Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.104796466407934 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 0.9643 | 0.9531 | 0.0112 |
4 | 0.947 | 0.935173720423769 | 0.0118262795762311 |
5 | 0.906 | 0.91911307273411 | -0.0131130727341101 |
6 | 0.9492 | 0.876738869047825 | 0.0724611309521748 |
7 | 0.9397 | 0.927532539523536 | 0.0121674604764642 |
8 | 0.9041 | 0.919307646386627 | -0.0152076463866273 |
9 | 0.8721 | 0.882113938782927 | -0.0100139387829274 |
10 | 0.8552 | 0.849064513383651 | 0.00613548661634866 |
11 | 0.8564 | 0.832807490700738 | 0.0235925092992623 |
12 | 0.8973 | 0.836479902308997 | 0.0608200976910032 |
13 | 0.9383 | 0.883753633633599 | 0.0545463663664008 |
14 | 0.9217 | 0.930469900084191 | -0.00876990008419076 |
15 | 0.9095 | 0.912950845544617 | -0.00345084554461683 |
16 | 0.892 | 0.900389209125421 | -0.0083892091254214 |
17 | 0.8742 | 0.88201004965312 | -0.00781004965312004 |
18 | 0.8532 | 0.863391584047003 | -0.0101915840470026 |
19 | 0.8607 | 0.841323542051777 | 0.0193764579482228 |
20 | 0.9005 | 0.850854126376253 | 0.0496458736237471 |
21 | 0.9111 | 0.895856838503756 | 0.0152431614962436 |
22 | 0.9059 | 0.908054267965448 | -0.00215426796544826 |
23 | 0.8883 | 0.902628508294974 | -0.0143285082949736 |
24 | 0.8924 | 0.883526931256763 | 0.00887306874323657 |
25 | 0.8833 | 0.888556797507249 | -0.00525679750724939 |
26 | 0.87 | 0.878905903703868 | -0.00890590370386757 |
27 | 0.8758 | 0.864672596465533 | 0.0111274035344671 |
28 | 0.8858 | 0.87163870903624 | 0.0141612909637597 |
29 | 0.917 | 0.883122762289017 | 0.0338772377109832 |
30 | 0.9554 | 0.91787297709279 | 0.0375270229072104 |
31 | 0.9922 | 0.960205676488275 | 0.0319943235117252 |
32 | 0.9778 | 1.00035856853742 | -0.0225585685374159 |
33 | 0.9808 | 0.983594510267473 | -0.00279451026747346 |
34 | 0.9811 | 0.986301655466102 | -0.00520165546610163 |
35 | 1.0014 | 0.986056540353783 | 0.0153434596462175 |
36 | 1.0183 | 1.00796448070718 | 0.0103355192928209 |
37 | 1.0622 | 1.02594760660756 | 0.0362523933924426 |
38 | 1.0773 | 1.07364672933392 | 0.0036532706660839 |
39 | 1.0807 | 1.08912957919055 | -0.00842957919055309 |
40 | 1.0848 | 1.09164618907808 | -0.00684618907807732 |
41 | 1.1582 | 1.09502873265433 | 0.0631712673456657 |
42 | 1.1663 | 1.17504885825067 | -0.00874885825067095 |
43 | 1.1372 | 1.1822320088209 | -0.0450320088208966 |
44 | 1.1139 | 1.14841281342122 | -0.034512813421216 |
45 | 1.1222 | 1.12149599252888 | 0.00070400747112398 |
46 | 1.1692 | 1.12986977002417 | 0.0393302299758251 |
47 | 1.1702 | 1.18099143914865 | -0.0107914391486528 |
48 | 1.2286 | 1.18086053445842 | 0.0477394655415824 |
49 | 1.2613 | 1.24426346175538 | 0.0170365382446214 |
50 | 1.2646 | 1.27874883076324 | -0.0141488307632389 |
51 | 1.2262 | 1.28056608329545 | -0.0543660832954473 |
52 | 1.1985 | 1.23646870987365 | -0.0379687098736452 |
53 | 1.2007 | 1.20478972324482 | -0.00408972324481893 |
54 | 1.2138 | 1.20656113470018 | 0.00723886529982432 |
55 | 1.2266 | 1.2204197422044 | 0.00618025779559961 |
56 | 1.2176 | 1.23386741138287 | -0.0162674113828691 |
57 | 1.2218 | 1.22316264415234 | -0.00136264415234022 |
58 | 1.249 | 1.2272198438602 | 0.0217801561397966 |
59 | 1.2991 | 1.25670232726147 | 0.0423976727385325 |
60 | 1.3408 | 1.31124545354839 | 0.0295545464516145 |
61 | 1.3119 | 1.3560426655828 | -0.0441426655828039 |
62 | 1.3014 | 1.3225166702119 | -0.021116670211899 |
63 | 1.3201 | 1.30980371779139 | 0.0102962822086099 |
64 | 1.2938 | 1.32958273178399 | -0.0357827317839914 |
65 | 1.2694 | 1.29953282793461 | -0.0301328279346063 |
66 | 1.2165 | 1.27197501404418 | -0.0554750140441813 |
67 | 1.2037 | 1.21326142859842 | -0.00956142859842046 |
68 | 1.2292 | 1.19945942466749 | 0.0297405753325057 |
69 | 1.2256 | 1.22807613187128 | -0.00247613187127982 |
70 | 1.2015 | 1.22421664200081 | -0.0227166420008096 |
71 | 1.1786 | 1.19773601819047 | -0.0191360181904707 |
72 | 1.1856 | 1.17283063110299 | 0.0127693688970085 |
73 | 1.2103 | 1.18116881584166 | 0.0291311841583426 |
74 | 1.1938 | 1.20892166100373 | -0.0151216610037304 |
75 | 1.202 | 1.19083696436432 | 0.0111630356356791 |
76 | 1.2271 | 1.20020681105333 | 0.0268931889466744 |
77 | 1.277 | 1.22812512222538 | 0.0488748777746215 |
78 | 1.265 | 1.28314703671228 | -0.0181470367122782 |
79 | 1.2684 | 1.26924529138906 | -0.000845291389056424 |
80 | 1.2811 | 1.2725567078384 | 0.00854329216160177 |
81 | 1.2727 | 1.28615201466842 | -0.0134520146684247 |
82 | 1.2611 | 1.27634229106511 | -0.015242291065106 |
83 | 1.2881 | 1.26314495282152 | 0.0249550471784781 |
84 | 1.3213 | 1.29276015358487 | 0.0285398464151303 |
85 | 1.2999 | 1.328951028641 | -0.0290510286410002 |
86 | 1.3074 | 1.30450658349391 | 0.00289341650609187 |
87 | 1.3242 | 1.31230980331959 | 0.0118901966804075 |
88 | 1.3516 | 1.33035585391659 | 0.0212441460834052 |
89 | 1.3511 | 1.35998216535799 | -0.00888216535798958 |
90 | 1.3419 | 1.35855134581442 | -0.0166513458144211 |
91 | 1.3716 | 1.34760634361213 | 0.0239936563878664 |
92 | 1.3622 | 1.37982079401779 | -0.0176207940177877 |
93 | 1.3896 | 1.36857419706942 | 0.0210258029305781 |
94 | 1.4227 | 1.39817762691994 | 0.0245223730800641 |
95 | 1.4684 | 1.43384748496666 | 0.0345525150333361 |
96 | 1.457 | 1.48316846644766 | -0.0261684664476642 |
97 | 1.4718 | 1.46902610363263 | 0.00277389636736536 |
98 | 1.4748 | 1.48411679817012 | -0.0093167981701161 |
99 | 1.5527 | 1.48614043064365 | 0.0665595693563477 |
100 | 1.575 | 1.57101563831783 | 0.00398436168216887 |
101 | 1.5557 | 1.59373318534301 | -0.0380331853430136 |
102 | 1.5553 | 1.57044744191283 | -0.0151474419128279 |
103 | 1.577 | 1.56846004352524 | 0.00853995647475614 |
104 | 1.4975 | 1.59105500078708 | -0.093555000787076 |
105 | 1.4369 | 1.5017507672898 | -0.0648507672897989 |
106 | 1.3322 | 1.43435463603398 | -0.102154636033985 |
107 | 1.2732 | 1.31894919115043 | -0.0457491911504346 |
108 | 1.3449 | 1.25515483757685 | 0.089745162423152 |
109 | 1.3239 | 1.336259813476 | -0.0123598134760003 |
110 | 1.2785 | 1.31396454869825 | -0.0354645486982545 |
111 | 1.305 | 1.26484798931193 | 0.0401520106880748 |
112 | 1.319 | 1.29555577815121 | 0.0234442218487909 |
113 | 1.365 | 1.31201264975865 | 0.052987350241354 |
114 | 1.4016 | 1.36356553682826 | 0.0380344631717404 |
115 | 1.4088 | 1.40415141417038 | 0.00464858582961947 |
116 | 1.4268 | 1.41183856953912 | 0.0149614304608814 |
117 | 1.4562 | 1.43140647458383 | 0.0247935254161729 |
118 | 1.4816 | 1.46340474843724 | 0.0181952515627628 |
119 | 1.4914 | 1.49071154650642 | 0.00068845349358182 |
120 | 1.4614 | 1.50058369399983 | -0.0391836939998318 |
121 | 1.4272 | 1.46647738132784 | -0.0392773813278398 |
122 | 1.3686 | 1.42816125055493 | -0.0595612505549252 |
123 | 1.3569 | 1.36331944196193 | -0.00641944196193145 |
124 | 1.3406 | 1.35094670712801 | -0.0103467071280101 |
125 | 1.2565 | 1.33356240878204 | -0.0770624087820371 |
126 | 1.2208 | 1.2413865406488 | -0.0205865406487955 |
127 | 1.277 | 1.20352914393324 | 0.0734708560667612 |
128 | 1.2894 | 1.267428630033 | 0.021971369966999 |
129 | 1.3067 | 1.28213115196768 | 0.0245688480323158 |
130 | 1.3898 | 1.30200588042518 | 0.0877941195748158 |
131 | 1.3661 | 1.39430639392802 | -0.0282063939280204 |
132 | 1.322 | 1.36765046351425 | -0.0456504635142538 |
133 | 1.336 | 1.31876645624808 | 0.0172335437519242 |
134 | 1.3649 | 1.33457247073696 | 0.0303275292630361 |
135 | 1.3999 | 1.36665068863861 | 0.0332493113613865 |
136 | 1.4442 | 1.40513509897978 | 0.0390649010202162 |
137 | 1.4349 | 1.45352896256728 | -0.018628962567278 |
138 | 1.4388 | 1.44227671311738 | -0.00347671311738162 |
139 | 1.4264 | 1.44581236586797 | -0.0194123658679661 |
140 | 1.4343 | 1.43137801852039 | 0.00292198147961487 |
141 | 1.377 | 1.43958423185436 | -0.0625842318543581 |
142 | 1.3706 | 1.37572562550317 | -0.00512562550316664 |
143 | 1.3556 | 1.3687884780623 | -0.0131884780623046 |
144 | 1.3179 | 1.35240637216408 | -0.0345063721640761 |
145 | 1.2905 | 1.31109022629272 | -0.0205902262927242 |
146 | 1.3224 | 1.28153244333471 | 0.0408675566652932 |
147 | 1.3201 | 1.31771521886396 | 0.00238478113604446 |
148 | 1.3162 | 1.31566513550017 | 0.000534864499830645 |
149 | 1.2789 | 1.31182118740976 | -0.0329211874097588 |
150 | 1.2526 | 1.27107116329926 | -0.0184711632992625 |
151 | 1.2288 | 1.24283545065506 | -0.014035450655056 |
152 | 1.24 | 1.21756458502196 | 0.022435414978037 |
153 | 1.2856 | 1.23111573723406 | 0.054484262765943 |
154 | 1.2974 | 1.28242549544677 | 0.0149745045532308 |
155 | 1.2828 | 1.29579477061016 | -0.0129947706101574 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
156 | 1.27983296456843 | 1.21601124951466 | 1.3436546796222 |
157 | 1.27686592913686 | 1.18176139635429 | 1.37197046191944 |
158 | 1.27389889370529 | 1.1514062450188 | 1.39639154239179 |
159 | 1.27093185827372 | 1.12246836699117 | 1.41939534955628 |
160 | 1.26796482284216 | 1.09405330398105 | 1.44187634170326 |
161 | 1.26499778741059 | 1.06573579936313 | 1.46425977545804 |
162 | 1.26203075197902 | 1.03728368267661 | 1.48677782128142 |
163 | 1.25906371654745 | 1.00855942779607 | 1.50956800529883 |
164 | 1.25609668111588 | 0.979477327307896 | 1.53271603492386 |
165 | 1.25312964568431 | 0.949982294933848 | 1.55627699643478 |
166 | 1.25016261025274 | 0.920038371166088 | 1.5802868493394 |
167 | 1.24719557482117 | 0.889622051962202 | 1.60476909768015 |