Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.109214153332466 |
beta | 0 |
gamma | 0.19831366914627 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
12 | 319.957 | 318.063496503496 | 1.89350349650351 |
13 | 250.746 | 248.144885429518 | 2.60111457048197 |
14 | 247.772 | 246.502464590782 | 1.26953540921812 |
15 | 280.449 | 277.597071006808 | 2.85192899319236 |
16 | 274.925 | 273.807406289255 | 1.11759371074498 |
17 | 296.013 | 292.233145794053 | 3.77985420594655 |
18 | 287.881 | 273.497278188422 | 14.3837218115779 |
19 | 279.098 | 288.458048459935 | -9.36004845993483 |
20 | 294.763 | 276.139481146142 | 18.6235188538581 |
21 | 261.924 | 279.066933625565 | -17.1429336255651 |
22 | 291.596 | 284.20791055247 | 7.38808944753038 |
23 | 287.537 | 328.067610182269 | -40.5306101822691 |
24 | 326.201 | 253.640688493104 | 72.5603115068962 |
25 | 255.598 | 259.40357198598 | -3.80557198597967 |
26 | 253.086 | 290.223442598656 | -37.1374425986561 |
27 | 285.261 | 281.7599935043 | 3.50100649570021 |
28 | 284.747 | 300.916337071989 | -16.1693370719893 |
29 | 300.402 | 281.874961765749 | 18.5270382342512 |
30 | 288.854 | 293.093784865289 | -4.23978486528858 |
31 | 295.433 | 286.277860159417 | 9.15513984058316 |
32 | 307.256 | 281.852908632638 | 25.4030913673617 |
33 | 273.189 | 295.974041775152 | -22.785041775152 |
34 | 287.54 | 328.073330078303 | -40.5333300783034 |
35 | 290.705 | 273.624189203286 | 17.0808107967138 |
36 | 337.006 | 259.837510111426 | 77.1684898885744 |
37 | 268.335 | 293.612652408014 | -25.2776524080138 |
38 | 259.06 | 293.623445876019 | -34.5634458760187 |
39 | 293.703 | 305.147747772582 | -11.4447477725824 |
40 | 294.262 | 292.751653001973 | 1.51034699802653 |
41 | 312.404 | 298.090139220683 | 14.3138607793167 |
42 | 301.014 | 295.666815768646 | 5.34718423135445 |
43 | 309.942 | 293.696263628259 | 16.2457363717409 |
44 | 317.079 | 298.304608871592 | 18.7743911284077 |
45 | 293.912 | 331.807451410354 | -37.8954514103542 |
46 | 304.06 | 287.824230834413 | 16.2357691655869 |
47 | 301.299 | 284.560050767672 | 16.7389492323284 |
48 | 357.634 | 293.637807686524 | 63.9961923134757 |
49 | 281.493 | 301.758186585579 | -20.2651865855792 |
50 | 282.478 | 318.92809460184 | -36.4500946018401 |
51 | 319.111 | 306.089644440547 | 13.0213555594528 |
52 | 315.223 | 314.947100564219 | 0.27589943578073 |
53 | 328.445 | 309.40662471719 | 19.0383752828104 |
54 | 321.081 | 310.856628249418 | 10.2243717505825 |
55 | 328.04 | 315.254054784252 | 12.7859452157484 |
56 | 326.362 | 338.091862690851 | -11.729862690851 |
57 | 313.566 | 306.528846027984 | 7.03715397201626 |
58 | 319.768 | 302.348936270604 | 17.4190637293956 |
59 | 324.315 | 319.849200052194 | 4.46579994780564 |
60 | 387.243 | 306.58282284674 | 80.66017715326 |
61 | 293.308 | 331.916063931288 | -38.6080639312884 |
62 | 295.109 | 327.581312483701 | -32.4723124837014 |
63 | 339.19 | 329.218667495197 | 9.97133250480277 |
64 | 335.678 | 328.051555514299 | 7.62644448570097 |
65 | 345.401 | 326.69817680736 | 18.7028231926399 |
66 | 351.002 | 332.474085023284 | 18.5279149767159 |
67 | 351.889 | 351.608157012828 | 0.280842987172036 |
68 | 355.773 | 324.672166911684 | 31.1008330883163 |
69 | 333.363 | 324.954367863702 | 8.40863213629751 |
70 | 336.214 | 339.182306049017 | -2.96830604901697 |
71 | 343.91 | 338.564137693838 | 5.34586230616219 |
72 | 405.788 | 334.602657365691 | 71.1853426343092 |
73 | 318.682 | 343.342811088997 | -24.660811088997 |
74 | 314.189 | 353.331175127708 | -39.1421751277085 |
75 | 362.141 | 346.385936777834 | 15.7550632221661 |
76 | 351.811 | 347.877016071612 | 3.93398392838787 |
77 | 373.727 | 352.009059599011 | 21.7179404009889 |
78 | 366.795 | 368.268090835501 | -1.47309083550061 |
79 | 362.393 | 346.58505198645 | 15.8079480135498 |
80 | 376.006 | 341.188362464264 | 34.8176375357356 |
81 | 346.423 | 356.290744689419 | -9.86774468941871 |
82 | 349.007 | 356.387799475893 | -7.38079947589256 |
83 | 357.224 | 362.667261590915 | -5.44326159091491 |
84 | 418.473 | 346.106783969297 | 72.366216030703 |
85 | 329.169 | 364.133667120869 | -34.9646671208695 |
86 | 323.456 | 367.342543942895 | -43.8865439428955 |
87 | 374.439 | 360.231662729728 | 14.2073372702717 |
88 | 358.806 | 368.627326846995 | -9.82132684699496 |
89 | 391.816 | 377.345011866786 | 14.4709881332136 |
90 | 376.944 | 360.456074188064 | 16.4879258119362 |
91 | 372.665 | 358.491804751897 | 14.173195248103 |
92 | 388.357 | 363.445625062217 | 24.911374937783 |
93 | 354.241 | 367.780383283184 | -13.539383283184 |
94 | 368.982 | 373.729516655785 | -4.74751665578469 |
95 | 378.233 | 370.99045825034 | 7.24254174966023 |
96 | 426.699 | 362.944376251712 | 63.7546237482878 |
97 | 343.241 | 375.35870260727 | -32.1177026072697 |
98 | 344.577 | 379.795720584117 | -35.2187205841174 |
99 | 373.623 | 378.548575748113 | -4.92557574811337 |
100 | 369.688 | 392.092305216982 | -22.4043052169818 |
101 | 398.816 | 371.532365741282 | 27.2836342587175 |
102 | 379.387 | 370.338231712603 | 9.04876828739674 |
103 | 384.666 | 376.629345308081 | 8.03665469191907 |
104 | 383.879 | 372.328626179091 | 11.5503738209088 |
105 | 351.578 | 382.571043415268 | -30.9930434152678 |
106 | 350.92 | 379.083705909653 | -28.1637059096534 |
107 | 336.629 | 377.153902942524 | -40.5249029425243 |
108 | 385.504 | 361.243102340613 | 24.2608976593868 |
109 | 311.33 | 371.289651050947 | -59.9596510509473 |
110 | 300.545 | 372.691882235478 | -72.146882235478 |
111 | 329.718 | 375.806388506976 | -46.0883885069759 |
112 | 331.023 | 361.437435356175 | -30.4144353561746 |
113 | 348.944 | 350.720575080979 | -1.7765750809794 |
114 | 345.65 | 355.650613028944 | -10.0006130289441 |
115 | 349.26 | 350.00068506412 | -0.740685064120441 |
116 | 354.597 | 351.385236927093 | 3.21176307290654 |
117 | 325.769 | 352.133365046417 | -26.3643650464174 |
118 | 339.734 | 348.216408186772 | -8.48240818677192 |
119 | 340.543 | 347.249837752482 | -6.70683775248159 |
120 | 401.585 | 339.036289611825 | 62.5487103881748 |
121 | 315.998 | 351.665232324248 | -35.667232324248 |
122 | 312.327 | 363.367196136422 | -51.0401961364216 |
123 | 362.217 | 351.226317853424 | 10.9906821465756 |
124 | 358.067 | 350.090503913944 | 7.97649608605639 |
125 | 367.321 | 354.632897768532 | 12.6881022314678 |
126 | 360.372 | 353.096711295303 | 7.27528870469729 |
127 | 363.83 | 356.054940710464 | 7.77505928953639 |
128 | 364.525 | 352.076674163388 | 12.4483258366117 |
129 | 347.945 | 355.557549739158 | -7.6125497391576 |
130 | 357.404 | 354.999643570993 | 2.40435642900707 |
131 | 368.182 | 360.015506315634 | 8.16649368436595 |
132 | 429.343 | 349.354802964187 | 79.988197035813 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
133 | 370.972265501231 | 314.075241776786 | 427.869289225676 |
134 | 375.363764428502 | 318.128420357055 | 432.59910849995 |
135 | 372.49514137615 | 314.923465065191 | 430.06681768711 |
136 | 376.998717793349 | 319.092662708143 | 434.904772878554 |
137 | 373.120610351566 | 314.882096309673 | 431.35912439346 |
138 | 375.372562248095 | 316.803476374362 | 433.941648121828 |
139 | 371.370705130697 | 312.472902774737 | 430.268507486656 |
140 | 369.948193170863 | 310.723498788886 | 429.17288755284 |
141 | 371.991221833224 | 312.441429835976 | 431.541013830473 |
142 | 377.762405238763 | 317.889280807241 | 437.635529670285 |
143 | 378.897468894394 | 318.70274876489 | 439.092189023899 |