Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.206908976421986 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 67.4 | 62.4 | 5.00000000000001 |
3 | 76.1 | 63.4345448821099 | 12.6654551178901 |
4 | 67.4 | 66.0551412364712 | 1.34485876352883 |
5 | 74.5 | 66.3334045866651 | 8.16659541333493 |
6 | 72.6 | 68.0231464844907 | 4.57685351550931 |
7 | 60.5 | 68.9701385606181 | -8.47013856061808 |
8 | 66.1 | 67.2175908608882 | -1.1175908608882 |
9 | 76.5 | 66.9863512798032 | 9.51364872019676 |
10 | 76.8 | 68.9548105985375 | 7.84518940146251 |
11 | 77 | 70.5780507074307 | 6.42194929256928 |
12 | 71 | 71.9068096621901 | -0.906809662190128 |
13 | 74.8 | 71.7191826031768 | 3.08081739682321 |
14 | 73.7 | 72.3566313772965 | 1.34336862270347 |
15 | 80.5 | 72.6345864039775 | 7.86541359602248 |
16 | 71.8 | 74.2620110802661 | -2.46201108026611 |
17 | 76.9 | 73.7525988877087 | 3.14740111229135 |
18 | 79.9 | 74.4038244302423 | 5.49617556975772 |
19 | 65.9 | 75.5410324916164 | -9.64103249161637 |
20 | 69.5 | 73.5462163271249 | -4.04621632712491 |
21 | 75.1 | 72.7090178484976 | 2.39098215150243 |
22 | 79.6 | 73.2037335181082 | 6.39626648189183 |
23 | 75.2 | 74.5271784687987 | 0.672821531201336 |
24 | 68 | 74.6663912831342 | -6.6663912831342 |
25 | 72.8 | 73.2870550863124 | -0.487055086312452 |
26 | 71.5 | 73.1862790169424 | -1.68627901694242 |
27 | 78.5 | 72.837372751585 | 5.66262724841501 |
28 | 76.8 | 74.0090211594138 | 2.79097884058621 |
29 | 75.3 | 74.5864997345349 | 0.713500265465086 |
30 | 76.7 | 74.7341293441391 | 1.9658706558609 |
31 | 69.7 | 75.1408856293213 | -5.4408856293213 |
32 | 67.8 | 74.0151175529293 | -6.21511755292933 |
33 | 77.5 | 72.7291539417104 | 4.77084605828961 |
34 | 82.5 | 73.716284816298 | 8.78371518370204 |
35 | 75.3 | 75.53371433414 | -0.233714334140004 |
36 | 70.9 | 75.4853567404879 | -4.58535674048794 |
37 | 76 | 74.5366052707839 | 1.46339472921608 |
38 | 73.7 | 74.8393947763073 | -1.13939477630734 |
39 | 79.7 | 74.603643769401 | 5.09635623059897 |
40 | 77.8 | 75.6581256205561 | 2.14187437944392 |
41 | 73.3 | 76.1012986560313 | -2.80129865603129 |
42 | 78.3 | 75.5216848184596 | 2.77831518154044 |
43 | 71.9 | 76.0965431688498 | -4.19654316884976 |
44 | 67 | 75.2282407172724 | -8.22824071727237 |
45 | 82 | 73.5257438527078 | 8.47425614729217 |
46 | 83.7 | 75.2791435180818 | 8.42085648191822 |
47 | 74.8 | 77.0214943133519 | -2.22149431335193 |
48 | 80 | 76.561847198849 | 3.43815280115099 |
49 | 74.3 | 77.2732318757175 | -2.97323187571754 |
50 | 76.8 | 76.6580435116476 | 0.141956488352406 |
51 | 89 | 76.6874155833491 | 12.3125844166509 |
52 | 81.9 | 79.2349998221076 | 2.66500017789241 |
53 | 76.8 | 79.7864122810797 | -2.98641228107972 |
54 | 88.9 | 79.1684967728275 | 9.73150322717254 |
55 | 75.8 | 81.182032144609 | -5.382032144609 |
56 | 75.5 | 80.0684413824977 | -4.56844138249772 |
57 | 89.1 | 79.1231898522013 | 9.97681014779872 |
58 | 88 | 81.1874814278388 | 6.81251857216121 |
59 | 85.9 | 82.5970526724604 | 3.30294732753957 |
60 | 89.3 | 83.2804621231774 | 6.01953787682261 |
61 | 82.9 | 84.5259585438041 | -1.62595854380412 |
62 | 81.2 | 84.189533125801 | -2.98953312580102 |
63 | 90.5 | 83.5709718867619 | 6.9290281132381 |
64 | 86.4 | 85.0046500012712 | 1.39534999872885 |
65 | 81.8 | 85.2933604412586 | -3.49336044125856 |
66 | 91.3 | 84.5705528080847 | 6.72944719191531 |
67 | 73.4 | 85.9629358384497 | -12.5629358384497 |
68 | 76.6 | 83.363551643261 | -6.76355164326097 |
69 | 91 | 81.9641120957766 | 9.03588790422342 |
70 | 87 | 83.8337184131033 | 3.16628158689674 |
71 | 89.7 | 84.4888504953119 | 5.21114950468815 |
72 | 90.7 | 85.5670841053088 | 5.13291589469118 |
73 | 86.5 | 86.6291304791395 | -0.129130479139519 |
74 | 86.6 | 86.6024122238759 | -0.00241222387587925 |
75 | 98.8 | 86.6019131131028 | 12.1980868868972 |
76 | 84.4 | 89.1258067851772 | -4.72580678517716 |
77 | 91.4 | 88.1479949404881 | 3.25200505951193 |
78 | 95.7 | 88.8208639786708 | 6.87913602132919 |
79 | 78.5 | 90.2442189715117 | -11.7442189715117 |
80 | 81.7 | 87.8142346452405 | -6.1142346452405 |
81 | 94.3 | 86.5491446131899 | 7.75085538681006 |
82 | 98.5 | 88.1528661676697 | 10.3471338323303 |
83 | 95.4 | 90.2937810378184 | 5.10621896218157 |
84 | 91.7 | 91.35030357667 | 0.349696423330045 |
85 | 92.8 | 91.4226589056796 | 1.37734109432039 |
86 | 90.5 | 91.7076431416894 | -1.20764314168937 |
87 | 102.2 | 91.4577709353594 | 10.7422290646406 |
88 | 91.8 | 93.6804345556147 | -1.8804345556147 |
89 | 95 | 93.2913557664839 | 1.70864423351607 |
90 | 102 | 93.6448895959101 | 8.35511040408994 |
91 | 88.9 | 95.373636937513 | -6.47363693751299 |
92 | 89.6 | 94.0341833450446 | -4.43418334504463 |
93 | 97.9 | 93.116711007854 | 4.783288992146 |
94 | 108.6 | 94.1064164371495 | 14.4935835628505 |
95 | 100.8 | 97.1052689768254 | 3.6947310231746 |
96 | 95.1 | 97.869741990985 | -2.76974199098501 |
97 | 101 | 97.2966575106773 | 3.70334248932271 |
98 | 100.9 | 98.0629123144831 | 2.83708768551691 |
99 | 102.5 | 98.6499312235128 | 3.85006877648718 |
100 | 105.4 | 99.44654501321 | 5.95345498678998 |
101 | 98.4 | 100.678368290701 | -2.27836829070111 |
102 | 105.3 | 100.20695343976 | 5.09304656024017 |
103 | 96.5 | 101.260750490409 | -4.76075049040864 |
104 | 88.1 | 100.275708479438 | -12.1757084794377 |
105 | 107.9 | 97.7564451007448 | 10.1435548992552 |
106 | 107 | 99.8552376622299 | 7.14476233777012 |
107 | 92.5 | 101.333553124316 | -8.83355312431625 |
108 | 95.7 | 99.5058116891947 | -3.80581168919473 |
109 | 85.2 | 98.7183550881286 | -13.5183550881286 |
110 | 85.5 | 95.921286073935 | -10.421286073935 |
111 | 94.7 | 93.7650284393764 | 0.934971560623609 |
112 | 86.2 | 93.9584824479687 | -7.75848244796869 |
113 | 88.8 | 92.3531827860715 | -3.55318278607155 |
114 | 93.4 | 91.6179973727652 | 1.78200262723476 |
115 | 83.4 | 91.9867097123477 | -8.58670971234767 |
116 | 82.9 | 90.2100423949331 | -7.31004239493308 |
117 | 96.7 | 88.6975290053961 | 8.00247099460385 |
118 | 96.2 | 90.3533120877363 | 5.84668791226373 |
119 | 92.8 | 91.5630442991215 | 1.23695570087845 |
120 | 92.8 | 91.8189815370696 | 0.981018462930351 |
121 | 90 | 92.0219630630856 | -2.02196306308564 |
122 | 95.4 | 91.6036007553395 | 3.79639924466048 |
123 | 108.3 | 92.3891098371414 | 15.9108901628586 |
124 | 96.3 | 95.6812158347011 | 0.618784165298862 |
125 | 95 | 95.8092478329692 | -0.809247832969248 |
126 | 109 | 95.6418071921779 | 13.3581928078221 |
127 | 92 | 98.4057371928919 | -6.40573719289188 |
128 | 92.3 | 97.0803326670824 | -4.78033266708238 |
129 | 107 | 96.0912389279798 | 10.9087610720202 |
130 | 105.5 | 98.3483595154235 | 7.15164048457652 |
131 | 105.4 | 99.8280981278253 | 5.57190187217475 |
132 | 103.9 | 100.980974640921 | 2.91902535907931 |
133 | 99.2 | 101.584947190118 | -2.38494719011761 |
134 | 102.2 | 101.09148020819 | 1.10851979181011 |
135 | 121.5 | 101.320842903657 | 20.1791570963432 |
136 | 102.3 | 105.49609164352 | -3.19609164351967 |
137 | 110 | 104.834791593008 | 5.16520840699187 |
138 | 105.9 | 105.903519577505 | -0.00351957750504539 |
139 | 91.9 | 105.902791345326 | -14.002791345326 |
140 | 100 | 103.005488121014 | -3.00548812101397 |
141 | 111.7 | 102.383625650247 | 9.31637434975347 |
142 | 104.9 | 104.311267130918 | 0.588732869081937 |
143 | 103.3 | 104.433081246246 | -1.13308124624579 |
144 | 101.8 | 104.198636565382 | -2.39863656538212 |
145 | 100.8 | 103.702337128831 | -2.90233712883055 |
146 | 104.2 | 103.101817524273 | 1.09818247572731 |
147 | 116.5 | 103.32904133625 | 13.17095866375 |
148 | 97.9 | 106.054230911863 | -8.15423091186278 |
149 | 100.7 | 104.367047340381 | -3.66704734038073 |
150 | 107 | 103.608302328692 | 3.39169767130841 |
151 | 96.3 | 104.310075022195 | -8.01007502219485 |
152 | 96 | 102.652718598289 | -6.6527185982892 |
153 | 104.5 | 101.276211402694 | 3.22378859730634 |
154 | 107.4 | 101.943242201563 | 5.45675779843683 |
155 | 102.4 | 103.07229437222 | -0.672294372220435 |
156 | 94.9 | 102.93319063181 | -8.03319063181003 |
157 | 98.8 | 101.27105138078 | -2.47105138077953 |
158 | 96.8 | 100.759768668896 | -3.95976866889629 |
159 | 108.2 | 99.9404569867471 | 8.25954301325291 |
160 | 103.8 | 101.649430577333 | 2.15056942266737 |
161 | 102.3 | 102.094402695301 | 0.205597304698841 |
162 | 107.2 | 102.136942623172 | 5.0630573768285 |
163 | 102 | 103.184534642577 | -1.18453464257686 |
164 | 92.6 | 102.939443792145 | -10.3394437921449 |
165 | 105.2 | 100.80012006034 | 4.39987993966047 |
166 | 113 | 101.710494715034 | 11.2895052849657 |
167 | 105.6 | 104.046394697857 | 1.55360530214284 |
168 | 101.6 | 104.367849580687 | -2.76784958068731 |
169 | 101.7 | 103.795156657057 | -2.09515665705726 |
170 | 102.7 | 103.361649937702 | -0.661649937701824 |
171 | 109 | 103.224748626342 | 5.77525137365774 |
172 | 105.5 | 104.419699976645 | 1.08030002335455 |
173 | 103.3 | 104.643223748706 | -1.34322374870639 |
174 | 108.6 | 104.365298697756 | 4.23470130224415 |
175 | 98.2 | 105.241496409656 | -7.04149640965603 |
176 | 90 | 103.784547595055 | -13.784547595055 |
177 | 112.4 | 100.932400961722 | 11.467599038278 |
178 | 111.9 | 103.30515014075 | 8.59484985925013 |
179 | 102.1 | 105.083501727628 | -2.98350172762798 |
180 | 102.4 | 104.466188439011 | -2.06618843901124 |
181 | 101.7 | 104.038675504 | -2.33867550400048 |
182 | 98.7 | 103.554782549285 | -4.85478254928456 |
183 | 114 | 102.550284461261 | 11.4497155387392 |
184 | 105.1 | 104.919333383704 | 0.180666616295767 |
185 | 98.3 | 104.956714928356 | -6.65671492835561 |
186 | 110 | 103.579380856197 | 6.42061914380341 |
187 | 96.5 | 104.907864591236 | -8.40786459123638 |
188 | 92.2 | 103.168201934769 | -10.968201934769 |
189 | 112 | 100.898782499256 | 11.1012175007437 |
190 | 111.4 | 103.195724049373 | 8.20427595062699 |
191 | 107.5 | 104.893262388601 | 2.60673761139924 |
192 | 103.4 | 105.432619799576 | -2.03261979957607 |
193 | 103.5 | 105.012052517391 | -1.51205251739071 |
194 | 107.4 | 104.699195278721 | 2.7008047212789 |
195 | 117.6 | 105.258016019117 | 12.3419839808834 |
196 | 110.2 | 107.811683291618 | 2.38831670838228 |
197 | 104.3 | 108.305847457121 | -4.00584745712064 |
198 | 115.9 | 107.477001660065 | 8.42299833993482 |
199 | 98.9 | 109.219795624985 | -10.3197956249852 |
200 | 101.9 | 107.084537275335 | -5.1845372753354 |
201 | 113.5 | 106.011809974474 | 7.48819002552588 |
202 | 109.5 | 107.561183707909 | 1.93881629209099 |
203 | 110 | 107.962342202376 | 2.03765779762418 |
204 | 114.2 | 108.383951891581 | 5.81604810841948 |
205 | 106.9 | 109.587344452515 | -2.68734445251462 |
206 | 109.2 | 109.031308762552 | 0.168691237448485 |
207 | 124.2 | 109.066212493823 | 15.1337875061767 |
208 | 104.7 | 112.197528976114 | -7.4975289761142 |
209 | 111.9 | 110.646222929972 | 1.25377707002778 |
210 | 119 | 110.905640660193 | 8.09435933980697 |
211 | 102.9 | 112.580436265984 | -9.68043626598423 |
212 | 106.3 | 110.577467106871 | -4.27746710687116 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
213 | 109.69242076611 | 96.9947578721548 | 122.390083660065 |
214 | 109.69242076611 | 96.7258043860414 | 122.659037146178 |
215 | 109.69242076611 | 96.4623172998781 | 122.922524232341 |
216 | 109.69242076611 | 96.2039762632572 | 123.180865268962 |
217 | 109.69242076611 | 95.9504910440558 | 123.434350488164 |
218 | 109.69242076611 | 95.7015977072184 | 123.683243825001 |
219 | 109.69242076611 | 95.4570553951562 | 123.927786137063 |
220 | 109.69242076611 | 95.2166435978924 | 124.168197934327 |
221 | 109.69242076611 | 94.9801598248669 | 124.404681707353 |
222 | 109.69242076611 | 94.7474176084468 | 124.637423923773 |
223 | 109.69242076611 | 94.518244783148 | 124.866596749071 |
224 | 109.69242076611 | 94.2924819954123 | 125.092359536807 |