Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.900361087365125 |
beta | 0.157393226075154 |
gamma | 1 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 2.43 | 2.45106837606838 | -0.0210683760683770 |
14 | 2.42 | 2.41981582945203 | 0.000184170547967710 |
15 | 2.41 | 2.40647434776039 | 0.00352565223960877 |
16 | 2.42 | 2.41580769559908 | 0.00419230440092111 |
17 | 2.39 | 2.38591869897887 | 0.00408130102113136 |
18 | 2.4 | 2.39650812340718 | 0.00349187659282268 |
19 | 2.39 | 2.40456168941889 | -0.0145616894188882 |
20 | 2.4 | 2.38846364604467 | 0.0115363539553281 |
21 | 2.41 | 2.38791475725939 | 0.0220852427406060 |
22 | 2.41 | 2.40957672679199 | 0.000423273208014052 |
23 | 2.41 | 2.40304508423965 | 0.00695491576034746 |
24 | 2.41 | 2.42337986471044 | -0.0133798647104402 |
25 | 2.42 | 2.41057736623144 | 0.00942263376856367 |
26 | 2.43 | 2.41427411583034 | 0.0157258841696613 |
27 | 2.43 | 2.42283995440373 | 0.00716004559627015 |
28 | 2.43 | 2.44360825013825 | -0.0136082501382502 |
29 | 2.44 | 2.40325499397821 | 0.0367450060217869 |
30 | 2.42 | 2.45339734278777 | -0.0333973427877710 |
31 | 2.44 | 2.43141338004267 | 0.00858661995733367 |
32 | 2.42 | 2.44701284489899 | -0.0270128448989913 |
33 | 2.42 | 2.41559929254193 | 0.00440070745806898 |
34 | 2.42 | 2.41946678627214 | 0.000533213727855308 |
35 | 2.43 | 2.41398688210335 | 0.0160131178966529 |
36 | 2.44 | 2.44203677083343 | -0.00203677083342546 |
37 | 2.43 | 2.44491219797826 | -0.0149121979782634 |
38 | 2.44 | 2.42707138323213 | 0.0129286167678688 |
39 | 2.44 | 2.43161329963331 | 0.0083867003666911 |
40 | 2.45 | 2.4509386467256 | -0.000938646725600734 |
41 | 2.45 | 2.42832712052782 | 0.0216728794721806 |
42 | 2.43 | 2.45709169193994 | -0.0270916919399391 |
43 | 2.44 | 2.44504339288516 | -0.00504339288516498 |
44 | 2.45 | 2.4429673780756 | 0.00703262192440146 |
45 | 2.46 | 2.4483052050997 | 0.0116947949002988 |
46 | 2.44 | 2.46235646261533 | -0.0223564626153276 |
47 | 2.43 | 2.43856807665296 | -0.0085680766529559 |
48 | 2.42 | 2.43996221513687 | -0.0199622151368728 |
49 | 2.41 | 2.42014982038177 | -0.0101498203817703 |
50 | 2.43 | 2.4047802178352 | 0.0252197821647990 |
51 | 2.41 | 2.41708718398364 | -0.00708718398364105 |
52 | 2.43 | 2.41650957906654 | 0.0134904209334632 |
53 | 2.43 | 2.4061454643738 | 0.0238545356261985 |
54 | 2.44 | 2.42932768189657 | 0.0106723181034329 |
55 | 2.43 | 2.45614127886923 | -0.0261412788692317 |
56 | 2.44 | 2.43594677486229 | 0.00405322513770656 |
57 | 2.43 | 2.43831837567344 | -0.00831837567343552 |
58 | 2.44 | 2.42737341463357 | 0.0126265853664287 |
59 | 2.44 | 2.43782942879536 | 0.00217057120464359 |
60 | 2.43 | 2.4506518752853 | -0.0206518752853011 |
61 | 2.43 | 2.43399344837853 | -0.00399344837852489 |
62 | 2.43 | 2.43136063103556 | -0.00136063103555939 |
63 | 2.43 | 2.41641950522681 | 0.0135804947731857 |
64 | 2.44 | 2.43933234493077 | 0.000667655069228168 |
65 | 2.47 | 2.41947039707318 | 0.0505296029268201 |
66 | 2.48 | 2.47015110593411 | 0.00984889406589273 |
67 | 2.49 | 2.49723332970381 | -0.00723332970381296 |
68 | 2.5 | 2.50442888684123 | -0.004428886841227 |
69 | 2.51 | 2.50408635682978 | 0.00591364317021581 |
70 | 2.49 | 2.51621464035644 | -0.0262146403564376 |
71 | 2.49 | 2.49332583718102 | -0.00332583718102297 |
72 | 2.48 | 2.50081476438049 | -0.0208147643804906 |
73 | 2.48 | 2.48753565957262 | -0.00753565957262392 |
74 | 2.48 | 2.48334008836706 | -0.00334008836706134 |
75 | 2.5 | 2.46918912757897 | 0.0308108724210334 |
76 | 2.5 | 2.50985431087844 | -0.00985431087844457 |
77 | 2.5 | 2.48752131239287 | 0.0124786876071328 |
78 | 2.5 | 2.49653118075069 | 0.00346881924931042 |
79 | 2.5 | 2.51190495870566 | -0.0119049587056574 |
80 | 2.48 | 2.51024975401399 | -0.0302497540139908 |
81 | 2.49 | 2.47910650380814 | 0.0108934961918634 |
82 | 2.48 | 2.48463979002433 | -0.00463979002432513 |
83 | 2.5 | 2.47863670998043 | 0.0213632900195657 |
84 | 2.5 | 2.50529085526093 | -0.00529085526092743 |
85 | 2.49 | 2.50819056065946 | -0.0181905606594572 |
86 | 2.48 | 2.49418843034905 | -0.0141884303490531 |
87 | 2.47 | 2.47150413971845 | -0.00150413971844499 |
88 | 2.46 | 2.47227425528616 | -0.0122742552861648 |
89 | 2.43 | 2.44289668298617 | -0.0128966829861699 |
90 | 2.42 | 2.41747487342962 | 0.00252512657037984 |
91 | 2.43 | 2.41964648114674 | 0.0103535188532646 |
92 | 2.45 | 2.42853767374426 | 0.0214623262557447 |
93 | 2.45 | 2.44771517972498 | 0.00228482027501853 |
94 | 2.46 | 2.44239163023426 | 0.0176083697657399 |
95 | 2.44 | 2.46060545010448 | -0.0206054501044814 |
96 | 2.45 | 2.44246396773228 | 0.00753603226772137 |
97 | 2.45 | 2.45309208148258 | -0.00309208148258167 |
98 | 2.42 | 2.45268730938122 | -0.0326873093812163 |
99 | 2.41 | 2.41159421423757 | -0.00159421423756534 |
100 | 2.39 | 2.40818036048418 | -0.0181803604841848 |
101 | 2.39 | 2.36955643722626 | 0.0204435627737425 |
102 | 2.38 | 2.37654746506049 | 0.00345253493950493 |
103 | 2.37 | 2.38132347653303 | -0.0113234765330308 |
104 | 2.37 | 2.3697219413628 | 0.000278058637201095 |
105 | 2.38 | 2.36283061899179 | 0.0171693810082090 |
106 | 2.39 | 2.36946016037513 | 0.0205398396248695 |
107 | 2.41 | 2.38394598870602 | 0.0260540112939807 |
108 | 2.42 | 2.41467121359233 | 0.00532878640766699 |
109 | 2.48 | 2.42599260208124 | 0.0540073979187623 |
110 | 2.53 | 2.48588031899439 | 0.0441196810056139 |
111 | 2.56 | 2.53975488255391 | 0.0202451174460863 |
112 | 2.56 | 2.58016210654684 | -0.0201621065468354 |
113 | 2.53 | 2.56913192617182 | -0.0391319261718244 |
114 | 2.57 | 2.53787763227208 | 0.0321223677279168 |
115 | 2.56 | 2.58814450077408 | -0.0281445007740806 |
116 | 2.57 | 2.58132013547017 | -0.0113201354701720 |
117 | 2.58 | 2.58279189600329 | -0.00279189600329000 |
118 | 2.57 | 2.58607879445085 | -0.0160787944508543 |
119 | 2.6 | 2.57724868737202 | 0.0227513126279781 |
120 | 2.63 | 2.61157185588040 | 0.0184281441195968 |
121 | 2.72 | 2.65003060372291 | 0.0699693962770889 |
122 | 2.83 | 2.73605959149173 | 0.0939404085082711 |
123 | 2.9 | 2.85222700587615 | 0.0477729941238461 |
124 | 2.92 | 2.93710916464554 | -0.0171091646455368 |
125 | 2.94 | 2.95108627446372 | -0.0110862744637235 |
126 | 2.95 | 2.98030593665009 | -0.0303059366500880 |
127 | 2.98 | 2.98763614517666 | -0.00763614517666156 |
128 | 3.02 | 3.02313560213474 | -0.00313560213474151 |
129 | 3.16 | 3.05616851420426 | 0.103831485795738 |
130 | 3.2 | 3.1925831141371 | 0.00741688586290401 |
131 | 3.18 | 3.25055823275868 | -0.0705582327586756 |
132 | 3.17 | 3.22899703712107 | -0.0589970371210691 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
133 | 3.22046737489036 | 3.17268429702831 | 3.26825045275241 |
134 | 3.25355836785959 | 3.18454673752015 | 3.32256999819903 |
135 | 3.27490433979872 | 3.18567329808711 | 3.36413538151033 |
136 | 3.29789773659158 | 3.18847357737136 | 3.4073218958118 |
137 | 3.31789290974848 | 3.18793633387395 | 3.447849485623 |
138 | 3.34676376296595 | 3.19577013123447 | 3.49775739469743 |
139 | 3.37951829467517 | 3.2069018258927 | 3.55213476345763 |
140 | 3.41930283631193 | 3.22443744669639 | 3.61416822592747 |
141 | 3.46322272283419 | 3.24546367206635 | 3.68098177360203 |
142 | 3.47923652709980 | 3.23793256794994 | 3.72054048624967 |
143 | 3.50440504159922 | 3.23890548859986 | 3.76990459459859 |
144 | 3.53916316453042 | 3.24882208397466 | 3.82950424508619 |