Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.999950687374048 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 0.9834 | 1.0137 | -0.0303 |
3 | 0.9643 | 0.983401494172566 | -0.0191014941725663 |
4 | 0.947 | 0.964300941944837 | -0.0173009419448373 |
5 | 0.906 | 0.947000853154879 | -0.0410008531548787 |
6 | 0.9492 | 0.906002021859735 | 0.0431979781402647 |
7 | 0.9397 | 0.949197869794262 | -0.00949786979426215 |
8 | 0.9041 | 0.939700468364901 | -0.0356004683649005 |
9 | 0.8721 | 0.90410175555258 | -0.0320017555525802 |
10 | 0.8552 | 0.872101578090601 | -0.0169015780906014 |
11 | 0.8564 | 0.855200833461198 | 0.0011991665388017 |
12 | 0.8973 | 0.856399940865949 | 0.0409000591340509 |
13 | 0.9383 | 0.897297983110683 | 0.0410020168893175 |
14 | 0.9217 | 0.938297978082878 | -0.0165979780828779 |
15 | 0.9095 | 0.921700818489885 | -0.0122008184898847 |
16 | 0.892 | 0.909500601654398 | -0.0175006016543985 |
17 | 0.8742 | 0.892000863000623 | -0.0178008630006233 |
18 | 0.8532 | 0.874200877807299 | -0.0210008778072988 |
19 | 0.8607 | 0.853201035608432 | 0.00749896439156805 |
20 | 0.9005 | 0.860699630206374 | 0.039800369793626 |
21 | 0.9111 | 0.900498037339252 | 0.0106019626607484 |
22 | 0.9059 | 0.911099477189381 | -0.00519947718938096 |
23 | 0.8883 | 0.905900256399874 | -0.0176002563998738 |
24 | 0.8924 | 0.888300867914861 | 0.00409913208513946 |
25 | 0.8833 | 0.892399797861033 | -0.00909979786103277 |
26 | 0.87 | 0.883300448734928 | -0.0133004487349281 |
27 | 0.8758 | 0.870000655880053 | 0.00579934411994654 |
28 | 0.8858 | 0.875799714019113 | 0.0100002859808873 |
29 | 0.917 | 0.885799506859638 | 0.031200493140362 |
30 | 0.9554 | 0.916998461421752 | 0.0384015385782477 |
31 | 0.9922 | 0.955398106319292 | 0.0368018936807079 |
32 | 0.9778 | 0.992198185201983 | -0.0143981852019825 |
33 | 0.9808 | 0.977800710012321 | 0.00299928998767873 |
34 | 0.9811 | 0.980799852097135 | 0.000300147902865255 |
35 | 1.0014 | 0.981099985198919 | 0.0203000148010813 |
36 | 1.0183 | 1.00139899895296 | 0.0169010010470365 |
37 | 1.0622 | 1.01829916656726 | 0.0439008334327429 |
38 | 1.0773 | 1.06219783513462 | 0.015102164865378 |
39 | 1.0807 | 1.07729925527259 | 0.00340074472740715 |
40 | 1.0848 | 1.08069983230035 | 0.0041001676996526 |
41 | 1.1582 | 1.08479979780996 | 0.073400202190036 |
42 | 1.1663 | 1.15819638044328 | 0.00810361955671546 |
43 | 1.1372 | 1.16629960038924 | -0.0290996003892399 |
44 | 1.1139 | 1.13720143497771 | -0.0233014349777094 |
45 | 1.1222 | 1.11390114905495 | 0.008298850945053 |
46 | 1.1692 | 1.12219959076187 | 0.0470004092381324 |
47 | 1.1702 | 1.1691976822864 | 0.00100231771360026 |
48 | 1.2286 | 1.17019995057308 | 0.0584000494269186 |
49 | 1.2613 | 1.22859712014021 | 0.032702879859793 |
50 | 1.2646 | 1.26129838733512 | 0.00330161266488194 |
51 | 1.2262 | 1.26459983718881 | -0.0383998371888097 |
52 | 1.1985 | 1.22620189359681 | -0.0277018935968079 |
53 | 1.2007 | 1.19850136605312 | 0.00219863394688313 |
54 | 1.2138 | 1.20069989157959 | 0.0131001084204134 |
55 | 1.2266 | 1.21379935399925 | 0.0128006460007464 |
56 | 1.2176 | 1.22659936876653 | -0.00899936876653173 |
57 | 1.2218 | 1.21760044378251 | 0.00419955621749413 |
58 | 1.249 | 1.22179979290886 | 0.027200207091145 |
59 | 1.2991 | 1.24899865868636 | 0.050101341313638 |
60 | 1.3408 | 1.2990975293713 | 0.0417024706287039 |
61 | 1.3119 | 1.34079794354166 | -0.0288979435416645 |
62 | 1.3014 | 1.31190142503348 | -0.0105014250334807 |
63 | 1.3201 | 1.30140051785284 | 0.0186994821471556 |
64 | 1.2938 | 1.32009907787943 | -0.0262990778794314 |
65 | 1.2694 | 1.29380129687659 | -0.0244012968765903 |
66 | 1.2165 | 1.26940120329203 | -0.0529012032920257 |
67 | 1.2037 | 1.21650260869725 | -0.0128026086972504 |
68 | 1.2292 | 1.20370063133025 | 0.0254993686697462 |
69 | 1.2256 | 1.22919874255917 | -0.00359874255917081 |
70 | 1.2015 | 1.22560017746345 | -0.0241001774634457 |
71 | 1.1786 | 1.20150118844304 | -0.0229011884430366 |
72 | 1.1856 | 1.17860112931774 | 0.00699887068226035 |
73 | 1.2103 | 1.18559965486731 | 0.0247003451326919 |
74 | 1.1938 | 1.21029878196112 | -0.0164987819611195 |
75 | 1.202 | 1.19380081359826 | 0.00819918640173656 |
76 | 1.2271 | 1.20199959567659 | 0.0251004043234122 |
77 | 1.277 | 1.22709876223315 | 0.0499012377668495 |
78 | 1.265 | 1.27699753923893 | -0.0119975392389275 |
79 | 1.2684 | 1.26500059163016 | 0.00339940836983521 |
80 | 1.2811 | 1.26839983236625 | 0.0127001676337533 |
81 | 1.2727 | 1.28109937372138 | -0.00839937372138388 |
82 | 1.2611 | 1.27270041419517 | -0.0116004141951744 |
83 | 1.2881 | 1.26110057204689 | 0.0269994279531138 |
84 | 1.3213 | 1.28809866858731 | 0.0332013314126915 |
85 | 1.2999 | 1.32129836275516 | -0.0213983627551628 |
86 | 1.3074 | 1.29990105520946 | 0.00749894479054136 |
87 | 1.3242 | 1.30739963020734 | 0.0168003697926595 |
88 | 1.3516 | 1.32419917152965 | 0.0274008284703513 |
89 | 1.3511 | 1.35159864879319 | -0.000498648793194834 |
90 | 1.3419 | 1.35110002458968 | -0.00920002458968128 |
91 | 1.3716 | 1.34190045367737 | 0.0296995463226284 |
92 | 1.3622 | 1.37159853543738 | -0.00939853543738112 |
93 | 1.3896 | 1.36220046346646 | 0.0273995365335373 |
94 | 1.4227 | 1.3895986488569 | 0.0331013511430964 |
95 | 1.4684 | 1.42269836768545 | 0.0457016323145474 |
96 | 1.457 | 1.4683977463325 | -0.0113977463325001 |
97 | 1.4718 | 1.4570005620528 | 0.0147994379471983 |
98 | 1.4748 | 1.47179927020085 | 0.00300072979914789 |
99 | 1.5527 | 1.47479985202613 | 0.0779001479738661 |
100 | 1.575 | 1.55269615853914 | 0.0223038414608585 |
101 | 1.5557 | 1.57499890013901 | -0.0192989001390087 |
102 | 1.5553 | 1.55570095167944 | -0.000400951679444095 |
103 | 1.577 | 1.55530001977198 | 0.0216999802280198 |
104 | 1.4975 | 1.57699892991699 | -0.0794989299169917 |
105 | 1.4369 | 1.49750392030099 | -0.0606039203009945 |
106 | 1.3322 | 1.43690298853845 | -0.104702988538453 |
107 | 1.2732 | 1.33220516317931 | -0.0590051631793098 |
108 | 1.3449 | 1.27320290969954 | 0.0716970903004588 |
109 | 1.3239 | 1.3448964644282 | -0.0209964644282041 |
110 | 1.2785 | 1.3239010353908 | -0.0454010353907968 |
111 | 1.305 | 1.27850223884428 | 0.026497761155724 |
112 | 1.319 | 1.30499869332582 | 0.0140013066741844 |
113 | 1.365 | 1.3189993095588 | 0.0460006904411989 |
114 | 1.4016 | 1.36499773158516 | 0.0366022684148413 |
115 | 1.4088 | 1.40159819504603 | 0.00720180495397149 |
116 | 1.4268 | 1.40879964486009 | 0.0180003551399139 |
117 | 1.4562 | 1.42679911235522 | 0.02940088764478 |
118 | 1.4816 | 1.45619855016502 | 0.0254014498349753 |
119 | 1.4914 | 1.48159874738781 | 0.00980125261219444 |
120 | 1.4614 | 1.4913995166745 | -0.0299995166744962 |
121 | 1.4272 | 1.46140147935494 | -0.0342014793549446 |
122 | 1.3686 | 1.42720168656476 | -0.0586016865647585 |
123 | 1.3569 | 1.36860288980305 | -0.0117028898030498 |
124 | 1.3406 | 1.35690057710023 | -0.0163005771002274 |
125 | 1.2565 | 1.34060080382426 | -0.0841008038242614 |
126 | 1.2208 | 1.25650414723148 | -0.035704147231481 |
127 | 1.277 | 1.22080176066526 | 0.0561982393347424 |
128 | 1.2894 | 1.27699722871724 | 0.0124027712827557 |
129 | 1.3067 | 1.28939938838678 | 0.0173006116132208 |
130 | 1.3898 | 1.30669914686141 | 0.0831008531385893 |
131 | 1.3661 | 1.38979590207871 | -0.0236959020787126 |
132 | 1.322 | 1.36610116850716 | -0.0441011685071557 |
133 | 1.336 | 1.32200217474443 | 0.0139978252555735 |
134 | 1.3649 | 1.33599930973048 | 0.0289006902695208 |
135 | 1.3999 | 1.36489857483107 | 0.035001425168929 |
136 | 1.4442 | 1.39989827398781 | 0.0443017260121872 |
137 | 1.4349 | 1.44419781536556 | -0.00929781536555607 |
138 | 1.4388 | 1.43490045849969 | 0.00389954150030869 |
139 | 1.4264 | 1.43879980770337 | -0.0123998077033689 |
140 | 1.4343 | 1.42640061146708 | 0.00789938853292083 |
141 | 1.377 | 1.43429961046041 | -0.057299610460408 |
142 | 1.3706 | 1.37700282559426 | -0.00640282559425787 |
143 | 1.3556 | 1.37060031574014 | -0.0150003157401437 |
144 | 1.3179 | 1.35560073970496 | -0.0377007397049591 |
145 | 1.2905 | 1.31790185912248 | -0.0274018591224752 |
146 | 1.3224 | 1.29050135125763 | 0.0318986487423707 |
147 | 1.3201 | 1.32239842699387 | -0.00229842699386618 |
148 | 1.3162 | 1.32010011334147 | -0.00390011334147067 |
149 | 1.2789 | 1.31620019232483 | -0.0373001923248304 |
150 | 1.2526 | 1.27890183937043 | -0.026301839370432 |
151 | 1.2288 | 1.25260129701277 | -0.0238012970127668 |
152 | 1.24 | 1.22880117370446 | 0.0111988262955434 |
153 | 1.2856 | 1.23999944775647 | 0.0456005522435323 |
154 | 1.2974 | 1.28559775131702 | 0.0118022486829761 |
155 | 1.2828 | 1.29739941800013 | -0.0145994180001254 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
156 | 1.28280071993564 | 1.22079299646245 | 1.34480844340882 |
157 | 1.28280071993564 | 1.19511071856675 | 1.37049072130452 |
158 | 1.28280071993564 | 1.17540372319074 | 1.39019771668054 |
159 | 1.28280071993564 | 1.15878985960651 | 1.40681158026477 |
160 | 1.28280071993564 | 1.14415270498656 | 1.42144873488472 |
161 | 1.28280071993564 | 1.13091967892305 | 1.43468176094823 |
162 | 1.28280071993564 | 1.11875063859212 | 1.44685080127916 |
163 | 1.28280071993564 | 1.107423960476 | 1.45817747939528 |
164 | 1.28280071993564 | 1.09678570353021 | 1.46881573634107 |
165 | 1.28280071993564 | 1.08672378376501 | 1.47887765610627 |
166 | 1.28280071993564 | 1.07715358655467 | 1.48844785331661 |
167 | 1.28280071993564 | 1.06800937458495 | 1.49759206528632 |