Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.405343002238435 |
beta | 0.0645195510983809 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 18843 | 18842.1805555556 | 0.819444444445253 |
14 | 18843 | 18800.8258088541 | 42.1741911458885 |
15 | 18701 | 18632.3368819187 | 68.6631180812547 |
16 | 18330 | 18259.547438349 | 70.4525616510073 |
17 | 20246 | 20194.7841805802 | 51.2158194198055 |
18 | 20538 | 20490.3545348324 | 47.6454651675595 |
19 | 20097 | 19387.8487213138 | 709.151278686215 |
20 | 19064 | 19014.5674401534 | 49.432559846573 |
21 | 19506 | 19180.1249136202 | 325.875086379849 |
22 | 18843 | 19407.4255614212 | -564.425561421165 |
23 | 19142 | 19328.9212381858 | -186.921238185758 |
24 | 19285 | 19427.7138505994 | -142.713850599444 |
25 | 19434 | 19577.1389090191 | -143.138909019101 |
26 | 19064 | 19510.5861601928 | -446.586160192797 |
27 | 19142 | 19155.5137615693 | -13.5137615692947 |
28 | 18622 | 18744.1097559272 | -122.109755927173 |
29 | 20246 | 20578.4486073918 | -332.448607391791 |
30 | 20759 | 20694.9414928807 | 64.0585071192763 |
31 | 20318 | 19971.4482530011 | 346.551746998943 |
32 | 19506 | 19028.3911353587 | 477.608864641315 |
33 | 20389 | 19512.6009611919 | 876.3990388081 |
34 | 19434 | 19428.7323353508 | 5.26766464922548 |
35 | 20318 | 19815.6368969765 | 502.36310302349 |
36 | 20246 | 20248.1430029815 | -2.14300298152375 |
37 | 20467 | 20485.9996697032 | -18.9996697031747 |
38 | 19655 | 20324.2703818225 | -669.270381822476 |
39 | 20538 | 20165.5917850625 | 372.408214937477 |
40 | 20467 | 19885.2617876901 | 581.73821230985 |
41 | 21792 | 21937.4490396091 | -145.449039609131 |
42 | 21493 | 22428.0451587153 | -935.045158715329 |
43 | 20318 | 21503.9482512598 | -1185.94825125979 |
44 | 19726 | 20013.9476648714 | -287.947664871379 |
45 | 20538 | 20401.2772714193 | 136.72272858068 |
46 | 19434 | 19456.5066361455 | -22.506636145521 |
47 | 20246 | 20083.9729659896 | 162.027034010418 |
48 | 20389 | 20025.8360917978 | 363.16390820215 |
49 | 20688 | 20358.6150806772 | 329.384919322805 |
50 | 20026 | 19917.3958203867 | 108.604179613299 |
51 | 20389 | 20679.7909046778 | -290.79090467783 |
52 | 20610 | 20224.0991896587 | 385.900810341296 |
53 | 21422 | 21728.3383427157 | -306.338342715699 |
54 | 20759 | 21643.83279537 | -884.832795369988 |
55 | 19876 | 20551.85356388 | -675.853563879955 |
56 | 18921 | 19776.9246238634 | -855.924623863411 |
57 | 19805 | 20146.0139225406 | -341.013922540635 |
58 | 17375 | 18859.867148559 | -1484.86714855905 |
59 | 18551 | 18913.0235876563 | -362.023587656342 |
60 | 19213 | 18657.082123005 | 555.91787699503 |
61 | 19876 | 18947.9548918056 | 928.045108194383 |
62 | 18921 | 18533.8152472372 | 387.184752762842 |
63 | 18921 | 19094.6192369152 | -173.619236915241 |
64 | 18921 | 19014.8773401235 | -93.877340123483 |
65 | 19434 | 19826.5051383776 | -392.50513837759 |
66 | 18701 | 19274.3214452462 | -573.321445246162 |
67 | 17739 | 18352.2836740438 | -613.283674043832 |
68 | 16934 | 17416.6743991959 | -482.674399195879 |
69 | 17518 | 18174.0526749963 | -656.05267499627 |
70 | 15238 | 16002.567114448 | -764.567114447986 |
71 | 16635 | 16956.796886815 | -321.796886814987 |
72 | 17447 | 17205.4713541382 | 241.528645861817 |
73 | 17596 | 17524.4246353758 | 71.5753646241938 |
74 | 16784 | 16353.3236370724 | 430.676362927628 |
75 | 16855 | 16511.2371048176 | 343.762895182372 |
76 | 16635 | 16615.1288480885 | 19.8711519115386 |
77 | 17375 | 17224.7548409977 | 150.245159002276 |
78 | 16855 | 16728.713953535 | 126.286046465029 |
79 | 15830 | 16028.456336152 | -198.45633615202 |
80 | 15089 | 15311.4739029501 | -222.473902950085 |
81 | 16342 | 16050.8386940612 | 291.161305938807 |
82 | 13621 | 14203.1595510915 | -582.159551091456 |
83 | 15388 | 15503.7825193008 | -115.782519300783 |
84 | 16193 | 16185.4958918459 | 7.50410815414398 |
85 | 16193 | 16316.9516712733 | -123.951671273302 |
86 | 15238 | 15283.4501633487 | -45.4501633486707 |
87 | 14355 | 15187.5465361851 | -832.546536185131 |
88 | 14284 | 14582.1226643146 | -298.122664314593 |
89 | 15089 | 15092.161228972 | -3.1612289719742 |
90 | 14355 | 14467.4600379739 | -112.460037973851 |
91 | 12959 | 13418.8435733546 | -459.843573354592 |
92 | 11997 | 12516.3170337982 | -519.317033798232 |
93 | 13030 | 13367.7217012159 | -337.721701215905 |
94 | 10601 | 10656.2823706672 | -55.2823706671534 |
95 | 12809 | 12372.0643611106 | 436.935638889379 |
96 | 13984 | 13289.8450940591 | 694.154905940939 |
97 | 14355 | 13578.1302055652 | 776.869794434753 |
98 | 13543 | 12936.6819585135 | 606.318041486511 |
99 | 12517 | 12634.1911583184 | -117.191158318408 |
100 | 13251 | 12652.5143564822 | 598.485643517823 |
101 | 13543 | 13740.820176685 | -197.820176685014 |
102 | 13322 | 13006.561684829 | 315.438315171043 |
103 | 11113 | 11970.3490485987 | -857.349048598711 |
104 | 10088 | 10906.4666311221 | -818.466631122124 |
105 | 10821 | 11771.9130078121 | -950.91300781206 |
106 | 8613 | 8991.15185093074 | -378.151850930741 |
107 | 10893 | 10871.5944354394 | 21.4055645606059 |
108 | 11705 | 11765.8656219288 | -60.8656219287805 |
109 | 12367 | 11769.5151464491 | 597.484853550866 |
110 | 11263 | 10921.4630154278 | 341.536984572183 |
111 | 10230 | 10042.0088985294 | 187.991101470623 |
112 | 10821 | 10578.2027427688 | 242.797257231205 |
113 | 11113 | 11008.086712797 | 104.913287203048 |
114 | 10529 | 10668.9518940507 | -139.951894050657 |
115 | 8321 | 8706.03422405533 | -385.034224055335 |
116 | 7359 | 7824.36566716361 | -465.365667163611 |
117 | 8242 | 8731.05602401265 | -489.056024012647 |
118 | 5813 | 6467.05767078636 | -654.05767078636 |
119 | 8463 | 8455.00361197293 | 7.99638802706613 |
120 | 10088 | 9276.30589859216 | 811.694101407837 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 10029.3433315125 | 9116.3718452625 | 10942.3148177626 |
122 | 8775.48716645979 | 7781.14913149633 | 9769.82520142326 |
123 | 7645.93768807576 | 6567.38245045927 | 8724.49292569225 |
124 | 8113.25647156729 | 6947.76218559821 | 9278.75075753637 |
125 | 8331.11579037419 | 7076.07200812555 | 9586.15957262284 |
126 | 7769.4857470575 | 6422.37941410924 | 9116.59208000576 |
127 | 5686.85820988366 | 4245.26227522384 | 7128.45414454348 |
128 | 4892.86208726968 | 3354.42613718521 | 6431.29803735415 |
129 | 5965.6391832268 | 4328.08165727565 | 7603.19670917795 |
130 | 3806.08860347082 | 2067.19025935618 | 5544.98694758546 |
131 | 6474.28431885793 | 4631.88269296724 | 8316.68594474861 |
132 | 7791.49766428505 | 5843.4823337408 | 9739.51299482929 |