Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.726816553788166 |
beta | 0.0787886111272481 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 74 | 77 | -3 |
4 | 62 | 79.6477557381837 | -17.6477557381837 |
5 | 56 | 70.6386837480392 | -14.6386837480392 |
6 | 66 | 62.9783728166606 | 3.02162718333943 |
7 | 65 | 68.3269012934794 | -3.32690129347937 |
8 | 59 | 68.8706996216654 | -9.87069962166544 |
9 | 61 | 64.0931127010467 | -3.09311270104666 |
10 | 69 | 64.0644614621956 | 4.93553853780443 |
11 | 74 | 70.1537998053721 | 3.84620019462785 |
12 | 69 | 75.6716411499497 | -6.67164114994971 |
13 | 66 | 73.1628906532663 | -7.16289065326627 |
14 | 68 | 69.8869099062462 | -1.88690990624623 |
15 | 58 | 70.3375456591506 | -12.3375456591506 |
16 | 64 | 62.4859784402105 | 1.51402155978948 |
17 | 66 | 64.7886598148854 | 1.21134018511459 |
18 | 57 | 66.9407145902942 | -9.94071459029421 |
19 | 68 | 60.4180176491019 | 7.58198235089809 |
20 | 62 | 67.0652881213165 | -5.06528812131646 |
21 | 59 | 64.2302500044309 | -5.23025000443094 |
22 | 73 | 60.975805290229 | 12.024194709771 |
23 | 61 | 70.9507405293717 | -9.95074052937166 |
24 | 61 | 64.3841012371349 | -3.3841012371349 |
25 | 57 | 62.396413978611 | -5.39641397861097 |
26 | 58 | 58.6371195804074 | -0.637119580407408 |
27 | 57 | 58.3004745672508 | -1.30047456725079 |
28 | 67 | 57.4072206657256 | 9.59277933427439 |
29 | 81 | 64.9806932554311 | 16.0193067445689 |
30 | 79 | 78.1424158175446 | 0.857584182455383 |
31 | 76 | 80.3334568815634 | -4.33345688156339 |
32 | 78 | 78.5034085376781 | -0.503408537678126 |
33 | 74 | 79.4282751090728 | -5.42827510907281 |
34 | 67 | 76.4628176800113 | -9.46281768001134 |
35 | 84 | 70.0231009292668 | 13.9768990707332 |
36 | 85 | 81.420143592873 | 3.57985640712698 |
37 | 79 | 85.4654435385075 | -6.46544353850747 |
38 | 82 | 81.8394104327403 | 0.160589567259734 |
39 | 87 | 83.0384840143745 | 3.96151598562554 |
40 | 90 | 87.226989521919 | 2.77301047808099 |
41 | 87 | 90.7104656280219 | -3.71046562802194 |
42 | 93 | 89.2691646541005 | 3.73083534589949 |
43 | 92 | 93.4499701989452 | -1.44997019894524 |
44 | 82 | 93.7822481615077 | -11.7822481615077 |
45 | 80 | 85.9301465907624 | -5.93014659076243 |
46 | 79 | 81.9918602613577 | -2.99186026135771 |
47 | 77 | 80.0178405965313 | -3.01784059653129 |
48 | 72 | 77.8521217541916 | -5.85212175419164 |
49 | 65 | 73.2912794755224 | -8.29127947552239 |
50 | 73 | 66.4828179727792 | 6.51718202722076 |
51 | 76 | 70.8105969871772 | 5.18940301282275 |
52 | 77 | 74.4704947065286 | 2.52950529347136 |
53 | 76 | 76.3419865158162 | -0.341986515816245 |
54 | 76 | 76.106846731765 | -0.106846731764961 |
55 | 76 | 76.036491871352 | -0.0364918713519558 |
56 | 75 | 76.0151823859737 | -1.01518238597369 |
57 | 78 | 75.2244101494049 | 2.77558985059511 |
58 | 73 | 77.3477777091485 | -4.34777770914855 |
59 | 80 | 74.0447888962874 | 5.95521110371256 |
60 | 77 | 78.5712072768309 | -1.57120727683086 |
61 | 83 | 77.5373252122098 | 5.46267478779023 |
62 | 84 | 81.9286044137378 | 2.07139558626221 |
63 | 85 | 83.9736639454509 | 1.02633605454909 |
64 | 81 | 85.3179299072943 | -4.31792990729433 |
65 | 84 | 82.5306292191558 | 1.46937078084417 |
66 | 83 | 84.0337777949763 | -1.03377779497626 |
67 | 83 | 83.6583974015512 | -0.658397401551156 |
68 | 88 | 83.5181466525223 | 4.48185334747771 |
69 | 92 | 87.3705679735474 | 4.62943202645258 |
70 | 92 | 91.5953557298721 | 0.404644270127932 |
71 | 89 | 92.7726697088956 | -3.77266970889563 |
72 | 82 | 90.6978013091687 | -8.69780130916872 |
73 | 73 | 84.5451872992056 | -11.5451872992056 |
74 | 81 | 75.6619124035898 | 5.33808759641022 |
75 | 91 | 79.355366059531 | 11.644633940469 |
76 | 80 | 88.2993504073032 | -8.29935040730315 |
77 | 81 | 82.2724555868784 | -1.27245558687839 |
78 | 82 | 81.2799572439532 | 0.72004275604678 |
79 | 84 | 81.7768728325893 | 2.22312716741071 |
80 | 87 | 83.4935621343052 | 3.50643786569478 |
81 | 85 | 86.3437785925695 | -1.34377859256949 |
82 | 74 | 85.5918261373761 | -11.5918261373761 |
83 | 81 | 76.7276187026834 | 4.27238129731663 |
84 | 82 | 79.638437190238 | 2.36156280976196 |
85 | 86 | 81.2956757495351 | 4.70432425046489 |
86 | 85 | 84.9250646071798 | 0.0749353928202225 |
87 | 82 | 85.1940281744556 | -3.19402817445555 |
88 | 86 | 82.9041493092841 | 3.09585069071591 |
89 | 88 | 85.3631420021316 | 2.63685799786843 |
90 | 86 | 87.6395305298137 | -1.63953052981365 |
91 | 83 | 86.713881587714 | -3.71388158771397 |
92 | 81 | 84.0678850238688 | -3.06788502386883 |
93 | 81 | 81.7157274290141 | -0.715727429014095 |
94 | 81 | 81.0321708753184 | -0.0321708753183714 |
95 | 82 | 80.8435922794086 | 1.1564077205914 |
96 | 86 | 81.5851138165905 | 4.41488618340955 |
97 | 85 | 84.9477693100171 | 0.0522306899829204 |
98 | 87 | 85.142565555852 | 1.857434444148 |
99 | 89 | 86.7557795092406 | 2.24422049075942 |
100 | 90 | 88.7786309515925 | 1.22136904840747 |
101 | 90 | 90.1279985694688 | -0.127998569468758 |
102 | 92 | 90.4892936444934 | 1.51070635550658 |
103 | 86 | 92.1281369840124 | -6.12813698401243 |
104 | 86 | 87.8640155843471 | -1.86401558434713 |
105 | 82 | 86.592385601138 | -4.59238560113799 |
106 | 80 | 83.0747487750433 | -3.07474877504328 |
107 | 79 | 80.4840804376933 | -1.48408043769334 |
108 | 77 | 78.9645505109054 | -1.96455051090541 |
109 | 79 | 76.9833072579444 | 2.01669274205562 |
110 | 76 | 78.011183147178 | -2.011183147178 |
111 | 78 | 75.9963620284441 | 2.00363797155586 |
112 | 78 | 77.0143174208955 | 0.985682579104477 |
113 | 77 | 77.3488509647118 | -0.348850964711843 |
114 | 72 | 76.6934465332636 | -4.69344653326357 |
115 | 75 | 72.6115485324359 | 2.3884514675641 |
116 | 79 | 73.8136655860387 | 5.18633441396133 |
117 | 81 | 77.3463250301298 | 3.65367496987017 |
118 | 86 | 79.9742494294789 | 6.02575057052105 |
119 | 88 | 84.6713014461131 | 3.32869855388694 |
120 | 97 | 87.5987088899929 | 9.40129111000711 |
121 | 94 | 95.4781408113965 | -1.47814081139654 |
122 | 96 | 95.3655759798108 | 0.634424020189172 |
123 | 94 | 96.8247884457941 | -2.82478844579413 |
124 | 91 | 95.608026894295 | -4.60802689429504 |
125 | 92 | 92.8313000726818 | -0.831300072681799 |
126 | 93 | 92.7519565362055 | 0.248043463794474 |
127 | 93 | 93.4713019251835 | -0.471301925183539 |
128 | 87 | 93.6408261355848 | -6.64082613558479 |
129 | 84 | 88.9459519966587 | -4.94595199665868 |
130 | 80 | 85.1997111561183 | -5.19971115611831 |
131 | 78 | 80.971273190964 | -2.97127319096396 |
132 | 75 | 78.1923512644155 | -3.19235126441555 |
133 | 73 | 75.0699365644123 | -2.06993656441226 |
134 | 81 | 72.6447768069053 | 8.35522319309472 |
135 | 76 | 78.2752564804217 | -2.27525648042167 |
136 | 77 | 76.0490352931913 | 0.950964706808719 |
137 | 71 | 76.2221419383054 | -5.22214193830537 |
138 | 71 | 71.6094872228529 | -0.609487222852906 |
139 | 78 | 70.3144841068568 | 7.68551589314316 |
140 | 67 | 75.4885366133339 | -8.48853661333393 |
141 | 76 | 68.4209250976285 | 7.57907490237153 |
142 | 68 | 73.4655343262575 | -5.46553432625745 |
143 | 82 | 68.7161225345427 | 13.2838774654573 |
144 | 64 | 78.3547930807135 | -14.3547930807135 |
145 | 71 | 67.0831950352736 | 3.91680496472644 |
146 | 81 | 69.3159922280771 | 11.6840077719229 |
147 | 69 | 77.863204146732 | -8.86320414673199 |
148 | 63 | 70.9688121036782 | -7.96881210367816 |
149 | 70 | 64.2681460392834 | 5.73185396071663 |
150 | 77 | 67.8535847220909 | 9.14641527790909 |
151 | 75 | 74.4445513469035 | 0.555448653096505 |
152 | 76 | 74.823268908904 | 1.17673109109596 |
153 | 68 | 75.7209301806318 | -7.7209301806318 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
154 | 69.7094859115687 | 58.2968687468474 | 81.12210307629 |
155 | 69.3097415084314 | 54.80725653648 | 83.8122264803829 |
156 | 68.9099971052942 | 51.5169017690233 | 86.3030924415651 |
157 | 68.5102527021569 | 48.318790400234 | 88.7017150040798 |
158 | 68.1105082990197 | 45.1605092097286 | 91.0605073883107 |
159 | 67.7107638958824 | 42.0125942217839 | 93.408933569981 |
160 | 67.3110194927452 | 38.8570253374854 | 95.7650136480049 |
161 | 66.9112750896079 | 35.682149759853 | 98.1404004193629 |
162 | 66.5115306864707 | 32.4801390705316 | 100.54292230241 |
163 | 66.1117862833334 | 29.2455950364493 | 102.977977530218 |
164 | 65.7120418801962 | 25.9747315992836 | 105.449352161109 |
165 | 65.3122974770589 | 22.6648689081153 | 107.959726046003 |