335 | -2.00025120033516 |
107 | 119 | 118.700132230529 | 0.299867769471206 |
108 | 122.3 | 118.999980176653 | 3.30001982334704 |
109 | 118.6 | 122.299781845717 | -3.69978184571708 |
110 | 118.1 | 118.600244581335 | -0.50024458133548 |
111 | 118.2 | 118.100033069649 | 0.0999669303508028 |
112 | 120.8 | 118.19999339149 | 2.60000660851 |
113 | 119.7 | 120.799828121464 | -1.09982812146362 |
114 | 119.7 | 119.700072706295 | -7.27062951142443e-05 |
115 | 117.1 | 119.700000004806 | -2.60000000480640 |
116 | 114.5 | 117.100171878100 | -2.60017187809983 |
117 | 116.5 | 114.500171889462 | 1.99982811053815 |
118 | 116.4 | 116.499867797440 | -0.0998677974403819 |
119 | 114.9 | 116.400006601957 | -1.50000660195663 |
120 | 115.5 | 114.900099160878 | 0.599900839121531 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 115.499960342378 | 110.656048602652 | 120.343872082105 |
122 | 115.499960342378 | 108.649861088484 | 122.350059596272 |
123 | 115.499960342378 | 107.110428851637 | 123.889491833120 |
124 | 115.499960342378 | 105.812617183386 | 125.187303501371 |
125 | 115.499960342378 | 104.669217231861 | 126.330703452896 |
126 | 115.499960342378 | 103.635501856128 | 127.364418828629 |
127 | 115.499960342378 | 102.684900685166 | 128.315019999591 |
128 | 115.499960342378 | 101.800101479461 | 129.199819205295 |
129 | 115.499960342378 | 100.969079030160 | 130.030841654597 |
130 | 115.499960342378 | 100.183077808529 | 130.816842876227 |
131 | 115.499960342378 | 99.4354880696372 | 131.564432615120 |
132 | 115.499960342378 | 98.7211746816814 | 132.278746003075 |