Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.0922981936893189 |
gamma | 0.433108278706043 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 101397 | 96474.2262810512 | 4922.77371894875 |
14 | 97994 | 98326.399919701 | -332.399919700954 |
15 | 94044 | 94389.1181365008 | -345.118136500751 |
16 | 91159 | 91555.1131305944 | -396.113130594356 |
17 | 87239 | 87704.6233375337 | -465.623337533689 |
18 | 89235 | 89703.7044534013 | -468.704453401326 |
19 | 118647 | 117845.772628058 | 801.22737194167 |
20 | 125620 | 127761.537998307 | -2141.53799830689 |
21 | 125154 | 125475.920836253 | -321.920836253063 |
22 | 117529 | 119486.218281902 | -1957.21828190197 |
23 | 109459 | 110229.333517919 | -770.333517919251 |
24 | 108483 | 108092.668042184 | 390.331957815768 |
25 | 107137 | 107271.619819706 | -134.619819706102 |
26 | 104699 | 103305.305135193 | 1393.69486480746 |
27 | 100804 | 100428.855794703 | 375.144205297096 |
28 | 96066 | 97795.786654125 | -1729.78665412503 |
29 | 91971 | 92003.6665251103 | -32.6665251103113 |
30 | 93228 | 94182.4737242207 | -954.47372422066 |
31 | 120144 | 122567.956054974 | -2423.956054974 |
32 | 127233 | 128506.074067418 | -1273.07406741826 |
33 | 127166 | 126309.573889743 | 856.426110257351 |
34 | 118194 | 120771.076124176 | -2577.07612417616 |
35 | 109940 | 110217.708812663 | -277.708812663244 |
36 | 106683 | 107989.967478415 | -1306.96747841456 |
37 | 102834 | 104784.426617862 | -1950.4266178619 |
38 | 99882 | 98332.860857286 | 1549.13914271408 |
39 | 96666 | 95047.2316276171 | 1618.76837238288 |
40 | 92540 | 93156.8721325465 | -616.872132546545 |
41 | 88744 | 88121.5113452989 | 622.488654701127 |
42 | 89321 | 90424.0899788703 | -1103.08997887027 |
43 | 115870 | 116820.025295937 | -950.025295936648 |
44 | 122401 | 123415.211564262 | -1014.21156426215 |
45 | 122030 | 121018.498579701 | 1011.50142029904 |
46 | 113802 | 115442.722074325 | -1640.72207432544 |
47 | 105791 | 105773.505002282 | 17.4949977184733 |
48 | 103076 | 103598.277304862 | -522.277304862204 |
49 | 98658 | 100997.683701730 | -2339.68370173041 |
50 | 96945 | 94064.2553937724 | 2880.7446062276 |
51 | 92497 | 92113.3864757153 | 383.613524284694 |
52 | 90687 | 88901.0424991477 | 1785.95750085231 |
53 | 88796 | 86338.3739136097 | 2457.6260863903 |
54 | 90015 | 90629.9056220935 | -614.905622093458 |
55 | 113228 | 117986.747390199 | -4758.74739019891 |
56 | 118711 | 120499.859214778 | -1788.85921477847 |
57 | 117460 | 117195.414722651 | 264.585277349222 |
58 | 106556 | 110890.555396084 | -4334.55539608361 |
59 | 97347 | 98582.3318794162 | -1235.33187941618 |
60 | 92657 | 94764.2323703424 | -2107.23237034245 |
61 | 93118 | 90080.1897047657 | 3037.81029523433 |
62 | 89037 | 88579.1159120853 | 457.884087914703 |
63 | 83570 | 84202.430136789 | -632.430136789088 |
64 | 81693 | 79848.9665253867 | 1844.03347461326 |
65 | 75956 | 77346.4914324392 | -1390.49143243923 |
66 | 73993 | 76760.1513256966 | -2767.15132569664 |
67 | 97088 | 95723.3323528899 | 1364.66764711009 |
68 | 102394 | 102503.882472263 | -109.882472262689 |
69 | 96549 | 100407.271713637 | -3858.27171363732 |
70 | 89727 | 90135.1862383517 | -408.1862383517 |
71 | 82336 | 82353.0623957618 | -17.0623957618373 |
72 | 82653 | 79599.7177472679 | 3053.28225273211 |
73 | 82303 | 80295.0255840808 | 2007.97441591919 |
74 | 79596 | 78167.0059579015 | 1428.99404209854 |
75 | 74472 | 75251.5873104856 | -779.587310485585 |
76 | 73562 | 71113.6564049752 | 2448.34359502481 |
77 | 66618 | 69682.3948193388 | -3064.39481933876 |
78 | 69029 | 67174.8464723161 | 1854.15352768388 |
79 | 89899 | 89683.6638490101 | 215.336150989882 |
80 | 93774 | 95210.2299628217 | -1436.22996282167 |
81 | 90305 | 92115.9084799315 | -1810.90847993149 |
82 | 83799 | 84634.4137413348 | -835.413741334778 |
83 | 80320 | 77177.4683906875 | 3142.5316093125 |
84 | 82497 | 78247.5141704439 | 4249.4858295561 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
85 | 80865.7303345807 | 77154.2174458363 | 84577.2432233252 |
86 | 77305.926861992 | 71933.2007533757 | 82678.6529706083 |
87 | 73436.8917096118 | 66745.9445427114 | 80127.8388765123 |
88 | 70538.5973525942 | 62627.2833485364 | 78449.911356652 |
89 | 66990.457145584 | 58042.1925031471 | 75938.7217880208 |
90 | 68031.4000167903 | 57533.4203068312 | 78529.3797267493 |
91 | 88779.3674221855 | 73558.2529477566 | 104000.481896614 |
92 | 94422.5236736776 | 76648.7716941604 | 112196.275653195 |
93 | 93291.4938017893 | 74135.0657599713 | 112447.921843607 |
94 | 88125.5085630536 | 68462.6563421975 | 107788.360783910 |
95 | 81897.5117310339 | 62096.8385146462 | 101698.184947422 |
96 | 80188.0238695286 | 59597.0776465497 | 100778.970092507 |