Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.0258617241640165 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 15928 | 17117 | -1189 |
4 | 16171 | 16666.250409969 | -495.250409968983 |
5 | 15937 | 16896.4423804743 | -959.442380474251 |
6 | 15713 | 16637.6295462792 | -924.629546279157 |
7 | 15594 | 16389.7170319994 | -795.717031999386 |
8 | 15683 | 16250.1384176052 | -567.138417605209 |
9 | 16438 | 16324.4712402863 | 113.528759713714 |
10 | 17032 | 17082.4072897547 | -50.4072897546866 |
11 | 17696 | 17675.1036703312 | 20.8963296688053 |
12 | 17745 | 18339.6440854451 | -594.644085445128 |
13 | 19394 | 18373.2655641316 | 1020.73443586842 |
14 | 20148 | 20048.6635165567 | 99.3364834432759 |
15 | 20108 | 20805.232529291 | -697.232529290959 |
16 | 18584 | 20747.2008939403 | -2163.20089394025 |
17 | 18441 | 19167.2567891098 | -726.256789109819 |
18 | 18391 | 19005.4745363576 | -614.474536357618 |
19 | 19178 | 18939.5831653925 | 238.416834607477 |
20 | 18079 | 19732.7490358052 | -1653.7490358052 |
21 | 18483 | 18590.9802344047 | -107.980234404698 |
22 | 19644 | 18992.1876793674 | 651.812320632642 |
23 | 19195 | 20170.0446698103 | -975.044669810268 |
24 | 19650 | 19695.828333512 | -45.8283335120395 |
25 | 20830 | 20149.6431337919 | 680.356866208145 |
26 | 23595 | 21347.2383353988 | 2247.76166460117 |
27 | 22937 | 24170.3693275552 | -1233.36932755519 |
28 | 21814 | 23480.4722702136 | -1666.4722702136 |
29 | 21928 | 22314.3744240344 | -386.374424034355 |
30 | 21777 | 22418.3821152559 | -641.382115255947 |
31 | 21383 | 22250.7948679075 | -867.794867907465 |
32 | 21467 | 21834.3521964027 | -367.352196402691 |
33 | 22052 | 21908.8518352283 | 143.148164771719 |
34 | 22680 | 22497.5538935802 | 182.446106419808 |
35 | 24320 | 23130.2722644592 | 1189.72773554078 |
36 | 24977 | 24801.0406749861 | 175.959325013944 |
37 | 25204 | 25462.5912865137 | -258.591286513652 |
38 | 25739 | 25682.9036699906 | 56.0963300093827 |
39 | 26434 | 26219.3544178039 | 214.645582196066 |
40 | 27525 | 26919.9055226437 | 605.094477356288 |
41 | 30695 | 28026.5543091103 | 2668.44569088973 |
42 | 32436 | 31265.5649155147 | 1170.43508448528 |
43 | 30160 | 33036.8343848216 | -2876.83438482157 |
44 | 30236 | 30686.4344874958 | -450.434487495753 |
45 | 31293 | 30750.7854750262 | 542.214524973824 |
46 | 31077 | 31821.8080775088 | -744.808077508773 |
47 | 32226 | 31586.5460564531 | 639.453943546891 |
48 | 33865 | 32752.0834379567 | 1112.91656204329 |
49 | 32810 | 34419.8653791018 | -1609.86537910184 |
50 | 32242 | 33323.2314847263 | -1081.23148472631 |
51 | 32700 | 32727.2689743109 | -27.2689743108676 |
52 | 32819 | 33184.563751619 | -365.563751619004 |
53 | 33947 | 33294.1096427103 | 652.890357289732 |
54 | 34148 | 34438.9945130398 | -290.994513039841 |
55 | 35261 | 34632.4688932104 | 628.531106789633 |
56 | 39506 | 35761.7237913227 | 3744.27620867734 |
57 | 41591 | 40103.5572298254 | 1487.44277017463 |
58 | 39148 | 42227.0250644574 | -3079.02506445738 |
59 | 41216 | 39704.3961675463 | 1511.60383245371 |
60 | 40225 | 41811.4888489065 | -1586.48884890648 |
61 | 41126 | 40779.4595119068 | 346.540488093226 |
62 | 42362 | 41689.4216464215 | 672.578353578494 |
63 | 40740 | 42942.8156822804 | -2202.81568228044 |
64 | 40256 | 41263.8470707211 | -1007.84707072113 |
65 | 39804 | 40753.7824077786 | -949.782407778628 |
66 | 41002 | 40277.2193971328 | 724.780602867177 |
67 | 41702 | 41493.9634731636 | 208.036526836397 |
68 | 42254 | 42199.3436564367 | 54.6563435633143 |
69 | 43605 | 42752.7571637177 | 852.242836282261 |
70 | 43271 | 44125.7976328704 | -854.797632870424 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
71 | 43769.6910922731 | 41474.8261750127 | 46064.5560095334 |
72 | 44268.3821845462 | 40980.7190438873 | 47556.045325205 |
73 | 44767.0732768192 | 40688.5911498098 | 48845.5554038287 |
74 | 45265.7643690923 | 40496.1404597519 | 50035.3882784327 |
75 | 45764.4554613654 | 40364.3016763787 | 51164.6092463521 |
76 | 46263.1465536385 | 40273.3129080675 | 52252.9801992094 |
77 | 46761.8376459115 | 40211.5937204318 | 53312.0815713913 |
78 | 47260.5287381846 | 40171.7015648835 | 54349.3559114858 |
79 | 47759.2198304577 | 40148.5380359684 | 55369.901624947 |
80 | 48257.9109227308 | 40138.4429486693 | 56377.3788967922 |
81 | 48756.6020150039 | 40138.6925379983 | 57374.5114920094 |
82 | 49255.2931072769 | 40147.2014992867 | 58363.3847152672 |