Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.0011609542690148 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 354 | 354 | 0 |
4 | 352 | 353 | -1 |
5 | 372 | 350.998839045731 | 21.0011609542690 |
6 | 371 | 371.023220433195 | -0.0232204331950925 |
7 | 356 | 370.023193475334 | -14.0231934753340 |
8 | 346 | 355.006913189004 | -9.00691318900368 |
9 | 347 | 344.996456574686 | 2.00354342531375 |
10 | 347 | 345.998782596979 | 1.00121740302097 |
11 | 348 | 345.999944964597 | 2.00005503540274 |
12 | 350 | 347.002266937029 | 2.99773306297112 |
13 | 353 | 349.005747168026 | 3.99425283197428 |
14 | 351 | 352.010384312902 | -1.01038431290249 |
15 | 348 | 350.009211302921 | -2.00921130292107 |
16 | 351 | 347.006878700482 | 3.99312129951841 |
17 | 370 | 350.011514531701 | 19.988485468299 |
18 | 370 | 369.034720249237 | 0.965279750763443 |
19 | 351 | 369.035840894884 | -18.0358408948840 |
20 | 335 | 350.014902108402 | -15.0149021084018 |
21 | 330 | 333.9974704937 | -3.99747049370023 |
22 | 328 | 328.992829613265 | -0.992829613265314 |
23 | 332 | 326.991676983487 | 5.00832301651263 |
24 | 334 | 330.997491417474 | 3.00250858252599 |
25 | 343 | 333.000977192631 | 9.99902280736939 |
26 | 334 | 342.012585600845 | -8.01258560084483 |
27 | 336 | 333.003283355386 | 2.99671664461431 |
28 | 343 | 335.006762406367 | 7.99323759363273 |
29 | 365 | 342.016042189675 | 22.9839578103251 |
30 | 364 | 364.042725513614 | -0.0427255136136182 |
31 | 351 | 363.042675911246 | -12.0426759112462 |
32 | 326 | 350.028694915237 | -24.0286949152367 |
33 | 320 | 325.000798699296 | -5.00079869929596 |
34 | 312 | 318.994993000697 | -6.99499300069749 |
35 | 315 | 310.986872133712 | 4.01312786628836 |
36 | 316 | 313.99153119164 | 2.00846880835991 |
37 | 319 | 314.993862932077 | 4.00613706792268 |
38 | 311 | 317.998513874009 | -6.99851387400861 |
39 | 315 | 309.99038891945 | 5.0096110805502 |
40 | 322 | 313.99620484882 | 8.0037951511801 |
41 | 336 | 321.005496888969 | 14.994503111031 |
42 | 339 | 335.022904821367 | 3.97709517863251 |
43 | 317 | 338.027522046993 | -21.0275220469934 |
44 | 295 | 316.003110055506 | -21.0031100555061 |
45 | 291 | 293.978726405225 | -2.97872640522462 |
46 | 283 | 289.975268240088 | -6.97526824008821 |
47 | 285 | 281.967170272647 | 3.03282972735263 |
48 | 289 | 283.970691249267 | 5.02930875073343 |
49 | 296 | 287.976530046731 | 8.02346995326911 |
50 | 283 | 294.985844928425 | -11.9858449284255 |
51 | 285 | 281.971929910588 | 3.02807008941193 |
52 | 289 | 283.975445361485 | 5.02455463851476 |
53 | 306 | 287.981278639643 | 18.0187213603573 |
54 | 306 | 305.002197551128 | 0.997802448871767 |
55 | 283 | 305.003355954141 | -22.0033559541409 |
56 | 258 | 281.977811064113 | -23.9778110641133 |
57 | 255 | 256.949973921997 | -1.94997392199673 |
58 | 248 | 253.947710091448 | -5.94771009144753 |
59 | 244 | 246.940805072026 | -2.94080507202600 |
60 | 249 | 242.937390931823 | 6.06260906817673 |
61 | 258 | 247.944429343702 | 10.0555706562976 |
62 | 252 | 256.956103401383 | -4.95610340138319 |
63 | 246 | 250.950349591982 | -4.95034959198165 |
64 | 249 | 244.944602462490 | 4.05539753751029 |
65 | 267 | 247.949310593573 | 19.0506894064266 |
66 | 284 | 265.971427572768 | 18.0285724272325 |
67 | 261 | 282.992357920891 | -21.9923579208912 |
68 | 235 | 259.966825799077 | -24.9668257990772 |
69 | 229 | 233.937840456082 | -4.937840456082 |
70 | 218 | 227.932107849125 | -9.9321078491248 |
71 | 218 | 216.920577126117 | 1.07942287388295 |
72 | 229 | 216.921830286711 | 12.0781697132894 |
73 | 237 | 227.935852489401 | 9.06414751059893 |
74 | 231 | 235.946375550149 | -4.9463755501485 |
75 | 229 | 229.940633034337 | -0.940633034337395 |
76 | 233 | 227.939541002401 | 5.0604589975994 |
77 | 245 | 231.945415963877 | 13.0545840361229 |
78 | 256 | 243.960571738944 | 12.039428261056 |
79 | 224 | 254.97454896458 | -30.9745489645802 |
80 | 194 | 222.938588929729 | -28.9385889297289 |
81 | 192 | 192.904992551372 | -0.904992551371691 |
82 | 178 | 190.903941896406 | -12.9039418964057 |
83 | 170 | 176.888961009974 | -6.888961009974 |
84 | 187 | 168.880963241280 | 18.1190367587196 |
85 | 192 | 185.901998614356 | 6.09800138564412 |
86 | 182 | 190.909078115097 | -8.90907811509697 |
87 | 178 | 180.898735082826 | -2.89873508282628 |
88 | 186 | 176.895369783957 | 9.10463021604286 |
89 | 204 | 184.905939843274 | 19.0940601567258 |
90 | 224 | 202.928107173926 | 21.071892826074 |
91 | 194 | 222.952570677859 | -28.9525706778587 |
92 | 173 | 192.918958067331 | -19.9189580673313 |
93 | 178 | 171.895833067929 | 6.10416693207134 |
94 | 168 | 176.902919726587 | -8.90291972658724 |
95 | 152 | 166.892583843924 | -14.8925838439239 |
96 | 163 | 150.875294235134 | 12.1247057648663 |
97 | 172 | 161.889370464052 | 10.1106295359480 |
98 | 170 | 170.901108442574 | -0.901108442574156 |
99 | 156 | 168.900062296881 | -12.9000622968809 |
100 | 155 | 154.885085914487 | 0.114914085513220 |
101 | 178 | 153.885219324485 | 24.1147806755151 |
102 | 194 | 176.913215482057 | 17.0867845179435 |
103 | 164 | 192.933052457486 | -28.9330524574864 |
104 | 135 | 162.899462506720 | -27.8994625067202 |
105 | 139 | 133.867072506620 | 5.13292749338018 |
106 | 135 | 137.873031600706 | -2.87303160070579 |
107 | 109 | 133.869696142404 | -24.8696961424039 |
108 | 121 | 107.840823562498 | 13.1591764375017 |
109 | 131 | 119.85610076456 | 11.1438992354398 |
110 | 135 | 129.869038321951 | 5.130961678049 |
111 | 119 | 133.874995133815 | -14.8749951338153 |
112 | 121 | 117.857725944713 | 3.14227405528689 |
113 | 151 | 119.861373981192 | 31.138626018808 |
114 | 169 | 149.897524502000 | 19.1024754980002 |
115 | 135 | 167.919701602478 | -32.9197016024779 |
116 | 105 | 133.881483334368 | -28.8814833343679 |
117 | 112 | 103.847953252995 | 8.15204674700465 |
118 | 105 | 110.857417406467 | -5.85741740646749 |
119 | 82 | 103.850617212724 | -21.8506172127241 |
120 | 81 | 80.8252496453903 | 0.174750354609671 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 79.8254525225605 | 53.0698731131734 | 106.581031931948 |
122 | 78.650905045121 | 40.7908312503085 | 116.510978839934 |
123 | 77.4763575676816 | 31.080512879325 | 123.872202256038 |
124 | 76.3018100902421 | 22.6974202604850 | 129.906199919999 |
125 | 75.1272626128027 | 15.1609743212278 | 135.093550904377 |
126 | 73.9527151353632 | 8.22485421333582 | 139.680576057391 |
127 | 72.7781676579237 | 1.74282118542384 | 143.813514130424 |
128 | 71.6036201804842 | -4.38035117145721 | 147.587591532426 |
129 | 70.4290727030448 | -10.2107685227119 | 151.068913928801 |
130 | 69.2545252256053 | -15.7965338487652 | 154.305584299976 |
131 | 68.0799777481658 | -21.1739398262426 | 157.333895322574 |
132 | 66.9054302707264 | -26.3711658331901 | 160.182026374643 |