Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.473971450972799 |
beta | 0.0065615366876307 |
gamma | 0.328170676425391 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 20.203 | 19.7520502136752 | 0.450949786324788 |
14 | 20.45 | 20.1878033285003 | 0.262196671499719 |
15 | 23.083 | 22.9987416156329 | 0.0842583843670681 |
16 | 21.738 | 21.8157292766096 | -0.0777292766096025 |
17 | 26.766 | 26.7729060076284 | -0.00690600762840177 |
18 | 25.28 | 25.1928794686559 | 0.0871205313440981 |
19 | 22.574 | 23.0523981013263 | -0.478398101326281 |
20 | 22.729 | 21.505930904748 | 1.22306909525199 |
21 | 21.378 | 23.9528809725080 | -2.57488097250796 |
22 | 22.902 | 22.5604949715285 | 0.341505028471538 |
23 | 24.989 | 22.6939130825353 | 2.29508691746474 |
24 | 21.116 | 20.6662442462503 | 0.449755753749734 |
25 | 15.169 | 21.5631443600254 | -6.39414436002542 |
26 | 15.846 | 18.7070404533627 | -2.86104045336273 |
27 | 20.927 | 19.9823294163029 | 0.944670583697079 |
28 | 18.273 | 19.1572331801393 | -0.884233180139319 |
29 | 22.538 | 23.7199366443331 | -1.18193664433310 |
30 | 15.596 | 21.5711168793076 | -5.97511687930761 |
31 | 14.034 | 16.4127369567014 | -2.37873695670139 |
32 | 11.366 | 14.2064255749357 | -2.84042557493574 |
33 | 14.861 | 14.0062712656517 | 0.854728734348273 |
34 | 15.149 | 14.6880411272139 | 0.46095887278606 |
35 | 13.577 | 15.1608610980324 | -1.58386109803237 |
36 | 13.026 | 10.9096068221584 | 2.11639317784157 |
37 | 13.19 | 11.3536651987690 | 1.83633480123103 |
38 | 13.196 | 12.9727423565462 | 0.223257643453822 |
39 | 15.826 | 16.340720977083 | -0.514720977083002 |
40 | 14.733 | 14.4775090737517 | 0.255490926248314 |
41 | 16.307 | 19.5018747509537 | -3.19487475095367 |
42 | 15.703 | 15.5381437967695 | 0.164856203230496 |
43 | 14.589 | 13.8964608467448 | 0.69253915325517 |
44 | 12.043 | 13.0613905059975 | -1.01839050599748 |
45 | 15.057 | 14.3636230692343 | 0.693376930765746 |
46 | 14.053 | 14.9013499437283 | -0.84834994372828 |
47 | 12.698 | 14.3969400845724 | -1.69894008457240 |
48 | 10.888 | 10.7258846941654 | 0.162115305834634 |
49 | 10.045 | 10.1852264162700 | -0.140226416269973 |
50 | 11.549 | 10.5727629558904 | 0.976237044109611 |
51 | 13.767 | 14.1563327990870 | -0.389332799086965 |
52 | 12.434 | 12.4719963747322 | -0.0379963747322165 |
53 | 13.116 | 16.7472035154773 | -3.63120351547726 |
54 | 14.211 | 13.1408618118764 | 1.07013818812356 |
55 | 12.266 | 12.0063803550454 | 0.259619644954562 |
56 | 12.602 | 10.6564505296472 | 1.94554947035279 |
57 | 15.714 | 13.6539062511671 | 2.06009374883288 |
58 | 13.742 | 14.5724271360866 | -0.830427136086591 |
59 | 12.745 | 13.9288861337279 | -1.1838861337279 |
60 | 10.491 | 10.8240310030629 | -0.333031003062949 |
61 | 10.057 | 9.99576593988131 | 0.0612340601186876 |
62 | 10.9 | 10.6714182488754 | 0.228581751124628 |
63 | 11.771 | 13.6624585669115 | -1.89145856691147 |
64 | 11.992 | 11.3197081958025 | 0.672291804197467 |
65 | 11.933 | 15.3063961280774 | -3.37339612807743 |
66 | 14.504 | 12.6297382988172 | 1.87426170118276 |
67 | 11.727 | 11.7348830753153 | -0.00788307531533405 |
68 | 11.477 | 10.5467820680298 | 0.930217931970176 |
69 | 13.578 | 13.0771956355327 | 0.500804364467331 |
70 | 11.555 | 12.7472486974918 | -1.19224869749179 |
71 | 11.846 | 11.8596459251731 | -0.0136459251731296 |
72 | 11.397 | 9.44841929888116 | 1.94858070111884 |
73 | 10.066 | 9.7688170299487 | 0.297182970051301 |
74 | 10.269 | 10.5851080689890 | -0.316108068989035 |
75 | 14.279 | 12.9502274095353 | 1.32877259046466 |
76 | 13.87 | 12.5845853906473 | 1.28541460935272 |
77 | 13.695 | 16.1736250841754 | -2.47862508417542 |
78 | 14.42 | 14.8398787055740 | -0.419878705573966 |
79 | 11.424 | 12.5385497457272 | -1.11454974572725 |
80 | 9.704 | 10.9902129166719 | -1.28621291667189 |
81 | 12.464 | 12.3914309301873 | 0.0725690698126975 |
82 | 14.301 | 11.5603717979225 | 2.7406282020775 |
83 | 13.464 | 12.7466564260035 | 0.71734357399654 |
84 | 9.893 | 11.0292620950649 | -1.13626209506491 |
85 | 11.572 | 9.60149309408338 | 1.97050690591662 |
86 | 12.38 | 11.1092619909836 | 1.27073800901636 |
87 | 16.692 | 14.5196279475516 | 2.17237205244843 |
88 | 16.052 | 14.5581426298284 | 1.49385737017159 |
89 | 16.459 | 17.6086504737641 | -1.14965047376408 |
90 | 14.761 | 17.2767763721974 | -2.51577637219739 |
91 | 13.654 | 13.8721952174728 | -0.218195217472841 |
92 | 13.48 | 12.7319213087774 | 0.748078691222647 |
93 | 18.068 | 15.3510749175141 | 2.71692508248591 |
94 | 16.56 | 16.2613451640843 | 0.298654835915684 |
95 | 14.53 | 15.9607364858548 | -1.43073648585482 |
96 | 10.65 | 12.9183565913382 | -2.26835659133818 |
97 | 11.651 | 11.4999247022647 | 0.151075297735261 |
98 | 13.735 | 12.0284823762784 | 1.70651762372159 |
99 | 13.36 | 15.8063437290606 | -2.44634372906059 |
100 | 17.818 | 13.5295266092454 | 4.28847339075461 |
101 | 20.613 | 17.4478903258188 | 3.16510967418117 |
102 | 16.231 | 18.9383066349928 | -2.70730663499282 |
103 | 13.862 | 15.8520225188341 | -1.99002251883408 |
104 | 12.004 | 14.0456998503392 | -2.04169985033923 |
105 | 17.734 | 15.6807199395748 | 2.05328006042518 |
106 | 15.034 | 15.8551839135026 | -0.821183913502637 |
107 | 12.609 | 14.7179826843134 | -2.10898268431336 |
108 | 12.32 | 11.2001470869607 | 1.11985291303927 |
109 | 10.833 | 11.8064362583755 | -0.97343625837554 |
110 | 11.35 | 12.0681687829837 | -0.71816878298368 |
111 | 13.648 | 13.9700103316430 | -0.322010331642952 |
112 | 14.89 | 13.8593944091262 | 1.03060559087377 |
113 | 16.325 | 16.0262823841779 | 0.298717615822106 |
114 | 18.045 | 15.1220414626911 | 2.92295853730894 |
115 | 15.616 | 14.8233442591850 | 0.792655740815043 |
116 | 11.926 | 14.3308440601420 | -2.40484406014198 |
117 | 16.855 | 16.5033528068680 | 0.351647193131967 |
118 | 15.083 | 15.3724927828561 | -0.289492782856074 |
119 | 12.52 | 14.2640544045649 | -1.74405440456491 |
120 | 12.355 | 11.4767694426125 | 0.878230557387475 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 11.6066269208744 | 8.14454377072808 | 15.0687100710206 |
122 | 12.3762828431977 | 8.54038424560877 | 16.2121814407867 |
123 | 14.6916133920903 | 10.5109555553541 | 18.8722712288265 |
124 | 14.9728306421709 | 10.4697653210477 | 19.4758959632940 |
125 | 16.5274033384787 | 11.7197592248363 | 21.3350474521211 |
126 | 15.9361710864376 | 10.8385573587785 | 21.0337848140966 |
127 | 13.8768136227748 | 8.50145312115497 | 19.2521741243946 |
128 | 12.4466635549264 | 6.80395337289073 | 18.0893737369621 |
129 | 16.2323455480606 | 10.3312498360947 | 22.1334412600265 |
130 | 14.8205436174045 | 8.6688780226641 | 20.9722092121449 |
131 | 13.5955270380566 | 7.20017036162475 | 19.9908837144884 |
132 | 12.0902829189264 | 5.45733826766284 | 18.7232275701900 |