Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.549951023915406 |
beta | 0 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 3233 | 3475.99346963565 | -242.99346963565 |
14 | 3554 | 3635.41124175158 | -81.4112417515762 |
15 | 3952 | 3960.20759885758 | -8.20759885757889 |
16 | 3951 | 3943.54749810755 | 7.45250189244643 |
17 | 3685 | 3687.13881766717 | -2.13881766717304 |
18 | 4312 | 4372.58790774295 | -60.5879077429518 |
19 | 3867 | 3507.19389379001 | 359.806106209986 |
20 | 4140 | 3654.15916915549 | 485.840830844509 |
21 | 4114 | 4603.99269052276 | -489.992690522761 |
22 | 3818 | 3929.48957769919 | -111.489577699195 |
23 | 3377 | 3966.2149123787 | -589.214912378702 |
24 | 3453 | 4239.86210717385 | -786.86210717385 |
25 | 3502 | 2469.6646157656 | 1032.3353842344 |
26 | 4017 | 3378.79733693817 | 638.202663061835 |
27 | 5410 | 4153.86011765594 | 1256.13988234406 |
28 | 5184 | 4846.08179089469 | 337.918209105306 |
29 | 5529 | 4703.37678392975 | 825.623216070252 |
30 | 6434 | 6096.47160154584 | 337.528398454157 |
31 | 4962 | 5347.75345996853 | -385.753459968526 |
32 | 2980 | 5134.27099399967 | -2154.27099399967 |
33 | 2937 | 4167.11792689324 | -1230.11792689324 |
34 | 3023 | 3285.799958616 | -262.799958615999 |
35 | 2731 | 3019.93403199535 | -288.934031995349 |
36 | 3163 | 3252.29238056144 | -89.2923805614373 |
37 | 3146 | 2639.19382644302 | 506.806173556982 |
38 | 3173 | 3026.66860624804 | 146.331393751962 |
39 | 3724 | 3579.41378313056 | 144.58621686944 |
40 | 3224 | 3365.28386943372 | -141.283869433721 |
41 | 4114 | 3185.16374706282 | 928.836252937181 |
42 | 3450 | 4160.97027043373 | -710.970270433727 |
43 | 2957 | 3014.55692393449 | -57.5569239344932 |
44 | 3882 | 2318.95685559063 | 1563.04314440937 |
45 | 4284 | 3741.77643351038 | 542.22356648962 |
46 | 4181 | 4361.54631962597 | -180.54631962597 |
47 | 3760 | 4076.98858855594 | -316.988588555939 |
48 | 4457 | 4604.95024191718 | -147.950241917182 |
49 | 4167 | 4083.7909881775 | 83.2090118225001 |
50 | 3962 | 4067.43124170638 | -105.431241706383 |
51 | 5247 | 4613.52498947583 | 633.475010524166 |
52 | 5157 | 4408.61379037105 | 748.386209628951 |
53 | 3697 | 5319.5862888327 | -1622.5862888327 |
54 | 3514 | 4100.45237461397 | -586.452374613966 |
55 | 3786 | 3275.39244395426 | 510.607556045737 |
56 | 3297 | 3412.17875264251 | -115.17875264251 |
57 | 3571 | 3418.58030478166 | 152.41969521834 |
58 | 3871 | 3492.12547521366 | 378.87452478634 |
59 | 3492 | 3473.12736122704 | 18.8726387729603 |
60 | 3051 | 4200.88030345826 | -1149.88030345826 |
61 | 3735 | 3292.66097295228 | 442.339027047721 |
62 | 3645 | 3405.65476851651 | 239.345231483492 |
63 | 4852 | 4351.29039818039 | 500.709601819607 |
64 | 4232 | 4154.6880570328 | 77.3119429672006 |
65 | 3804 | 3609.4868358689 | 194.513164131103 |
66 | 4464 | 3834.23784792159 | 629.762152078406 |
67 | 4259 | 4154.79706495227 | 104.202935047731 |
68 | 3373 | 3740.78890013843 | -367.788900138431 |
69 | 4134 | 3743.18827419066 | 390.811725809341 |
70 | 4488 | 4052.58756075839 | 435.412439241608 |
71 | 3333 | 3863.50754039384 | -530.507540393835 |
72 | 4772 | 3674.40370147726 | 1097.59629852274 |
73 | 4929 | 4891.04975053604 | 37.950249463961 |
74 | 5555 | 4625.76751206444 | 929.232487935558 |
75 | 7183 | 6448.19400670231 | 734.805993297688 |
76 | 9266 | 5931.39221183828 | 3334.60778816172 |
77 | 4003 | 6806.20009983782 | -2803.20009983782 |
78 | 3051 | 5679.74465653584 | -2628.74465653584 |
79 | 3507 | 3982.93664240292 | -475.936642402925 |
80 | 3273 | 3111.96037507528 | 161.039624924722 |
81 | 3942 | 3707.92097643141 | 234.079023568589 |
82 | 3216 | 3930.35484471544 | -714.354844715442 |
83 | 3232 | 2835.84387544918 | 396.156124550821 |
84 | 3593 | 3752.35338979882 | -159.353389798823 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
85 | 3760.95923125354 | 2059.01391811387 | 5462.9045443932 |
86 | 3808.33059897879 | 1855.86753399937 | 5760.7936639582 |
87 | 4620.03458681008 | 2256.92333432362 | 6983.14583929654 |
88 | 4536.57569210004 | 2006.77083084815 | 7066.38055335194 |
89 | 2521.11024569083 | 453.307264545565 | 4588.91322683609 |
90 | 2568.19920018454 | 269.60134613058 | 4866.7970542385 |
91 | 3154.68190284977 | 340.575581635867 | 5968.78822406367 |
92 | 2859.81293725648 | 59.3361186917973 | 5660.28975582117 |
93 | 3324.49962004933 | 19.0281173174685 | 6629.9711227812 |
94 | 3008.56818875554 | -207.236169611215 | 6224.37254712229 |
95 | 2805.93444270211 | -401.269663933178 | 6013.13854933741 |
96 | 3189.50695822277 | -113.34442829618 | 6492.35834474172 |