Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.809612696837393 |
beta | 0.0473915804428729 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 15579 | 15454.8089922599 | 124.191007740068 |
14 | 16348 | 16400.3568648049 | -52.3568648048931 |
15 | 15928 | 15936.5540171057 | -8.55401710571641 |
16 | 16171 | 16076.2728073862 | 94.7271926137564 |
17 | 15937 | 15798.0691121036 | 138.930887896397 |
18 | 15713 | 15559.5426103057 | 153.457389694258 |
19 | 15594 | 16823.7277073958 | -1229.72770739577 |
20 | 15683 | 15533.7166358653 | 149.283364134701 |
21 | 16438 | 14883.7372210847 | 1554.26277891533 |
22 | 17032 | 15974.9812595649 | 1057.01874043512 |
23 | 17696 | 17782.119494987 | -86.1194949869605 |
24 | 17745 | 17470.5171076639 | 274.482892336076 |
25 | 19394 | 18165.2386096222 | 1228.76139037782 |
26 | 20148 | 20284.2813371777 | -136.281337177661 |
27 | 20108 | 19784.1173922728 | 323.882607727217 |
28 | 18584 | 20388.1215868341 | -1804.12158683409 |
29 | 18441 | 18583.4361742659 | -142.436174265898 |
30 | 18391 | 18113.6623134266 | 277.337686573439 |
31 | 19178 | 19399.4258170136 | -221.425817013573 |
32 | 18079 | 19280.3705972743 | -1201.37059727426 |
33 | 18483 | 17739.5313206564 | 743.468679343609 |
34 | 19644 | 18045.9440438363 | 1598.0559561637 |
35 | 19195 | 20194.7067486545 | -999.706748654538 |
36 | 19650 | 19187.1453712384 | 462.854628761623 |
37 | 20830 | 20267.1571421582 | 562.842857841795 |
38 | 23595 | 21617.9561405674 | 1977.04385943264 |
39 | 22937 | 22906.270793313 | 30.7292066869595 |
40 | 21814 | 22854.2970962679 | -1040.29709626792 |
41 | 21928 | 22036.523182401 | -108.523182400986 |
42 | 21777 | 21678.9926122309 | 98.0073877691466 |
43 | 21383 | 22953.1198399603 | -1570.11983996029 |
44 | 21467 | 21533.3512110903 | -66.351211090263 |
45 | 22052 | 21290.9246274714 | 761.075372528609 |
46 | 22680 | 21772.2164187407 | 907.783581259286 |
47 | 24320 | 22925.1230107501 | 1394.87698924988 |
48 | 24977 | 24250.4879120826 | 726.512087917421 |
49 | 25204 | 25855.807168598 | -651.807168598043 |
50 | 25739 | 26775.2833638674 | -1036.2833638674 |
51 | 26434 | 25146.2164174611 | 1287.78358253885 |
52 | 27525 | 25857.9406595961 | 1667.05934040385 |
53 | 30695 | 27545.775993465 | 3149.22400653503 |
54 | 32436 | 29963.6984070832 | 2472.30159291681 |
55 | 30160 | 33490.5159313452 | -3330.5159313452 |
56 | 30236 | 31219.031903182 | -983.031903181985 |
57 | 31293 | 30567.4040801462 | 725.595919853771 |
58 | 31077 | 31174.6265685892 | -97.626568589174 |
59 | 32226 | 31914.283426123 | 311.716573876969 |
60 | 33865 | 32338.4654570235 | 1526.53454297652 |
61 | 32810 | 34687.7878220401 | -1877.78782204006 |
62 | 32242 | 35041.5558079968 | -2799.55580799683 |
63 | 32700 | 32348.1411361482 | 351.858863851827 |
64 | 32819 | 32283.520450614 | 535.479549385975 |
65 | 33947 | 33339.0582727946 | 607.941727205391 |
66 | 34148 | 33376.8975300232 | 771.102469976795 |
67 | 35261 | 34203.2095336903 | 1057.79046630974 |
68 | 39506 | 36009.7786326968 | 3496.22136730315 |
69 | 41591 | 39512.8140826866 | 2078.18591731336 |
70 | 39148 | 41116.2647384111 | -1968.26473841108 |
71 | 41216 | 40712.1178795365 | 503.882120463517 |
72 | 40225 | 41672.6791013547 | -1447.67910135468 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
73 | 40997.3016953853 | 38461.3126987876 | 43533.290691983 |
74 | 43097.4483953332 | 39719.5888451858 | 46475.3079454806 |
75 | 43455.1965481117 | 39405.1938536652 | 47505.1992425583 |
76 | 43144.8518217076 | 38527.1422562548 | 47762.5613871603 |
77 | 44066.256247659 | 38810.605364051 | 49321.9071312669 |
78 | 43575.0176789178 | 37847.9201627327 | 49302.115195103 |
79 | 43927.9349360529 | 37653.2372013262 | 50202.6326707795 |
80 | 45622.2336409007 | 38633.3451178593 | 52611.1221639422 |
81 | 45944.7049508275 | 38434.4723638857 | 53454.9375377692 |
82 | 44812.764952376 | 37013.4819096258 | 52612.0479951263 |
83 | 46591.9877975456 | 38035.98929011 | 55147.9863049811 |
84 | 46655.3880697114 | 37999.7133236478 | 55311.062815775 |