Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.660335318562836 |
beta | 0.204922662099265 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 26.931 | 20.533 | 6.398 |
4 | 24.74 | 22.5585878295139 | 2.18141217048609 |
5 | 25.806 | 22.0949974065599 | 3.71100259344012 |
6 | 24.364 | 23.1436137921659 | 1.22038620783408 |
7 | 24.477 | 22.7127280331666 | 1.76427196683342 |
8 | 23.901 | 22.8797264242921 | 1.02127357570793 |
9 | 23.175 | 22.6942930982063 | 0.480706901793653 |
10 | 23.227 | 22.2169526438535 | 1.01004735614654 |
11 | 21.672 | 22.225831643249 | -0.553831643248994 |
12 | 21.87 | 21.1270828970961 | 0.742917102903913 |
13 | 21.439 | 20.9851529597071 | 0.453847040292946 |
14 | 21.089 | 20.713753375082 | 0.375246624917981 |
15 | 23.709 | 20.4412286596001 | 3.26777134039994 |
16 | 21.669 | 22.5209273818803 | -0.85192738188029 |
17 | 21.752 | 21.7649627065185 | -0.0129627065184863 |
18 | 20.761 | 21.5612419540641 | -0.800241954064106 |
19 | 23.479 | 20.7293660311368 | 2.7496339688632 |
20 | 23.824 | 22.6136726223878 | 1.21032737761217 |
21 | 23.105 | 23.6452993876586 | -0.540299387658632 |
22 | 23.11 | 23.4478134152256 | -0.337813415225558 |
23 | 21.759 | 23.3383239572017 | -1.57932395720174 |
24 | 22.073 | 22.1953107997344 | -0.122310799734429 |
25 | 21.937 | 21.9978640771515 | -0.0608640771515283 |
26 | 20.035 | 21.8327568105106 | -1.79775681051055 |
27 | 23.59 | 20.2774496622111 | 3.31255033778892 |
28 | 21.672 | 22.5449054106038 | -0.872905410603835 |
29 | 22.222 | 21.9304373765722 | 0.291562623427755 |
30 | 22.123 | 22.1243622880064 | -0.00136228800644034 |
31 | 23.95 | 22.124674193093 | 1.82532580690701 |
32 | 23.504 | 23.5782116009096 | -0.0742116009095852 |
33 | 22.238 | 23.7673752283907 | -1.52937522839075 |
34 | 23.142 | 22.7886914238195 | 0.353308576180453 |
35 | 21.059 | 23.1010191228925 | -2.04201912289253 |
36 | 21.573 | 21.5553060701573 | 0.0176939298426753 |
37 | 21.548 | 21.3720885936315 | 0.175911406368467 |
38 | 20 | 21.3171516267447 | -1.31715162674471 |
39 | 22.424 | 20.0980585152961 | 2.32594148470388 |
40 | 20.615 | 21.5993694395753 | -0.98436943957526 |
41 | 21.761 | 20.7815625648091 | 0.97943743519087 |
42 | 22.874 | 21.3930619212585 | 1.48093807874148 |
43 | 24.104 | 22.5361169571671 | 1.56788304283285 |
44 | 23.748 | 23.9487471059544 | -0.20074710595442 |
45 | 23.262 | 24.1663236711128 | -0.904323671112795 |
46 | 22.907 | 23.796932807655 | -0.889932807655011 |
47 | 21.519 | 23.316621104406 | -1.797621104406 |
48 | 22.025 | 21.9936808587338 | 0.0313191412661631 |
49 | 22.604 | 21.8826924860851 | 0.721307513914937 |
50 | 20.894 | 22.32493345841 | -1.43093345841001 |
51 | 24.677 | 21.1523431191904 | 3.52465688080961 |
52 | 23.673 | 23.7290524667336 | -0.056052466733604 |
53 | 25.32 | 23.9337080773137 | 1.38629192268633 |
54 | 23.583 | 25.2783844245591 | -1.69538442455908 |
55 | 24.671 | 24.3587055669506 | 0.312294433049431 |
56 | 24.454 | 24.8070269228112 | -0.353026922811182 |
57 | 24.122 | 24.7682423080814 | -0.646242308081412 |
58 | 24.252 | 24.4483892142491 | -0.196389214249063 |
59 | 22.084 | 24.399015075287 | -2.31501507528695 |
60 | 22.991 | 22.6373750043143 | 0.35362499568572 |
61 | 23.287 | 22.6857839356871 | 0.601216064312904 |
62 | 23.049 | 22.979041152041 | 0.069958847958965 |
63 | 25.076 | 22.9309571335918 | 2.14504286640821 |
64 | 24.037 | 24.5433865871555 | -0.506386587155465 |
65 | 24.43 | 24.3364604740724 | 0.0935395259275573 |
66 | 24.667 | 24.5383443128147 | 0.128655687185283 |
67 | 26.451 | 24.7808259810847 | 1.6701740189153 |
68 | 25.618 | 26.2672307070104 | -0.649230707010435 |
69 | 25.014 | 26.134198186919 | -1.12019818691905 |
70 | 25.11 | 25.5385865958361 | -0.428586595836066 |
71 | 22.964 | 25.3416752249488 | -2.3776752249488 |
72 | 23.981 | 23.5359703185633 | 0.445029681436662 |
73 | 23.798 | 23.654417535922 | 0.143582464077962 |
74 | 22.27 | 23.5932377536632 | -1.32323775366318 |
75 | 24.775 | 22.384407324169 | 2.39059267583096 |
76 | 22.646 | 23.9514397284824 | -1.30543972848235 |
77 | 23.988 | 22.9012023335183 | 1.08679766648166 |
78 | 24.737 | 23.5777067103015 | 1.15929328969851 |
79 | 26.276 | 24.458955375919 | 1.81704462408102 |
80 | 25.816 | 26.0204187257454 | -0.204418725745406 |
81 | 25.21 | 26.2193769645512 | -1.00937696455125 |
82 | 25.199 | 25.7502063079399 | -0.55120630793991 |
83 | 23.162 | 25.5089939637899 | -2.34699396378987 |
84 | 24.707 | 23.7643698479715 | 0.942630152028546 |
85 | 24.364 | 24.3195552377484 | 0.0444447622516186 |
86 | 22.644 | 24.2876512537704 | -1.64365125377043 |
87 | 25.565 | 22.9186227891029 | 2.64637721089707 |
88 | 24.062 | 24.7405532390089 | -0.67855323900891 |
89 | 25.431 | 24.2750944368818 | 1.1559055631182 |
90 | 24.635 | 25.1774080213587 | -0.542408021358675 |
91 | 27.009 | 24.8848677736342 | 2.12413222636577 |
92 | 26.606 | 26.64057085638 | -0.0345708563799612 |
93 | 26.268 | 26.966128003516 | -0.698128003516029 |
94 | 26.462 | 26.7590458747677 | -0.297045874767711 |
95 | 25.246 | 26.7766168852162 | -1.53061688521619 |
96 | 25.18 | 25.7724978768615 | -0.592497876861504 |
97 | 24.657 | 25.3076765497571 | -0.650676549757069 |
98 | 23.304 | 24.7163897546322 | -1.41238975463215 |
99 | 26.982 | 23.4309955350657 | 3.55100446493428 |
100 | 26.199 | 25.9036194738066 | 0.295380526193387 |
101 | 27.21 | 26.2664101468073 | 0.943589853192744 |
102 | 26.122 | 27.1849207138986 | -1.06292071389856 |
103 | 26.706 | 26.6346295306269 | 0.0713704693730755 |
104 | 26.878 | 26.8430085629233 | 0.0349914370767195 |
105 | 26.152 | 27.0321001951219 | -0.880100195121909 |
106 | 26.379 | 26.4978313938928 | -0.118831393892794 |
107 | 24.712 | 26.4501752815295 | -1.73817528152945 |
108 | 25.688 | 25.0980033757521 | 0.589996624247934 |
109 | 24.99 | 25.3630425763476 | -0.373042576347583 |
110 | 24.239 | 24.9416737268806 | -0.70267372688059 |
111 | 26.721 | 24.2075536141722 | 2.51344638582782 |
112 | 23.475 | 25.937264912639 | -2.46226491263898 |
113 | 24.767 | 24.048150351511 | 0.718849648488966 |
114 | 26.219 | 24.3569111479805 | 1.86208885201953 |
115 | 28.361 | 25.6725666954239 | 2.68843330457612 |
116 | 28.599 | 27.8976792045656 | 0.70132079543442 |
117 | 27.914 | 28.9055322388762 | -0.991532238876164 |
118 | 27.784 | 28.661362791854 | -0.877362791854043 |
119 | 25.693 | 28.3738607730715 | -2.68086077307152 |
120 | 26.881 | 26.5326775032871 | 0.348322496712896 |
121 | 26.217 | 26.7389051220778 | -0.521905122077811 |
122 | 24.218 | 26.2998677232028 | -2.08186772320277 |
123 | 27.914 | 24.5490184307885 | 3.36498156921155 |
124 | 26.975 | 26.8502575711528 | 0.124742428847195 |
125 | 28.527 | 27.028732221536 | 1.49826777846395 |
126 | 27.139 | 28.3169362780652 | -1.17793627806516 |
127 | 28.982 | 27.678552682231 | 1.30344731776899 |
128 | 28.169 | 28.855093769407 | -0.686093769407005 |
129 | 28.056 | 28.6250299977794 | -0.56902999777936 |
130 | 29.136 | 28.3952677548492 | 0.740732245150763 |
131 | 26.291 | 29.1306219423596 | -2.83962194235958 |
132 | 26.987 | 27.1174907781151 | -0.130490778115142 |
133 | 26.589 | 26.8756368960123 | -0.286636896012318 |
134 | 24.848 | 26.4918871801118 | -1.64388718011182 |
135 | 27.543 | 24.9894501803029 | 2.55354981969712 |
136 | 26.896 | 26.6042694942084 | 0.29173050579158 |
137 | 28.878 | 26.7650059236424 | 2.1129940763576 |
138 | 27.39 | 28.4143124511391 | -1.02431245113907 |
139 | 28.065 | 27.8533370977408 | 0.211662902259246 |
140 | 28.141 | 28.1371616541111 | 0.0038383458888589 |
141 | 29.048 | 28.2842717118731 | 0.763728288126945 |
142 | 28.484 | 29.0365098702151 | -0.552509870215065 |
143 | 26.634 | 28.8448251359239 | -2.2108251359239 |
144 | 27.735 | 27.2589325532002 | 0.476067446799821 |
145 | 27.132 | 27.5117103783438 | -0.379710378343777 |
146 | 24.924 | 27.1480063565142 | -2.2240063565142 |
147 | 28.963 | 25.2655012011663 | 3.69749879883373 |
148 | 26.589 | 27.7935119662539 | -1.20451196625391 |
149 | 27.931 | 26.9215601367825 | 1.00943986321746 |
150 | 28.009 | 27.6481539455745 | 0.360846054425483 |
151 | 29.229 | 27.9952872028236 | 1.23371279717644 |
152 | 28.759 | 29.0857483415485 | -0.326748341548516 |
153 | 28.405 | 29.1015670524301 | -0.696567052430147 |
154 | 27.945 | 28.7789235755717 | -0.833923575571667 |
155 | 25.912 | 28.2527341389109 | -2.3407341389109 |
156 | 26.619 | 26.4148017759479 | 0.204198224052067 |
157 | 26.076 | 26.2850097637772 | -0.209009763777161 |
158 | 25.286 | 25.854079208805 | -0.568079208805045 |
159 | 27.66 | 25.1091712617818 | 2.55082873821817 |
160 | 25.951 | 26.7689605924133 | -0.817960592413257 |
161 | 26.398 | 26.0935348246031 | 0.304465175396924 |
162 | 25.565 | 26.2004859522873 | -0.6354859522873 |
163 | 28.865 | 25.6007616733944 | 3.26423832660561 |
164 | 30 | 28.0178721976255 | 1.98212780237454 |
165 | 29.261 | 29.856576778957 | -0.595576778957042 |
166 | 29.012 | 29.9125399215708 | -0.90053992157075 |
167 | 26.992 | 29.6452661651048 | -2.65326616510479 |
168 | 27.897 | 27.8615715673062 | 0.0354284326937844 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
169 | 27.8581110662751 | 24.8700799155817 | 30.8461422169685 |
170 | 27.831255919855 | 24.0128096773908 | 31.6497021623193 |
171 | 27.8044007734349 | 23.0801259775668 | 32.528675569303 |
172 | 27.7775456270148 | 22.0792982558495 | 33.4757929981801 |
173 | 27.7506904805946 | 21.0156140148399 | 34.4857669463494 |
174 | 27.7238353341745 | 19.8931623706796 | 35.5545082976695 |
175 | 27.6969801877544 | 18.7152461506903 | 36.6787142248185 |
176 | 27.6701250413343 | 17.4846182901599 | 37.8556317925087 |
177 | 27.6432698949142 | 16.2036276591262 | 39.0829121307021 |
178 | 27.616414748494 | 14.8743145506856 | 40.3585149463025 |
179 | 27.5895596020739 | 13.4984763325967 | 41.6806428715512 |
180 | 27.5627044556538 | 12.0777144241265 | 43.0476944871811 |