Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.594091053904783 |
beta | 0.374196561823787 |
gamma | 0.693700862612219 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
5 | 200779 | 193857.86875 | 6921.13124999998 |
6 | 204428 | 202551.478155215 | 1876.52184478543 |
7 | 207617 | 210393.918864677 | -2776.91886467711 |
8 | 212071 | 206924.464049405 | 5146.53595059502 |
9 | 214239 | 224646.345835572 | -10407.3458355723 |
10 | 215883 | 220255.125632632 | -4372.12563263174 |
11 | 223484 | 220316.192412998 | 3167.80758700179 |
12 | 221529 | 221172.28584846 | 356.714151539549 |
13 | 225247 | 229166.872676244 | -3919.87267624363 |
14 | 226699 | 229269.353236709 | -2570.35323670949 |
15 | 231406 | 231864.630352412 | -458.630352412263 |
16 | 232324 | 228309.265272053 | 4014.73472794739 |
17 | 237192 | 236620.575448753 | 571.424551246804 |
18 | 236727 | 240117.463158815 | -3390.46315881546 |
19 | 240698 | 242983.992694058 | -2285.99269405808 |
20 | 240688 | 239360.235012365 | 1327.76498763464 |
21 | 245283 | 244265.9632392 | 1017.03676079967 |
22 | 243556 | 246171.349805591 | -2615.34980559099 |
23 | 247826 | 249241.026895512 | -1415.0268955116 |
24 | 245798 | 246777.547048244 | -979.547048243956 |
25 | 250479 | 249337.381124557 | 1141.61887544286 |
26 | 249216 | 249434.025038334 | -218.025038333988 |
27 | 251896 | 253938.908589686 | -2042.90858968601 |
28 | 247616 | 250758.440679939 | -3142.44067993888 |
29 | 249994 | 251683.178258106 | -1689.17825810626 |
30 | 246552 | 248138.500344917 | -1586.50034491657 |
31 | 248771 | 249435.591086078 | -664.59108607826 |
32 | 247551 | 245189.82881535 | 2361.17118465033 |
33 | 249745 | 249442.377324503 | 302.622675496677 |
34 | 245742 | 247201.669079551 | -1459.66907955092 |
35 | 249019 | 248953.641809106 | 65.3581908937776 |
36 | 245841 | 246275.742891004 | -434.742891004193 |
37 | 248771 | 247948.28297532 | 822.717024679645 |
38 | 244723 | 245296.617566287 | -573.617566287227 |
39 | 246878 | 247977.661584934 | -1099.66158493413 |
40 | 246014 | 244181.084601035 | 1832.91539896512 |
41 | 248496 | 247773.278821491 | 722.721178508742 |
42 | 244351 | 244865.181820142 | -514.181820142257 |
43 | 248016 | 247642.779986517 | 373.220013483427 |
44 | 246509 | 246083.780703617 | 425.21929638306 |
45 | 249426 | 248750.925691315 | 675.074308685347 |
46 | 247840 | 245679.501734709 | 2160.49826529145 |
47 | 251035 | 251103.843136672 | -68.8431366720179 |
48 | 250161 | 250006.452020969 | 154.547979031107 |
49 | 254278 | 253232.567542782 | 1045.43245721792 |
50 | 250801 | 251531.187881904 | -730.187881904189 |
51 | 253985 | 254699.595714861 | -714.595714860945 |
52 | 249174 | 253227.049688093 | -4053.04968809334 |
53 | 251287 | 253214.524668936 | -1927.52466893601 |
54 | 247947 | 247596.251904122 | 350.748095877643 |
55 | 249992 | 250000.816227863 | -8.8162278632517 |
56 | 243805 | 246754.018924213 | -2949.01892421348 |
57 | 255812 | 246987.817578133 | 8824.18242186715 |
58 | 250417 | 249780.655217727 | 636.344782272761 |
59 | 253033 | 253699.236931496 | -666.23693149563 |
60 | 248705 | 250533.415141752 | -1828.41514175225 |
61 | 253950 | 256296.606901658 | -2346.60690165771 |
62 | 251484 | 249212.671099804 | 2271.32890019621 |
63 | 251093 | 253164.489084398 | -2071.48908439768 |
64 | 245996 | 247952.863976388 | -1956.86397638821 |
65 | 252721 | 252581.568103102 | 139.431896898343 |
66 | 248019 | 247915.279431006 | 103.720568993769 |
67 | 250464 | 248515.016731504 | 1948.98326849574 |
68 | 245571 | 245776.496867017 | -205.496867017326 |
69 | 252690 | 252477.589619012 | 212.410380987654 |
70 | 250183 | 248302.468241621 | 1880.53175837855 |
71 | 253639 | 251330.245378833 | 2308.75462116735 |
72 | 254436 | 249131.649158065 | 5304.35084193503 |
73 | 265280 | 261381.487880857 | 3898.51211914272 |
74 | 268705 | 262843.121427061 | 5861.87857293943 |
75 | 270643 | 272219.00667257 | -1576.00667256973 |
76 | 271480 | 271554.64455014 | -74.644550140365 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
77 | 282015.865498848 | 276525.680709346 | 287506.050288351 |
78 | 282650.455993896 | 275563.000601895 | 289737.911385897 |
79 | 286082.545418822 | 276985.700226495 | 295179.390611149 |
80 | 286760.633392828 | 275328.962373197 | 298192.304412459 |