Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.608148513917232 |
beta | FALSE |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
2 | 675 | 464 | 211 |
3 | 703 | 592.319336436536 | 110.680663563464 |
4 | 887 | 659.62961750203 | 227.370382497970 |
5 | 1139 | 797.904577726963 | 341.095422273037 |
6 | 1077 | 1005.34125188628 | 71.6587481137188 |
7 | 1318 | 1048.92041306081 | 269.079586939191 |
8 | 1260 | 1212.56076398334 | 47.4392360166596 |
9 | 1120 | 1241.41086486824 | -121.410864868241 |
10 | 963 | 1167.57502782521 | -204.575027825214 |
11 | 996 | 1043.16302866873 | -47.1630286687339 |
12 | 960 | 1014.48090287201 | -54.4809028720076 |
13 | 530 | 981.348422753527 | -451.348422753527 |
14 | 883 | 706.861550197083 | 176.138449802917 |
15 | 894 | 813.979886688412 | 80.020113311588 |
16 | 1045 | 862.643999682343 | 182.356000317657 |
17 | 1199 | 973.543530279416 | 225.456469720584 |
18 | 1287 | 1110.65454729301 | 176.345452706985 |
19 | 1565 | 1217.89877229283 | 347.101227707171 |
20 | 1577 | 1428.98786810179 | 148.012131898208 |
21 | 1076 | 1519.00122615741 | -443.001226157408 |
22 | 918 | 1249.59068880627 | -331.590688806269 |
23 | 1008 | 1047.93430417995 | -39.9343041799452 |
24 | 1063 | 1023.64831643859 | 39.3516835614071 |
25 | 544 | 1047.57998431660 | -503.579984316604 |
26 | 635 | 741.328565215998 | -106.328565215998 |
27 | 804 | 676.665006292938 | 127.334993707062 |
28 | 980 | 754.103593485548 | 225.896406514452 |
29 | 1018 | 891.482157406555 | 126.517842593445 |
30 | 1064 | 968.423795363773 | 95.5762046362272 |
31 | 1404 | 1026.54832217914 | 377.451677820856 |
32 | 1286 | 1256.09499912146 | 29.9050008785368 |
33 | 1104 | 1274.28168096444 | -170.281680964439 |
34 | 999 | 1170.72512973859 | -171.725129738587 |
35 | 996 | 1066.29074728582 | -70.2907472858215 |
36 | 1015 | 1023.54353378182 | -8.54353378181736 |
37 | 615 | 1018.34779640880 | -403.347796408803 |
38 | 722 | 773.052433431 | -51.0524334309995 |
39 | 832 | 742.004971908079 | 89.9950280919213 |
40 | 977 | 796.73531450212 | 180.264685497880 |
41 | 1270 | 906.363015099413 | 363.636984900587 |
42 | 1437 | 1127.50830707205 | 309.491692927952 |
43 | 1520 | 1315.72522019591 | 204.27477980409 |
44 | 1708 | 1439.95462396454 | 268.045376035463 |
45 | 1151 | 1602.96602106289 | -451.966021062889 |
46 | 934 | 1328.10355701241 | -394.103557012409 |
47 | 1159 | 1088.43006448582 | 70.5699355141824 |
48 | 1209 | 1131.34706589600 | 77.6529341039975 |
49 | 699 | 1178.57158237266 | -479.571582372661 |
50 | 830 | 886.920837235792 | -56.9208372357921 |
51 | 996 | 852.30451465992 | 143.695485340080 |
52 | 1124 | 939.692710526105 | 184.307289473895 |
53 | 1458 | 1051.77891472377 | 406.221085276233 |
54 | 1270 | 1298.82166405635 | -28.8216640563533 |
55 | 1753 | 1281.29381189186 | 471.70618810814 |
56 | 2258 | 1568.16122919539 | 689.838770804612 |
57 | 1208 | 1987.68565250270 | -779.685652502702 |
58 | 1241 | 1513.52098161060 | -272.520981610597 |
59 | 1265 | 1347.78775163285 | -82.787751632847 |
60 | 1828 | 1297.44050350678 | 530.559496493218 |
61 | 809 | 1620.09947284381 | -811.099472843807 |
62 | 997 | 1126.83053379480 | -129.830533794796 |
63 | 1164 | 1047.87428760641 | 116.125712393590 |
64 | 1205 | 1118.49596702615 | 86.5040329738486 |
65 | 1538 | 1171.10326612704 | 366.896733872955 |
66 | 1513 | 1394.23096959297 | 118.769030407032 |
67 | 1378 | 1466.46017893440 | -88.4601789343951 |
68 | 2083 | 1412.66325257459 | 670.33674742541 |
69 | 1357 | 1820.32754934546 | -463.327549345464 |
70 | 1536 | 1538.55558875411 | -2.55558875410725 |
71 | 1526 | 1537.00141125111 | -11.0014112511135 |
72 | 1376 | 1530.31091934776 | -154.310919347757 |
73 | 779 | 1436.46696306522 | -657.466963065217 |
74 | 1005 | 1036.62940652743 | -31.6294065274296 |
75 | 1193 | 1017.39402995169 | 175.605970048311 |
76 | 1522 | 1124.18853967156 | 397.811460328437 |
77 | 1539 | 1366.11698808955 | 172.883011910454 |
78 | 1546 | 1471.25553486442 | 74.7444651355763 |
79 | 2116 | 1516.71127026016 | 599.288729739837 |
80 | 2326 | 1881.16782065879 | 444.83217934121 |
81 | 1596 | 2151.69184946771 | -555.69184946771 |
82 | 1356 | 1813.74867701800 | -457.748677018004 |
83 | 1553 | 1535.36949934193 | 17.6305006580740 |
84 | 1613 | 1546.09146211675 | 66.9085378832497 |
85 | 814 | 1586.78178999882 | -772.781789998824 |
86 | 1150 | 1116.81569282874 | 33.1843071712592 |
87 | 1225 | 1136.99667992032 | 88.003320079685 |
88 | 1691 | 1190.51576824656 | 500.484231753442 |
89 | 1759 | 1494.88451002642 | 264.115489973579 |
90 | 1754 | 1655.50595275637 | 98.4940472436256 |
91 | 2100 | 1715.40496121728 | 384.595038782721 |
92 | 2062 | 1949.29586251293 | 112.704137487069 |
93 | 2012 | 2017.83671623802 | -5.83671623801547 |
94 | 1897 | 2014.28712593171 | -117.287125931710 |
95 | 1964 | 1942.95913459472 | 21.0408654052826 |
96 | 2186 | 1955.75510562247 | 230.244894377528 |
97 | 966 | 2095.77819597520 | -1129.77819597520 |
98 | 1549 | 1408.70526503679 | 140.294734963211 |
99 | 1538 | 1494.02529961508 | 43.9747003849222 |
100 | 1612 | 1520.76844830412 | 91.2315516958763 |
101 | 2078 | 1576.25078089033 | 501.749219109666 |
102 | 2137 | 1881.38882285101 | 255.611177148991 |
103 | 2907 | 2036.83838037480 | 870.161619625198 |
104 | 2249 | 2566.02587621768 | -317.025876217678 |
105 | 1883 | 2373.22706072259 | -490.227060722589 |
106 | 1739 | 2075.09620226213 | -336.096202262134 |
107 | 1828 | 1870.69979632319 | -42.6997963231918 |
108 | 1868 | 1844.73197864467 | 23.2680213553258 |
109 | 1138 | 1858.88239125371 | -720.88239125371 |
110 | 1430 | 1420.47883630367 | 9.52116369633404 |
111 | 1809 | 1426.26911785635 | 382.730882143646 |
112 | 1763 | 1659.02633506224 | 103.973664937756 |
113 | 2200 | 1722.25776488067 | 477.742235119332 |
114 | 2067 | 2012.79599520399 | 54.2040047960136 |
115 | 2503 | 2045.76008016904 | 457.239919830955 |
116 | 2141 | 2323.82985791787 | -182.829857917875 |
117 | 2103 | 2212.64215152542 | -109.642151525421 |
118 | 1972 | 2145.96344001255 | -173.963440012548 |
119 | 2181 | 2040.16783249299 | 140.832167507013 |
120 | 2344 | 2125.81470587412 | 218.185294125880 |
121 | 970 | 2258.50376825537 | -1288.50376825537 |
122 | 1199 | 1474.90211641411 | -275.902116414113 |
123 | 1718 | 1307.11265433025 | 410.887345669749 |
124 | 1683 | 1556.99318298670 | 126.006817013295 |
125 | 2025 | 1633.62404149678 | 391.375958503219 |
126 | 2051 | 1871.63874904345 | 179.361250956554 |
127 | 2439 | 1980.71702726701 | 458.28297273299 |
128 | 2353 | 2259.42113608815 | 93.578863911851 |
129 | 2230 | 2316.33098311020 | -86.3309831102042 |
130 | 1852 | 2263.82892402672 | -411.82892402672 |
131 | 2147 | 2013.37577589174 | 133.624224108262 |
132 | 2286 | 2094.63914920652 | 191.360850793480 |
133 | 1007 | 2211.01496623851 | -1204.01496623851 |
134 | 1665 | 1478.79505378645 | 186.204946213545 |
135 | 1642 | 1592.03531511026 | 49.9646848897396 |
136 | 1518 | 1622.42126397430 | -104.421263974298 |
137 | 1831 | 1558.91762746697 | 272.08237253303 |
138 | 2207 | 1724.38411798601 | 482.615882013993 |
139 | 2822 | 2017.88624942567 | 804.11375057433 |
140 | 2393 | 2506.90683185786 | -113.906831857861 |
141 | 2306 | 2437.63456133848 | -131.634561338483 |
142 | 1785 | 2357.58119848034 | -572.581198480338 |
143 | 2047 | 2009.36679352757 | 37.6332064724272 |
144 | 2171 | 2032.25337211772 | 138.746627882280 |
145 | 1212 | 2116.63192767536 | -904.631927675356 |
146 | 1335 | 1566.48136521751 | -231.481365217507 |
147 | 2011 | 1425.70631696095 | 585.293683039052 |
148 | 1860 | 1781.65180050629 | 78.3481994937092 |
149 | 1954 | 1829.29914159648 | 124.700858403519 |
150 | 2152 | 1905.13578331878 | 246.864216681216 |
151 | 2835 | 2055.26588983281 | 779.734110167193 |
152 | 2224 | 2529.46003018156 | -305.460030181560 |
153 | 2182 | 2343.69496676553 | -161.694966765532 |
154 | 1992 | 2245.36041301918 | -253.360413019177 |
155 | 2389 | 2091.27965435611 | 297.720345643892 |
156 | 2724 | 2272.33784012237 | 451.662159877635 |
157 | 891 | 2547.01551144460 | -1656.01551144460 |
158 | 1247 | 1539.91213913568 | -292.912139135680 |
159 | 2017 | 1361.778057012 | 655.221942988001 |
160 | 2257 | 1760.25030792611 | 496.749692073887 |
161 | 2255 | 2062.34789494969 | 192.652105050310 |
162 | 2255 | 2179.50898633906 | 75.4910136609378 |
163 | 3057 | 2225.41873411107 | 831.581265888933 |
164 | 3330 | 2731.14364516283 | 598.856354837168 |
165 | 1896 | 3095.33724740695 | -1199.33724740695 |
166 | 2096 | 2365.96208271083 | -269.962082710828 |
167 | 2374 | 2201.78504329624 | 172.214956703763 |
168 | 2535 | 2306.51731328995 | 228.482686710049 |
169 | 1041 | 2445.46871966848 | -1404.46871966848 |
170 | 1728 | 1591.34315495886 | 136.656845041142 |
171 | 2201 | 1674.45081218725 | 526.549187812754 |
172 | 2455 | 1994.67091825990 | 460.329081740102 |
173 | 2204 | 2274.61936523302 | -70.6193652330248 |
174 | 2660 | 2231.67230321278 | 428.327696787218 |
175 | 3670 | 2492.15915548352 | 1177.84084451648 |
176 | 2665 | 3208.46131470723 | -543.461314707234 |
177 | 2639 | 2877.95612379652 | -238.956123796524 |
178 | 2226 | 2732.63531221825 | -506.635312218246 |
179 | 2586 | 2424.52579999473 | 161.474200005273 |
180 | 2684 | 2522.72609476391 | 161.273905236092 |
181 | 1185 | 2620.80458056687 | -1435.80458056687 |
182 | 1749 | 1747.62215861957 | 1.37784138042798 |
183 | 2459 | 1748.46009080749 | 710.539909192507 |
184 | 2618 | 2180.5738806618 | 437.426119338199 |
185 | 2585 | 2446.59392508591 | 138.406074914092 |
186 | 3310 | 2530.76537386203 | 779.23462613797 |
187 | 3923 | 3004.65575374069 | 918.344246259314 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
188 | 3563.14544236773 | 2697.56123263648 | 4428.72965209897 |
189 | 3563.14544236773 | 2550.06255680919 | 4576.22832792627 |
190 | 3563.14544236773 | 2421.46341926008 | 4704.82746547538 |
191 | 3563.14544236773 | 2305.95064808853 | 4820.34023664693 |
192 | 3563.14544236773 | 2200.19289013479 | 4926.09799460067 |
193 | 3563.14544236773 | 2102.07030107149 | 5024.22058366397 |
194 | 3563.14544236773 | 2010.13498606378 | 5116.15589867167 |
195 | 3563.14544236773 | 1923.34594661682 | 5202.94493811864 |
196 | 3563.14544236773 | 1840.92498750706 | 5285.36589722840 |
197 | 3563.14544236773 | 1762.27226415222 | 5364.01862058324 |
198 | 3563.14544236773 | 1686.9138167704 | 5439.37706796506 |
199 | 3563.14544236773 | 1614.46742335916 | 5511.8234613763 |