Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.698186625912078 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 42206 | 42364 | -158 |
3 | 42046 | 42253.6865131059 | -207.686513105895 |
4 | 41715 | 42108.682567273 | -393.682567273048 |
5 | 44991 | 41833.8186639483 | 3157.18133605173 |
6 | 44818 | 44038.1204483588 | 779.879551641185 |
7 | 42364 | 44582.621921137 | -2218.621921137 |
8 | 40733 | 43033.6097678438 | -2300.60976784379 |
9 | 40891 | 41427.3547964926 | -536.35479649256 |
10 | 40891 | 41052.8790508377 | -161.879050837662 |
11 | 41067 | 40939.8572625275 | 127.142737472532 |
12 | 41382 | 41028.6266214126 | 353.373378587363 |
13 | 41873 | 41275.3471882957 | 597.652811704298 |
14 | 41873 | 41692.6203883664 | 180.379611633609 |
15 | 41558 | 41818.5590207962 | -260.559020796194 |
16 | 40733 | 41636.6401972155 | -903.640197215544 |
17 | 44991 | 41005.7306968831 | 3985.2693031169 |
18 | 45640 | 43788.1924249773 | 1851.80757502274 |
19 | 44660 | 45081.0997076208 | -421.099707620815 |
20 | 42364 | 44787.0935235845 | -2423.09352358447 |
21 | 43346 | 43095.3220320836 | 250.677967916381 |
22 | 41873 | 43270.3420366937 | -1397.34203669366 |
23 | 42538 | 42294.7365148494 | 243.263485150601 |
24 | 42855 | 42464.5798267543 | 390.420173245693 |
25 | 43186 | 42737.1659702007 | 448.834029799276 |
26 | 42364 | 43050.5358870608 | -686.535887060803 |
27 | 42538 | 42571.2057125063 | -33.2057125062638 |
28 | 41382 | 42548.0219281305 | -1166.02192813051 |
29 | 44991 | 41733.9210123896 | 3257.07898761042 |
30 | 46131 | 44007.9700010784 | 2123.02999892157 |
31 | 45151 | 45490.2411527356 | -339.241152735602 |
32 | 43346 | 45253.3875169366 | -1907.38751693661 |
33 | 45309 | 43921.6750621798 | 1387.32493782018 |
34 | 43186 | 44890.2867795602 | -1704.28677956018 |
35 | 45151 | 43700.3765433525 | 1450.6234566475 |
36 | 44991 | 44713.1824400181 | 277.817559981864 |
37 | 45482 | 44907.150944841 | 574.849055159 |
38 | 43678 | 45308.5028670712 | -1630.50286707121 |
39 | 45640 | 44170.1075717708 | 1469.89242822921 |
40 | 45482 | 45196.3668066899 | 285.633193310146 |
41 | 48426 | 45395.7920821756 | 3030.20791782445 |
42 | 47762 | 47511.4427241335 | 250.557275866529 |
43 | 45151 | 47686.3784631684 | -2535.37846316845 |
44 | 43835 | 45916.2111285587 | -2081.21112855872 |
45 | 45640 | 44463.1373528996 | 1176.86264710036 |
46 | 43186 | 45284.8071136406 | -2098.8071136406 |
47 | 44991 | 43819.4480565276 | 1171.5519434724 |
48 | 45309 | 44637.4099550213 | 671.590044978664 |
49 | 45973 | 45106.3051425211 | 866.694857478869 |
50 | 44502 | 45711.4199007597 | -1209.41990075965 |
51 | 45309 | 44867.0191009374 | 441.980899062648 |
52 | 45800 | 45175.6042535715 | 624.395746428512 |
53 | 47604 | 45611.5490130043 | 1992.45098699573 |
54 | 46131 | 47002.65164491 | -871.651644910009 |
55 | 44169 | 46394.0761239796 | -2225.07612397958 |
56 | 42046 | 44840.5577325808 | -2794.55773258075 |
57 | 44011 | 42889.4348983537 | 1121.56510164631 |
58 | 38611 | 43672.4966524129 | -5061.49665241286 |
59 | 41224 | 40138.6273825994 | 1085.37261740056 |
60 | 42695 | 40896.4200281997 | 1798.5799718003 |
61 | 44169 | 42152.164510144 | 2016.83548985601 |
62 | 42046 | 43560.2920758263 | -1514.29207582629 |
63 | 42046 | 42503.0336007597 | -457.033600759736 |
64 | 42046 | 42183.9388531169 | -137.938853116852 |
65 | 43186 | 42087.631790677 | 1098.36820932299 |
66 | 41558 | 42854.4977847533 | -1296.49778475332 |
67 | 39420 | 41949.3003709139 | -2529.30037091392 |
68 | 37631 | 40183.3766790274 | -2552.37667902736 |
69 | 38929 | 38401.3414174406 | 527.65858255943 |
70 | 33862 | 38769.7455828313 | -4907.74558283129 |
71 | 36967 | 35343.2232535194 | 1623.77674648059 |
72 | 38771 | 36476.9224613792 | 2294.07753862082 |
73 | 39102 | 38078.6167176495 | 1023.38328235046 |
74 | 37298 | 38793.1292385686 | -1495.12923856863 |
75 | 37455 | 37749.2500001899 | -294.250000189902 |
76 | 36967 | 37543.8085853827 | -576.808585382685 |
77 | 38611 | 37141.0885453572 | 1469.91145464277 |
78 | 37455 | 38167.3610642638 | -712.36106426378 |
79 | 35178 | 37670.0000963743 | -2492.00009637432 |
80 | 33531 | 35930.1189573142 | -2399.11895731416 |
81 | 36315 | 34255.0861873453 | 2059.91381265472 |
82 | 30269 | 35693.2904618724 | -5424.29046187236 |
83 | 34195 | 31906.1234063306 | 2288.87659366937 |
84 | 35984 | 33504.1864323938 | 2479.81356760622 |
85 | 35984 | 35235.5591000518 | 748.44089994824 |
86 | 33862 | 35758.1105266812 | -1896.11052668122 |
87 | 31900 | 34434.2715157013 | -2534.27151570129 |
88 | 31742 | 32664.8770370087 | -922.877037008715 |
89 | 33531 | 32020.5366324079 | 1510.46336759214 |
90 | 31900 | 33075.1219545908 | -1175.12195459081 |
91 | 28798 | 32254.6675220798 | -3456.66752207985 |
92 | 26660 | 29841.2684879391 | -3181.26848793905 |
93 | 28956 | 27620.1493762245 | 1335.85062377553 |
94 | 23558 | 28552.8224159609 | -4994.82241596085 |
95 | 28464 | 25065.5042063311 | 3398.49579366887 |
96 | 31075 | 27438.2885176892 | 3636.71148231081 |
97 | 31900 | 29977.3918369395 | 1922.60816306051 |
98 | 30096 | 31319.7311432577 | -1223.73114325773 |
99 | 27816 | 30465.3384253231 | -2649.33842532308 |
100 | 29447 | 28615.6057692475 | 831.394230752459 |
101 | 30096 | 29196.0741020194 | 899.925897980633 |
102 | 29604 | 29824.3903283014 | -220.390328301364 |
103 | 24696 | 29670.516748601 | -4974.51674860098 |
104 | 22418 | 26197.3756843521 | -3779.37568435214 |
105 | 24047 | 23558.6661272402 | 488.333872759835 |
106 | 19140 | 23899.6143061809 | -4759.61430618093 |
107 | 24207 | 20576.5152531056 | 3630.48474689439 |
108 | 26011 | 23111.2711489651 | 2899.72885103493 |
109 | 27482 | 25135.8230515291 | 2346.17694847094 |
110 | 25029 | 26773.8924189747 | -1744.89241897468 |
111 | 22733 | 25555.6318683912 | -2822.63186839118 |
112 | 24047 | 23584.9080480072 | 462.091951992763 |
113 | 24696 | 23907.5344688302 | 788.465531169808 |
114 | 23398 | 24458.0305576856 | -1060.03055768562 |
115 | 18491 | 23717.9313992514 | -5226.9313992514 |
116 | 16353 | 20068.5578017342 | -3715.55780173416 |
117 | 18316 | 17474.4050367601 | 841.59496323991 |
118 | 12918 | 18061.9953845292 | -5143.99538452916 |
119 | 18807 | 14470.5266032974 | 4336.47339670256 |
120 | 22418 | 17498.1943324987 | 4919.80566750131 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
121 | 20933.1368516346 | 16556.0273189716 | 25310.2463842975 |
122 | 20933.1368516346 | 15594.7415606096 | 26271.5321426595 |
123 | 20933.1368516346 | 14781.8897662424 | 27084.3839370267 |
124 | 20933.1368516346 | 14064.5695244655 | 27801.7041788036 |
125 | 20933.1368516346 | 13415.3849569414 | 28450.8887463277 |
126 | 20933.1368516346 | 12817.9677238547 | 29048.3059794144 |
127 | 20933.1368516346 | 12261.6118188171 | 29604.661884452 |
128 | 20933.1368516346 | 11738.8602179299 | 30127.4134853392 |
129 | 20933.1368516346 | 11244.2721483065 | 30622.0015549626 |
130 | 20933.1368516346 | 10773.7335393477 | 31092.5401639214 |
131 | 20933.1368516346 | 10324.0439552549 | 31542.2297480142 |
132 | 20933.1368516346 | 9892.65549861733 | 31973.6182046518 |