Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.988821404765565 |
beta | 0.0840238422818096 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 96.4 | 96.26 | 0.140000000000015 |
4 | 96.66 | 96.3200668369934 | 0.339933163006563 |
5 | 96.95 | 96.6060750670451 | 0.343924932954863 |
6 | 97.14 | 96.9246053011242 | 0.215394698875755 |
7 | 97.27 | 97.1339380653324 | 0.13606193466758 |
8 | 97.34 | 97.276129542039 | 0.0638704579610163 |
9 | 97.42 | 97.3522431911119 | 0.0677568088880633 |
10 | 97.47 | 97.4378292927537 | 0.0321707072462658 |
11 | 97.29 | 97.490899984879 | -0.20089998487903 |
12 | 97.36 | 97.2968136981955 | 0.0631863018045351 |
13 | 97.47 | 97.3691113914425 | 0.100888608557497 |
14 | 97.48 | 97.487072219655 | -0.00707221965501503 |
15 | 97.84 | 97.4976914776992 | 0.342308522300783 |
16 | 97.9 | 97.8822264494716 | 0.0177735505284176 |
17 | 97.53 | 97.9473310024303 | -0.417331002430302 |
18 | 97.61 | 97.5475210916592 | 0.0624789083408217 |
19 | 97.73 | 97.6273485243456 | 0.102651475654383 |
20 | 97.76 | 97.7554282055766 | 0.00457179442344113 |
21 | 97.87 | 97.7869044442247 | 0.0830955557752588 |
22 | 97.85 | 97.9029306177132 | -0.0529306177131588 |
23 | 98.13 | 97.8800534814364 | 0.249946518563632 |
24 | 98.21 | 98.1774344404816 | 0.0325655595184315 |
25 | 98.3 | 98.2625701498662 | 0.0374298501338046 |
26 | 98.34 | 98.3556256170745 | -0.0156256170745337 |
27 | 98.38 | 98.3949204549331 | -0.0149204549330904 |
28 | 98.42 | 98.4336729125725 | -0.0136729125725026 |
29 | 98.16 | 98.4725229586883 | -0.312522958688305 |
30 | 98.18 | 98.1898978455771 | -0.00989784557712881 |
31 | 98.22 | 98.205692563649 | 0.0143074363510038 |
32 | 98.29 | 98.2466107098506 | 0.0433892901494346 |
33 | 98.45 | 98.3198905962561 | 0.130109403743916 |
34 | 98.54 | 98.4897312715596 | 0.0502687284404004 |
35 | 98.54 | 98.5848003340279 | -0.0448003340279257 |
36 | 98.78 | 98.5821408559396 | 0.197859144060374 |
37 | 98.84 | 98.8358673065028 | 0.00413269349716927 |
38 | 99.14 | 98.8983762591576 | 0.241623740842428 |
39 | 99.2 | 99.2157966483854 | -0.0157966483854182 |
40 | 99.33 | 99.2773617889238 | 0.0526382110762285 |
41 | 98.56 | 99.4109702066606 | -0.850970206660605 |
42 | 98.65 | 98.580368782511 | 0.0696312174890039 |
43 | 98.77 | 98.6658630318436 | 0.104136968156411 |
44 | 98.82 | 98.7941294816354 | 0.0258705183645702 |
45 | 98.9 | 98.8471538315893 | 0.0528461684106816 |
46 | 98.89 | 98.9312429830935 | -0.0412429830934684 |
47 | 98.9 | 98.9188681119632 | -0.018868111963215 |
48 | 99.07 | 98.9270503432953 | 0.142949656704658 |
49 | 99.09 | 99.1071183592539 | -0.0171183592539279 |
50 | 99.12 | 99.1274854232323 | -0.00748542323226786 |
51 | 99.03 | 99.1567558173409 | -0.126755817340893 |
52 | 99 | 99.0575576397449 | -0.0575576397448714 |
53 | 99.21 | 99.0220019493618 | 0.187998050638214 |
54 | 99.35 | 99.2448767195963 | 0.105123280403731 |
55 | 99.37 | 99.3945372660523 | -0.0245372660523202 |
56 | 99.39 | 99.4139480205279 | -0.0239480205278824 |
57 | 99.41 | 99.4319517225127 | -0.021951722512739 |
58 | 99.43 | 99.450105557197 | -0.0201055571969988 |
59 | 99.6 | 99.4684144580123 | 0.131585541987675 |
60 | 99.73 | 99.6476514932827 | 0.0823485067172669 |
61 | 99.78 | 99.7850437847509 | -0.00504378475085332 |
62 | 99.8 | 99.8356016470976 | -0.0356016470976357 |
63 | 99.88 | 99.8529852933978 | 0.0270147066021877 |
64 | 99.74 | 99.934529835908 | -0.194529835908028 |
65 | 100.15 | 99.7808439641753 | 0.369156035824687 |
66 | 100.27 | 100.215213919863 | 0.0547860801371058 |
67 | 100.26 | 100.343280012467 | -0.0832800124674691 |
68 | 100.36 | 100.327904113094 | 0.0320958869061769 |
69 | 100.37 | 100.429281045698 | -0.0592810456979151 |
70 | 100.54 | 100.435377171027 | 0.104622828972524 |
71 | 99.8 | 100.612237499106 | -0.812237499105819 |
72 | 99.82 | 99.8150023031957 | 0.00499769680429551 |
73 | 99.82 | 99.8262819932381 | -0.006281993238062 |
74 | 99.82 | 99.8258861475969 | -0.00588614759688255 |
75 | 99.67 | 99.8253926745345 | -0.155392674534511 |
76 | 99.78 | 99.6641532133551 | 0.115846786644923 |
77 | 99.44 | 99.7807462180967 | -0.340746218096683 |
78 | 99.61 | 99.417539532193 | 0.192460467806953 |
79 | 99.71 | 99.5975695264082 | 0.112430473591772 |
80 | 99.71 | 99.707805387296 | 0.00219461270394561 |
81 | 99.77 | 99.7092200078263 | 0.0607799921736927 |
82 | 99.77 | 99.7736149853254 | -0.00361498532538462 |
83 | 99.89 | 99.7740344811991 | 0.11596551880092 |
84 | 99.96 | 99.9023326848458 | 0.0576673151541769 |
85 | 100.02 | 99.9777756411667 | 0.0422243588333373 |
86 | 100 | 100.041456464581 | -0.04145646458052 |
87 | 100.04 | 100.018947505945 | 0.0210524940548709 |
88 | 99.99 | 100.059997881093 | -0.0699978810931441 |
89 | 99.97 | 100.005199952268 | -0.0351999522682007 |
90 | 99.77 | 99.9818863872763 | -0.211886387276337 |
91 | 99.93 | 99.7662570032445 | 0.16374299675546 |
92 | 99.9 | 99.9356625114937 | -0.0356625114937259 |
93 | 100.01 | 99.9049285803913 | 0.105071419608677 |
94 | 100.08 | 100.022085186852 | 0.0579148131477893 |
95 | 100.21 | 100.097424159033 | 0.112575840966826 |
96 | 100.28 | 100.23616644129 | 0.0438335587096361 |
97 | 100.48 | 100.310576775981 | 0.16942322401907 |
98 | 100.72 | 100.523249316299 | 0.196750683700699 |
99 | 100.74 | 100.779290780381 | -0.0392907803807816 |
100 | 100.88 | 100.798664934626 | 0.0813350653743043 |
101 | 101.03 | 100.944074196359 | 0.085925803640535 |
102 | 101.47 | 101.101161987125 | 0.368838012875059 |
103 | 101.46 | 101.568644175137 | -0.108644175136831 |
104 | 101.46 | 101.554955100266 | -0.0949551002656221 |
105 | 101.45 | 101.546912771607 | -0.0969127716066964 |
106 | 101.74 | 101.528882699301 | 0.211117300698518 |
107 | 102.41 | 101.832979946745 | 0.577020053255168 |
108 | 102.54 | 102.546831133154 | -0.00683113315386663 |
109 | 102.67 | 102.682790207458 | -0.0127902074575132 |
110 | 102.87 | 102.811794152602 | 0.0582058473977725 |
111 | 102.9 | 103.015836524463 | -0.115836524463063 |
112 | 102.88 | 103.038157845431 | -0.158157845431035 |
113 | 102.82 | 103.005490461174 | -0.185490461173657 |
114 | 102.94 | 102.930384605519 | 0.00961539448123006 |
115 | 102.97 | 103.049002487083 | -0.0790024870825334 |
116 | 103.01 | 103.073429222546 | -0.0634292225459205 |
117 | 103.11 | 103.107985145406 | 0.00201485459388095 |
118 | 103.21 | 103.207420975892 | 0.0025790241076038 |
119 | 104.66 | 103.307628946388 | 1.35237105361156 |
120 | 104.79 | 104.854901340193 | -0.0649013401931313 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 104.995352154434 | 104.571122863828 | 105.41958144504 |
122 | 105.199978803056 | 104.578083777736 | 105.821873828376 |
123 | 105.404605451678 | 104.612876565578 | 106.196334337778 |
124 | 105.6092321003 | 104.659127474479 | 106.559336726121 |
125 | 105.813858748922 | 104.710758289044 | 106.9169592088 |
126 | 106.018485397544 | 104.764804899126 | 107.272165895961 |
127 | 106.223112046166 | 104.819603588089 | 107.626620504242 |
128 | 106.427738694787 | 104.874136778843 | 107.981340610732 |
129 | 106.632365343409 | 104.927745665766 | 108.336985021052 |
130 | 106.836991992031 | 104.979986693778 | 108.693997290284 |
131 | 107.041618640653 | 105.030553027721 | 109.052684253585 |
132 | 107.246245289275 | 105.079228538061 | 109.413262040489 |