Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.859998440553193 |
beta | 0.0713194296639774 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 1.0137 | 1.07518811431624 | -0.0614881143162398 |
14 | 0.9834 | 0.987017021911577 | -0.00361702191157653 |
15 | 0.9643 | 0.963026463475407 | 0.0012735365245935 |
16 | 0.947 | 0.947582389518923 | -0.00058238951892331 |
17 | 0.906 | 0.90678150143204 | -0.000781501432040699 |
18 | 0.9492 | 0.945723944333983 | 0.00347605566601727 |
19 | 0.9397 | 0.887370248845404 | 0.0523297511545964 |
20 | 0.9041 | 0.957036112891393 | -0.0529361128913926 |
21 | 0.8721 | 0.896564182795004 | -0.0244641827950045 |
22 | 0.8552 | 0.889294234023439 | -0.0340942340234387 |
23 | 0.8564 | 0.815717966731732 | 0.0406820332682678 |
24 | 0.8973 | 0.8214943888695 | 0.0758056111305005 |
25 | 0.9383 | 0.8764681080107 | 0.0618318919893 |
26 | 0.9217 | 0.909748193147141 | 0.0119518068528588 |
27 | 0.9095 | 0.908080518081188 | 0.00141948191881203 |
28 | 0.892 | 0.900760105001888 | -0.0087601050018884 |
29 | 0.8742 | 0.860654922085992 | 0.0135450779140076 |
30 | 0.8532 | 0.921149384218215 | -0.0679493842182153 |
31 | 0.8607 | 0.812463783404426 | 0.0482362165955741 |
32 | 0.9005 | 0.867875021730493 | 0.0326249782695065 |
33 | 0.9111 | 0.894222659114398 | 0.0168773408856017 |
34 | 0.9059 | 0.932944847692385 | -0.0270448476923846 |
35 | 0.8883 | 0.888118920605185 | 0.000181079394815264 |
36 | 0.8924 | 0.873716916431145 | 0.0186830835688550 |
37 | 0.8833 | 0.883840396382622 | -0.000540396382622488 |
38 | 0.87 | 0.858902929733969 | 0.0110970702660314 |
39 | 0.8758 | 0.857379024348628 | 0.0184209756513719 |
40 | 0.8858 | 0.866650874839171 | 0.0191491251608291 |
41 | 0.917 | 0.858778311669086 | 0.0582216883309142 |
42 | 0.9554 | 0.9541334241941 | 0.00126657580590062 |
43 | 0.9922 | 0.933333126354961 | 0.058866873645039 |
44 | 0.9778 | 1.00844666252811 | -0.0306466625281139 |
45 | 0.9808 | 0.9870409001049 | -0.00624090010490086 |
46 | 0.9811 | 1.00717912096454 | -0.02607912096454 |
47 | 1.0014 | 0.974501480444845 | 0.0268985195551548 |
48 | 1.0183 | 0.994811536879122 | 0.0234884631208777 |
49 | 1.0622 | 1.01581584890246 | 0.0463841510975367 |
50 | 1.0773 | 1.04518031198103 | 0.0321196880189711 |
51 | 1.0807 | 1.07636822566147 | 0.00433177433852650 |
52 | 1.0848 | 1.08636821396511 | -0.00156821396510587 |
53 | 1.1582 | 1.07762118846067 | 0.0805788115393287 |
54 | 1.1663 | 1.19707304991013 | -0.0307730499101331 |
55 | 1.1372 | 1.16766118027058 | -0.0304611802705801 |
56 | 1.1139 | 1.15882011924888 | -0.0449201192488764 |
57 | 1.1222 | 1.1330800188951 | -0.0108800188951006 |
58 | 1.1692 | 1.15069065227706 | 0.0185093477229406 |
59 | 1.1702 | 1.17075022270366 | -0.000550222703664005 |
60 | 1.2286 | 1.17226767792138 | 0.0563323220786183 |
61 | 1.2613 | 1.23202824188678 | 0.0292717581132225 |
62 | 1.2646 | 1.25093459729483 | 0.0136654027051726 |
63 | 1.2262 | 1.26748518764415 | -0.041285187644154 |
64 | 1.1985 | 1.23975443868747 | -0.0412544386874714 |
65 | 1.2007 | 1.20826968130461 | -0.00756968130460822 |
66 | 1.2138 | 1.23080963754201 | -0.0170096375420106 |
67 | 1.2266 | 1.20860721210141 | 0.0179927878985868 |
68 | 1.2176 | 1.23771338760201 | -0.0201133876020145 |
69 | 1.2218 | 1.23789538929663 | -0.0160953892966329 |
70 | 1.249 | 1.25463817115914 | -0.00563817115914067 |
71 | 1.2991 | 1.24928426678652 | 0.0498157332134752 |
72 | 1.3408 | 1.30319090956326 | 0.037609090436737 |
73 | 1.3119 | 1.34302351950686 | -0.0311235195068611 |
74 | 1.3014 | 1.30406331330588 | -0.00266331330588421 |
75 | 1.3201 | 1.29413474682630 | 0.0259652531736971 |
76 | 1.2938 | 1.32362503759217 | -0.0298250375921731 |
77 | 1.2694 | 1.30676794420661 | -0.0373679442066110 |
78 | 1.2165 | 1.30061464605355 | -0.0841146460535516 |
79 | 1.2037 | 1.21974136717618 | -0.0160413671761772 |
80 | 1.2292 | 1.20629478225293 | 0.0229052177470728 |
81 | 1.2256 | 1.23872525622995 | -0.0131252562299464 |
82 | 1.2015 | 1.25435855940209 | -0.0528585594020885 |
83 | 1.1786 | 1.20813476898104 | -0.0295347689810443 |
84 | 1.1856 | 1.17920016452589 | 0.00639983547410972 |
85 | 1.2103 | 1.16776499411458 | 0.0425350058854206 |
86 | 1.1938 | 1.18584809702119 | 0.00795190297881443 |
87 | 1.202 | 1.17942034285751 | 0.022579657142487 |
88 | 1.2271 | 1.18834434334750 | 0.0387556566525016 |
89 | 1.277 | 1.22377293544824 | 0.0532270645517645 |
90 | 1.265 | 1.28890561493379 | -0.0239056149337915 |
91 | 1.2684 | 1.27295429340549 | -0.00455429340548652 |
92 | 1.2811 | 1.27915563097058 | 0.00194436902942252 |
93 | 1.2727 | 1.29154633429204 | -0.0188463342920409 |
94 | 1.2611 | 1.29937674392037 | -0.0382767439203742 |
95 | 1.2881 | 1.27253297797409 | 0.0155670220259145 |
96 | 1.3213 | 1.29375736321546 | 0.0275426367845437 |
97 | 1.2999 | 1.31320135349621 | -0.0133013534962094 |
98 | 1.3074 | 1.28263628972595 | 0.0247637102740519 |
99 | 1.3242 | 1.29795842111513 | 0.0262415788848662 |
100 | 1.3516 | 1.31776478535101 | 0.0338352146489931 |
101 | 1.3511 | 1.35615448294248 | -0.00505448294247746 |
102 | 1.3419 | 1.36195841002156 | -0.0200584100215606 |
103 | 1.3716 | 1.35385284364131 | 0.0177471563586877 |
104 | 1.3622 | 1.38333901629522 | -0.0211390162952225 |
105 | 1.3896 | 1.37474730337604 | 0.0148526966239597 |
106 | 1.4227 | 1.41268544594394 | 0.0100145540560628 |
107 | 1.4684 | 1.44171916606334 | 0.0266808339366584 |
108 | 1.457 | 1.48166851206183 | -0.0246685120618342 |
109 | 1.4718 | 1.45478091868475 | 0.0170190813152504 |
110 | 1.4748 | 1.46176838680960 | 0.0130316131904047 |
111 | 1.5527 | 1.47263609040293 | 0.0800639095970745 |
112 | 1.575 | 1.54852212049079 | 0.0264778795092062 |
113 | 1.5557 | 1.58341806835461 | -0.0277180683546092 |
114 | 1.5553 | 1.57451887755431 | -0.0192188775543141 |
115 | 1.577 | 1.57936774184362 | -0.00236774184362409 |
116 | 1.4975 | 1.59181686520620 | -0.0943168652061963 |
117 | 1.4369 | 1.52654873491655 | -0.0896487349165489 |
118 | 1.3322 | 1.46874643113537 | -0.13654643113537 |
119 | 1.2732 | 1.35988994788131 | -0.0866899478813117 |
120 | 1.3449 | 1.27401676859847 | 0.0708832314015333 |
121 | 1.3239 | 1.31986564027861 | 0.00403435972139055 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
122 | 1.29905739024732 | 1.22415693785220 | 1.37395784264244 |
123 | 1.29123263801043 | 1.18938855171837 | 1.39307672430249 |
124 | 1.26898110035171 | 1.14332478653317 | 1.39463741417026 |
125 | 1.25011398323685 | 1.10211343894329 | 1.39811452753041 |
126 | 1.24453765187573 | 1.07495468365181 | 1.41412062009966 |
127 | 1.24774815221630 | 1.05697502864644 | 1.43852127578615 |
128 | 1.22897997975374 | 1.01719146429816 | 1.44076849520932 |
129 | 1.23088210956139 | 0.998114920311562 | 1.46364929881121 |
130 | 1.23451475412627 | 0.98071333276193 | 1.4883161754906 |
131 | 1.24934592134310 | 0.974390695828924 | 1.52430114685728 |
132 | 1.26468149323295 | 0.9684072663467 | 1.56095572011921 |
133 | 1.24045939599681 | 0.922667804859097 | 1.55825098713451 |