Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.74849268925821 |
beta | 0 |
gamma | 0.105416678642104 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 74.29 | 73.9403611099298 | 0.349638890070239 |
14 | 63.98 | 64.6912005135862 | -0.711200513586213 |
15 | 61.18 | 62.1791200456466 | -0.999120045646642 |
16 | 76.48 | 77.2457571681103 | -0.765757168110298 |
17 | 107.98 | 108.403843873499 | -0.423843873499322 |
18 | 124.97 | 125.327597717670 | -0.357597717670401 |
19 | 145.57 | 150.560664175104 | -4.99066417510409 |
20 | 140.2 | 155.995349759207 | -15.7953497592069 |
21 | 143.84 | 135.495970582961 | 8.34402941703857 |
22 | 138.8 | 129.873828284223 | 8.92617171577743 |
23 | 104.06 | 98.9415392666272 | 5.11846073337283 |
24 | 74.7 | 81.0765682372002 | -6.37656823720023 |
25 | 60.18 | 64.1470623862881 | -3.96706238628814 |
26 | 55.16 | 53.2426132870618 | 1.91738671293820 |
27 | 35.62 | 52.924864229907 | -17.3048642299070 |
28 | 56.18 | 50.0958968719459 | 6.08410312805406 |
29 | 85.44 | 77.0744390135175 | 8.36556098648252 |
30 | 114.08 | 96.4410631378694 | 17.6389368621306 |
31 | 133.64 | 131.767674531578 | 1.87232546842216 |
32 | 67.14 | 141.103337539617 | -73.963337539617 |
33 | 95.58 | 80.529662110612 | 15.0503378893880 |
34 | 89.37 | 83.7893621415126 | 5.58063785848745 |
35 | 75.24 | 63.4640873668122 | 11.7759126331878 |
36 | 69.18 | 56.6559767110528 | 12.5240232889472 |
37 | 54.49 | 55.4764753113273 | -0.98647531132729 |
38 | 57.5 | 47.7224815623175 | 9.77751843768252 |
39 | 62.16 | 52.6181478350113 | 9.54185216498865 |
40 | 76.67 | 76.246233489518 | 0.423766510482011 |
41 | 110.04 | 108.232643320302 | 1.80735667969819 |
42 | 127.38 | 127.281784120441 | 0.098215879559362 |
43 | 156.47 | 152.617946490412 | 3.85205350958793 |
44 | 167.56 | 161.113657385402 | 6.44634261459765 |
45 | 153.54 | 161.200553578699 | -7.66055357869945 |
46 | 124.08 | 142.181983996835 | -18.1019839968354 |
47 | 100.97 | 93.3659841320764 | 7.60401586792356 |
48 | 79.17 | 77.9019480809574 | 1.26805191904263 |
49 | 68.13 | 65.9722406964607 | 2.15775930353934 |
50 | 61.77 | 59.3267780723277 | 2.44322192767229 |
51 | 54.31 | 58.4775322174813 | -4.16753221748134 |
52 | 60.3 | 70.3034402120837 | -10.0034402120837 |
53 | 84.18 | 88.6959212452881 | -4.51592124528811 |
54 | 104.05 | 98.8661350545624 | 5.18386494543761 |
55 | 114.66 | 123.010550881149 | -8.35055088114902 |
56 | 105.55 | 120.756598292350 | -15.2065982923496 |
57 | 96.61 | 105.652630103138 | -9.0426301031379 |
58 | 70.94 | 89.8723850666105 | -18.9323850666105 |
59 | 63.91 | 54.980782438769 | 8.92921756123096 |
60 | 58.61 | 48.2089974292791 | 10.4010025707209 |
61 | 44.53 | 46.7339612442915 | -2.2039612442915 |
62 | 49.58 | 39.4461578855268 | 10.1338421144732 |
63 | 57.39 | 44.7435870772542 | 12.6464129227458 |
64 | 76.76 | 68.6814747894087 | 8.0785252105913 |
65 | 104.57 | 105.953836131095 | -1.38383613109522 |
66 | 125.41 | 122.109366109465 | 3.30063389053487 |
67 | 143.11 | 148.881218725698 | -5.77121872569847 |
68 | 136.35 | 149.493664080602 | -13.1436640806019 |
69 | 135.15 | 135.362769212441 | -0.212769212440804 |
70 | 131.7 | 122.710894572195 | 8.9891054278049 |
71 | 96.87 | 95.5027202216624 | 1.36727977833762 |
72 | 70.63 | 75.8540139476447 | -5.22401394764471 |
73 | 66.29 | 59.8029919220972 | 6.48700807790281 |
74 | 63.49 | 57.1487245984807 | 6.34127540151931 |
75 | 62.97 | 59.0339261919402 | 3.93607380805975 |
76 | 66.43 | 78.3361487778237 | -11.9061487778237 |
77 | 101.49 | 98.0656799999367 | 3.4243200000633 |
78 | 127.69 | 117.206540064767 | 10.4834599352330 |
79 | 133.21 | 149.187182864173 | -15.9771828641726 |
80 | 158.72 | 141.654181455443 | 17.0658185445569 |
81 | 148.61 | 150.160184673231 | -1.55018467323075 |
82 | 134.31 | 135.583012920392 | -1.27301292039161 |
83 | 100.99 | 99.214030933917 | 1.77596906608306 |
84 | 75.16 | 78.8518713111839 | -3.69187131118389 |
85 | 59.74 | 63.5664037170366 | -3.82640371703663 |
86 | 52.87 | 53.6288643023088 | -0.758864302308758 |
87 | 52.07 | 50.4985612444984 | 1.57143875550164 |
88 | 57.38 | 64.8213137810088 | -7.44131378100882 |
89 | 79.43 | 84.0520226134744 | -4.62202261347444 |
90 | 101.4 | 93.8253991405378 | 7.57460085946222 |
91 | 120.19 | 117.860597971883 | 2.32940202811672 |
92 | 134.38 | 124.074671892463 | 10.3053281075366 |
93 | 135.97 | 127.583773974502 | 8.3862260254984 |
94 | 113.83 | 121.715057179198 | -7.88505717919814 |
95 | 84.38 | 85.3111441316457 | -0.931144131645723 |
96 | 70.28 | 66.1556347357461 | 4.12436526425391 |
97 | 65.96 | 57.7838575722381 | 8.17614242776192 |
98 | 56.36 | 56.5526307231324 | -0.192630723132424 |
99 | 49.57 | 53.7732891473396 | -4.20328914733956 |
100 | 68.33 | 63.2342288915095 | 5.09577110849053 |
101 | 90.32 | 95.3816340095591 | -5.06163400955913 |
102 | 117.06 | 107.126508098302 | 9.93349190169766 |
103 | 134.69 | 135.654762487717 | -0.96476248771711 |
104 | 131.67 | 140.328159021533 | -8.65815902153287 |
105 | 129.25 | 129.538107198813 | -0.288107198813236 |
106 | 118.77 | 117.148323053472 | 1.62167694652797 |
107 | 88.44 | 87.337613256133 | 1.10238674386690 |
108 | 76.79 | 69.082331157393 | 7.70766884260705 |
109 | 75.28 | 62.6143024380525 | 12.6656975619475 |
110 | 73.89 | 63.631057718951 | 10.258942281049 |
111 | 76.24 | 67.9393905836877 | 8.30060941631234 |
112 | 88.58 | 93.2425600715202 | -4.66256007152019 |
113 | 105.83 | 127.476367216397 | -21.6463672163974 |
114 | 115.84 | 130.818857639880 | -14.9788576398797 |
115 | 127.76 | 141.319582691019 | -13.5595826910191 |
116 | 131.75 | 136.178176242322 | -4.42817624232239 |
117 | 119.63 | 128.793420868578 | -9.1634208685779 |
118 | 93.38 | 110.449148843292 | -17.0691488432919 |
119 | 75.55 | 71.9470579183833 | 3.6029420816167 |
120 | 51.79 | 58.5446657421842 | -6.75466574218419 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 44.6962662586782 | 27.8923503336645 | 61.5001821836918 |
122 | 39.2576865681958 | 17.1248583829175 | 61.3905147534741 |
123 | 37.1917991982208 | 10.4702798047833 | 63.9133185916583 |
124 | 46.3148294515892 | 9.11858477355128 | 83.5110741296271 |
125 | 65.189461790653 | 10.0085767818953 | 120.370346799411 |
126 | 76.4354264307423 | 9.09730288897072 | 143.773549972514 |
127 | 90.0040091335248 | 8.252607843439 | 171.755410423611 |
128 | 93.2868471630865 | 6.08784036517878 | 180.485853960994 |
129 | 90.024187813059 | 3.37882098114349 | 176.669554644974 |
130 | 81.0858415420205 | 0.474262489647515 | 161.697420594394 |
131 | 59.967722270763 | -2.55556753736494 | 122.491012078891 |
132 | 46.7077712362005 | -5.62863102895467 | 99.0441735013557 |