Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.148526946869307 |
beta | 0.0795472752444786 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 17 | 26 | -9 |
4 | 18 | 25.5569232528617 | -7.55692325286173 |
5 | 18 | 25.2388978913124 | -7.2388978913124 |
6 | 16 | 24.8825809102517 | -8.88258091025172 |
7 | 20 | 24.1771857798909 | -4.17718577989094 |
8 | 16 | 24.1213155316231 | -8.12131553162307 |
9 | 18 | 23.3836830893196 | -5.3836830893196 |
10 | 17 | 22.9890550830283 | -5.98905508302831 |
11 | 23 | 22.4337528525002 | 0.566247147499805 |
12 | 30 | 22.8587798093853 | 7.1412201906147 |
13 | 23 | 24.3447403399755 | -1.34474033997553 |
14 | 18 | 24.554419070337 | -6.55441907033703 |
15 | 15 | 23.9128802275712 | -8.91288022757119 |
16 | 12 | 22.8157414371093 | -10.8157414371093 |
17 | 21 | 21.3081894267768 | -0.308189426776799 |
18 | 15 | 21.3576508040598 | -6.35765080405982 |
19 | 20 | 20.4334890557634 | -0.433489055763431 |
20 | 31 | 20.3841033288207 | 10.6158966711793 |
21 | 27 | 22.1012750340763 | 4.89872496592368 |
22 | 34 | 23.0271706950317 | 10.9728293049683 |
23 | 21 | 24.9848775621701 | -3.9848775621701 |
24 | 31 | 24.6738809107723 | 6.32611908922769 |
25 | 19 | 25.9690876636974 | -6.96908766369744 |
26 | 16 | 25.2072587787402 | -9.20725877874017 |
27 | 20 | 24.0042182015492 | -4.00421820154925 |
28 | 21 | 23.5266598623420 | -2.52665986234204 |
29 | 22 | 23.2387064832902 | -1.23870648329019 |
30 | 17 | 23.1274136768620 | -6.12741367686195 |
31 | 24 | 22.2176212516666 | 1.78237874833337 |
32 | 25 | 22.5037047972468 | 2.49629520275324 |
33 | 26 | 22.9253176870707 | 3.07468231292934 |
34 | 25 | 23.4691637553480 | 1.53083624465204 |
35 | 17 | 23.8017937791299 | -6.8017937791299 |
36 | 32 | 22.8164410980599 | 9.1835589019401 |
37 | 33 | 24.3138470032792 | 8.6861529967208 |
38 | 13 | 25.8400008780270 | -12.8400008780270 |
39 | 32 | 24.0172373347638 | 7.98276266523617 |
40 | 25 | 25.3815309397272 | -0.381530939727174 |
41 | 29 | 25.4989937976147 | 3.50100620238531 |
42 | 22 | 26.2344821302549 | -4.23448213025485 |
43 | 18 | 25.7710119564238 | -7.77101195642385 |
44 | 17 | 24.6904579676335 | -7.69045796763348 |
45 | 20 | 23.5310063179338 | -3.53100631793384 |
46 | 15 | 22.9476267867037 | -7.94762678670368 |
47 | 20 | 21.614359575383 | -1.61435957538298 |
48 | 33 | 21.2026796872420 | 11.7973203127580 |
49 | 29 | 22.9223799893022 | 6.07762001069784 |
50 | 23 | 23.8643572257781 | -0.864357225778079 |
51 | 26 | 23.765051471862 | 2.23494852813801 |
52 | 18 | 24.1524818634737 | -6.15248186347368 |
53 | 20 | 23.2214617833056 | -3.22146178330556 |
54 | 11 | 22.6877158731788 | -11.6877158731788 |
55 | 28 | 20.7584137346555 | 7.24158626534453 |
56 | 26 | 21.7261817675308 | 4.27381823246925 |
57 | 22 | 22.3036510700095 | -0.303651070009476 |
58 | 17 | 22.1976552213480 | -5.19765522134802 |
59 | 12 | 21.3033580290765 | -9.30335802907654 |
60 | 14 | 19.6893349597043 | -5.68933495970425 |
61 | 17 | 18.5448726999083 | -1.54487269990830 |
62 | 21 | 17.9977222280022 | 3.00227777199780 |
63 | 19 | 18.1614177860952 | 0.838582213904758 |
64 | 18 | 18.0136540256654 | -0.0136540256653888 |
65 | 10 | 17.7391488974229 | -7.73914889742285 |
66 | 29 | 16.2257622247569 | 12.7742377752431 |
67 | 31 | 17.9100927642886 | 13.0899072357114 |
68 | 19 | 19.7959648522645 | -0.795964852264529 |
69 | 9 | 19.6100064981797 | -10.6100064981797 |
70 | 20 | 17.8410421884716 | 2.15895781152840 |
71 | 28 | 17.9941210630760 | 10.0058789369240 |
72 | 19 | 19.4308977731317 | -0.430897773131665 |
73 | 30 | 19.3124408831866 | 10.6875591168134 |
74 | 29 | 20.9716470400241 | 8.02835295997589 |
75 | 26 | 22.3307437244628 | 3.66925627553723 |
76 | 23 | 23.0857490343136 | -0.0857490343135936 |
77 | 13 | 23.2820217525548 | -10.2820217525548 |
78 | 21 | 21.8423920125394 | -0.842392012539364 |
79 | 19 | 21.7948488682669 | -2.79484886826687 |
80 | 28 | 21.4242923695104 | 6.57570763048958 |
81 | 23 | 22.5232074376231 | 0.476792562376861 |
82 | 18 | 22.7219025345379 | -4.72190253453788 |
83 | 21 | 22.0926624490011 | -1.09266244900113 |
84 | 20 | 21.9895526000421 | -1.98955260004211 |
85 | 23 | 21.7297240025554 | 1.27027599744462 |
86 | 21 | 21.9690759955399 | -0.96907599553992 |
87 | 21 | 21.8643743245678 | -0.86437432456782 |
88 | 15 | 21.7650111648746 | -6.76501116487458 |
89 | 28 | 20.7093164060992 | 7.29068359390076 |
90 | 19 | 21.8274098750796 | -2.82740987507958 |
91 | 26 | 21.4092882086725 | 4.59071179132748 |
92 | 10 | 22.1471963695456 | -12.1471963695456 |
93 | 16 | 20.2555560547833 | -4.25555605478331 |
94 | 22 | 19.4857579532780 | 2.51424204672196 |
95 | 19 | 19.7511628480767 | -0.751162848076692 |
96 | 31 | 19.522692199166 | 11.477307800834 |
97 | 31 | 21.2460823643632 | 9.75391763563685 |
98 | 29 | 22.8287443473442 | 6.17125565265579 |
99 | 19 | 23.9521973386665 | -4.95219733866645 |
100 | 22 | 23.3650080332532 | -1.36500803325317 |
101 | 23 | 23.2944855507969 | -0.294485550796914 |
102 | 15 | 23.3794851827804 | -8.37948518278036 |
103 | 20 | 22.1646416078252 | -2.16464160782524 |
104 | 18 | 21.8472947200561 | -3.84729472005612 |
105 | 23 | 21.2345730469301 | 1.76542695306987 |
106 | 25 | 21.4763501550301 | 3.52364984496993 |
107 | 21 | 22.0209023607957 | -1.02090236079569 |
108 | 24 | 21.8784042290333 | 2.12159577096666 |
109 | 25 | 22.2277182217393 | 2.77228177826071 |
110 | 17 | 22.7064308910620 | -5.70643089106197 |
111 | 13 | 21.8584052644378 | -8.85840526443783 |
112 | 28 | 20.4375652118241 | 7.5624347881759 |
113 | 21 | 21.5450119133312 | -0.545011913331233 |
114 | 25 | 21.4418450405144 | 3.5581549594856 |
115 | 9 | 21.9901483103863 | -12.9901483103863 |
116 | 16 | 19.9271051355717 | -3.92710513557175 |
117 | 19 | 19.1637696837105 | -0.163769683710452 |
118 | 17 | 18.9574560318428 | -1.95745603184277 |
119 | 25 | 18.4616044485199 | 6.53839555148008 |
120 | 20 | 19.3048663425635 | 0.695133657436497 |
121 | 29 | 19.2884593320552 | 9.7115406679448 |
122 | 14 | 20.7259727436083 | -6.7259727436083 |
123 | 22 | 19.6426056850003 | 2.35739431499966 |
124 | 15 | 19.9362158138169 | -4.93621581381692 |
125 | 19 | 19.0882073335956 | -0.088207333595605 |
126 | 20 | 18.9592165892842 | 1.04078341071582 |
127 | 15 | 19.01020815968 | -4.01020815968 |
128 | 20 | 18.2636111092391 | 1.73638889076095 |
129 | 18 | 18.3910538588709 | -0.391053858870901 |
130 | 33 | 18.1978937645785 | 14.8021062354215 |
131 | 22 | 20.436212963451 | 1.56378703654902 |
132 | 16 | 20.7267610392656 | -4.72676103926561 |
133 | 17 | 20.0271469404274 | -3.02714694042744 |
134 | 16 | 19.5442058540098 | -3.54420585400977 |
135 | 21 | 18.9425930987127 | 2.05740690128731 |
136 | 26 | 19.1972788689491 | 6.80272113105094 |
137 | 18 | 20.2371452382789 | -2.23714523827891 |
138 | 18 | 19.9079161772403 | -1.9079161772403 |
139 | 17 | 19.6050446380504 | -2.60504463805042 |
140 | 22 | 19.1678523588344 | 2.83214764116561 |
141 | 30 | 19.5716912289917 | 10.4283087710083 |
142 | 30 | 21.2269742901924 | 8.7730257098076 |
143 | 24 | 22.7400557557215 | 1.25994424427852 |
144 | 21 | 23.1521283023901 | -2.15212830239013 |
145 | 21 | 23.0319889205597 | -2.03198892055972 |
146 | 29 | 22.9056857001207 | 6.09431429987925 |
147 | 31 | 24.0583612852257 | 6.94163871477434 |
148 | 20 | 25.4189022425882 | -5.41890224258817 |
149 | 16 | 24.8795459263428 | -8.87954592634277 |
150 | 22 | 23.7212796987443 | -1.72127969874426 |
151 | 20 | 23.6058721273291 | -3.60587212732912 |
152 | 28 | 23.1679487275985 | 4.83205127240148 |
153 | 38 | 24.0403745982060 | 13.9596254017940 |
154 | 22 | 26.4334229591065 | -4.43342295910651 |
155 | 20 | 26.0422274926932 | -6.04222749269321 |
156 | 17 | 25.3406928030624 | -8.34069280306238 |
157 | 28 | 24.1992295108641 | 3.80077048913593 |
158 | 22 | 24.9060064681551 | -2.90600646815513 |
159 | 31 | 24.5823121043630 | 6.41768789563703 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
160 | 25.7192620280444 | 13.5977102203377 | 37.8408138357511 |
161 | 25.9030123626268 | 13.6266298026009 | 38.1793949226526 |
162 | 26.0867626972091 | 13.6342796791011 | 38.5392457153172 |
163 | 26.2705130317915 | 13.6199267599969 | 38.9210993035861 |
164 | 26.4542633663739 | 13.5829934602471 | 39.3255332725007 |
165 | 26.6380137009562 | 13.5230557380148 | 39.7529716638977 |
166 | 26.8217640355386 | 13.4398376321801 | 40.2036904388971 |
167 | 27.005514370121 | 13.3332027218802 | 40.6778260183618 |
168 | 27.1892647047034 | 13.2031430793353 | 41.1753863300714 |
169 | 27.3730150392857 | 13.0497663739683 | 41.6962637046031 |
170 | 27.5567653738681 | 12.8732818104176 | 42.2402489373186 |
171 | 27.7405157084505 | 12.6739855527340 | 42.8070458641669 |