Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.632771665684048 |
beta | -6.91178884959509e-18 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 97 | 97.7 | -0.700000000000003 |
4 | 96.5 | 97.2570598340212 | -0.757059834021163 |
5 | 98.4 | 96.7780138218251 | 1.62198617817491 |
6 | 106.3 | 97.8043607175053 | 8.49563928249466 |
7 | 103.1 | 103.180160537340 | -0.0801605373403191 |
8 | 102.4 | 103.129437220605 | -0.729437220605348 |
9 | 95 | 102.667870015511 | -7.66787001551097 |
10 | 98.1 | 97.8158591335473 | 0.284140866452660 |
11 | 106.1 | 97.9956554229015 | 8.1043445770985 |
12 | 99.1 | 103.123855040230 | -4.02385504022959 |
13 | 101.2 | 100.577673583952 | 0.622326416047642 |
14 | 95.5 | 100.971464106834 | -5.47146410683401 |
15 | 99.8 | 97.5092766502222 | 2.29072334977782 |
16 | 97.1 | 98.9587814798824 | -1.85878147988244 |
17 | 97.5 | 97.7825972267146 | -0.282597226714557 |
18 | 96.8 | 97.6037777088487 | -0.803777708848699 |
19 | 97.7 | 97.0951699491808 | 0.604830050819203 |
20 | 100.9 | 97.4778892678934 | 3.42211073210657 |
21 | 94.3 | 99.6433039760038 | -5.34330397600377 |
22 | 99.5 | 96.2622126188517 | 3.23778738114834 |
23 | 100.8 | 98.3109927331517 | 2.48900726684830 |
24 | 97 | 99.885966007295 | -2.88596600729500 |
25 | 99.2 | 98.0598084897514 | 1.14019151024860 |
26 | 101 | 98.7812893708902 | 2.21871062910978 |
27 | 102.3 | 100.185226591343 | 2.11477340865709 |
28 | 97 | 101.523395283683 | -4.52339528368319 |
29 | 91.2 | 98.6611189154796 | -7.4611189154796 |
30 | 97.6 | 93.9399342714648 | 3.66006572853517 |
31 | 95.7 | 96.2559201590231 | -0.555920159023117 |
32 | 100.5 | 95.9041496340107 | 4.59585036598928 |
33 | 94.4 | 98.8122735253324 | -4.41227352533240 |
34 | 102.9 | 96.0203118572542 | 6.8796881427458 |
35 | 105.1 | 100.373583582726 | 4.72641641727374 |
36 | 98.8 | 103.364325971801 | -4.564325971801 |
37 | 100.7 | 100.476149823900 | 0.223850176100484 |
38 | 99.6 | 100.617795872694 | -1.01779587269429 |
39 | 107.7 | 99.9737634830032 | 7.72623651699683 |
40 | 102.9 | 104.862707033332 | -1.96270703333217 |
41 | 101.6 | 103.620761634601 | -2.02076163460079 |
42 | 102.7 | 102.342080929124 | 0.357919070875980 |
43 | 110.5 | 102.568561975782 | 7.9314380242177 |
44 | 109.8 | 107.587351225636 | 2.21264877436367 |
45 | 94.3 | 108.987452676164 | -14.6874526761642 |
46 | 102.5 | 99.6936487816122 | 2.80635121838785 |
47 | 105 | 101.469428316566 | 3.53057168343412 |
48 | 102.3 | 103.703474041509 | -1.40347404150943 |
49 | 107.7 | 102.815395434519 | 4.88460456548083 |
50 | 100.3 | 105.906234801626 | -5.60623480162639 |
51 | 99.5 | 102.358768267985 | -2.85876826798538 |
52 | 95 | 100.549820709248 | -5.54982070924757 |
53 | 97.7 | 97.0380514148092 | 0.661948585190842 |
54 | 96.3 | 97.4569137236576 | -1.15691372365757 |
55 | 97.8 | 96.724851499686 | 1.07514850031397 |
56 | 106.4 | 97.4051750070874 | 8.9948249929126 |
57 | 96.1 | 103.096845400389 | -6.99684540038922 |
58 | 106.2 | 98.6694398818512 | 7.53056011814884 |
59 | 114.7 | 103.434564951346 | 11.2654350486539 |
60 | 111.9 | 110.563013051738 | 1.33698694826174 |
61 | 121 | 111.409020509988 | 9.59097949001232 |
62 | 117.7 | 117.477920577424 | 0.222079422575689 |
63 | 115.4 | 117.618446143562 | -2.21844614356168 |
64 | 114.3 | 116.214676282070 | -1.91467628206981 |
65 | 109.5 | 115.003123381819 | -5.50312338181875 |
66 | 108.1 | 111.520902833040 | -3.42090283304047 |
67 | 108.2 | 109.356252449234 | -1.15625244923416 |
68 | 99.1 | 108.624608660981 | -9.524608660981 |
69 | 101.2 | 102.597706173583 | -1.39770617358333 |
70 | 98.1 | 101.713277309988 | -3.61327730998813 |
71 | 95.5 | 99.4268978079686 | -3.92689780796856 |
72 | 97.9 | 96.9420681410493 | 0.957931858950744 |
73 | 98.2 | 97.5482202790493 | 0.651779720950657 |
74 | 98.7 | 97.9606480187344 | 0.739351981265628 |
75 | 95.6 | 98.4284890034466 | -2.82848900344663 |
76 | 95.8 | 96.6387013053667 | -0.838701305366698 |
77 | 94.4 | 96.1079948833584 | -1.70799488335842 |
78 | 96.5 | 95.0272241160359 | 1.47277588396412 |
79 | 103.3 | 95.9591549653112 | 7.34084503468884 |
80 | 104.3 | 100.604233705440 | 3.69576629456031 |
81 | 104.5 | 102.942809899628 | 1.55719010037242 |
82 | 102.3 | 103.928155673227 | -1.62815567322694 |
83 | 103.8 | 102.897904895886 | 0.902095104113798 |
84 | 103.1 | 103.468725117522 | -0.36872511752172 |
85 | 102.2 | 103.235406310728 | -1.03540631072795 |
86 | 106.3 | 102.580230534829 | 3.71976946517114 |
87 | 102.1 | 104.933995255266 | -2.83399525526586 |
88 | 94 | 103.140723357051 | -9.14072335705059 |
89 | 102.6 | 97.3567326128526 | 5.24326738714738 |
90 | 102.6 | 100.674523651045 | 1.92547634895529 |
91 | 106.7 | 101.892910527608 | 4.80708947239162 |
92 | 107.9 | 104.934700540146 | 2.96529945985412 |
93 | 109.3 | 106.811058018610 | 2.48894198139021 |
94 | 105.9 | 108.385989981965 | -2.48598998196502 |
95 | 109.1 | 106.812925960203 | 2.28707403979683 |
96 | 108.5 | 108.260121609908 | 0.239878390091846 |
97 | 111.7 | 108.411909858368 | 3.28809014163183 |
98 | 109.8 | 110.492520134208 | -0.692520134207854 |
99 | 109.1 | 110.054313015365 | -0.954313015365415 |
100 | 108.5 | 109.450450779049 | -0.950450779048666 |
101 | 108.5 | 108.849032456439 | -0.349032456439346 |
102 | 106.2 | 108.628174607600 | -2.42817460760043 |
103 | 117.1 | 107.091694516577 | 10.0083054834226 |
104 | 109.8 | 113.424666647997 | -3.6246666479975 |
105 | 115.2 | 111.131080295595 | 4.0689197044053 |
106 | 115.9 | 113.705777394486 | 2.19422260551411 |
107 | 119.2 | 115.094219287459 | 4.10578071254136 |
108 | 121 | 117.692240987867 | 3.30775901213312 |
109 | 118.6 | 119.785297167656 | -1.18529716765578 |
110 | 117.6 | 119.035274704548 | -1.43527470454765 |
111 | 114.6 | 118.127073539037 | -3.52707353903685 |
112 | 110.6 | 115.895241340750 | -5.29524134075037 |
113 | 102.5 | 112.544562657365 | -10.0445626573647 |
114 | 101.6 | 106.188648013596 | -4.58864801359627 |
115 | 107.4 | 103.285081566795 | 4.11491843320485 |
116 | 105.8 | 105.888885357928 | -0.0888853579281772 |
117 | 102.8 | 105.832641221937 | -3.03264122193704 |
118 | 104 | 103.913671784510 | 0.0863282154901697 |
119 | 100.4 | 103.968297833221 | -3.56829783322107 |
120 | 100.6 | 101.710380069637 | -1.11038006963700 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 101.007763023430 | 92.3740976712982 | 109.641428375563 |
122 | 101.007763023430 | 90.790813232796 | 111.224712814065 |
123 | 101.007763023430 | 89.4219117972113 | 112.593614249650 |
124 | 101.007763023430 | 88.1984759922245 | 113.817050054636 |
125 | 101.007763023430 | 87.0821133129301 | 114.933412733931 |
126 | 101.007763023430 | 86.0488323975035 | 115.966693649357 |
127 | 101.007763023430 | 85.082453259315 | 116.933072787546 |
128 | 101.007763023430 | 84.1714517678505 | 117.844074279010 |
129 | 101.007763023430 | 83.3072753943704 | 118.708250652490 |
130 | 101.007763023430 | 82.4833697022379 | 119.532156344623 |
131 | 101.007763023430 | 81.694580128579 | 120.320945918282 |
132 | 101.007763023430 | 80.936766059111 | 121.078759987750 |