Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0 |
gamma | 0.220439902518461 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 1152.6 | 1138.42606036325 | 14.1739396367516 |
14 | 1211.85 | 1205.69543851981 | 6.15456148018666 |
15 | 1239.62 | 1230.78877185315 | 8.83122814685294 |
16 | 1244.13 | 1234.85210518648 | 9.27789481351965 |
17 | 1198.42 | 1187.73335518648 | 10.6866448135202 |
18 | 1227.99 | 1214.70877185315 | 13.2812281468528 |
19 | 1304.92 | 1283.14335518648 | 21.7766448135201 |
20 | 1340.26 | 1255.77585518648 | 84.4841448135198 |
21 | 1307.32 | 1342.94418851981 | -35.6241885198135 |
22 | 1356.51 | 1323.79002185315 | 32.719978146853 |
23 | 1383.29 | 1397.20710518648 | -13.9171051864801 |
24 | 1437.87 | 1379.69418851981 | 58.1758114801864 |
25 | 1494.56 | 1468.39710518648 | 26.1628948135199 |
26 | 1521.42 | 1547.65543851981 | -26.2354385198132 |
27 | 1498.76 | 1540.35877185315 | -41.5987718531471 |
28 | 1488.75 | 1493.99210518648 | -5.24210518648056 |
29 | 1524.62 | 1432.35335518648 | 92.26664481352 |
30 | 1439.27 | 1540.90877185315 | -101.638771853147 |
31 | 1423.11 | 1494.42335518648 | -71.3133551864801 |
32 | 1466.85 | 1373.96585518648 | 92.88414481352 |
33 | 1425.83 | 1469.53418851981 | -43.7041885198134 |
34 | 1363.45 | 1442.30002185315 | -78.850021853147 |
35 | 1389.18 | 1404.14710518648 | -14.96710518648 |
36 | 1395.89 | 1385.58418851981 | 10.3058114801865 |
37 | 1368.43 | 1426.41710518648 | -57.9871051864802 |
38 | 1349.03 | 1421.52543851981 | -72.4954385198134 |
39 | 1299.88 | 1367.96877185315 | -68.0887718531469 |
40 | 1365.41 | 1295.11210518648 | 70.2978948135194 |
41 | 1451.04 | 1309.01335518648 | 142.02664481352 |
42 | 1433.75 | 1467.32877185315 | -33.5787718531471 |
43 | 1464.65 | 1488.90335518648 | -24.2533551864799 |
44 | 1475.57 | 1415.50585518648 | 60.0641448135198 |
45 | 1471.16 | 1478.25418851981 | -7.09418851981331 |
46 | 1429.12 | 1487.63002185315 | -58.5100218531472 |
47 | 1452.46 | 1469.81710518648 | -17.3571051864799 |
48 | 1538.09 | 1448.86418851981 | 89.2258114801864 |
49 | 1631.59 | 1568.61710518648 | 62.9728948135198 |
50 | 1665.5 | 1684.68543851981 | -19.1854385198133 |
51 | 1690.6 | 1684.43877185315 | 6.16122814685286 |
52 | 1711.74 | 1685.83210518648 | 25.9078948135195 |
53 | 1734.1 | 1655.34335518648 | 78.75664481352 |
54 | 1748.09 | 1750.38877185315 | -2.29877185314717 |
55 | 1703.45 | 1803.24335518648 | -99.7933551864799 |
56 | 1745.74 | 1654.30585518648 | 91.4341448135199 |
57 | 1751.01 | 1748.42418851981 | 2.58581148018652 |
58 | 1795.65 | 1767.48002185315 | 28.1699781468531 |
59 | 1852.13 | 1836.34710518648 | 15.78289481352 |
60 | 1877.1 | 1848.53418851981 | 28.5658114801863 |
61 | 1989.31 | 1907.62710518648 | 81.6828948135199 |
62 | 2097.76 | 2042.40543851981 | 55.3545614801869 |
63 | 2154.87 | 2116.69877185315 | 38.1712281468526 |
64 | 2152.18 | 2150.10210518648 | 2.07789481351938 |
65 | 2250.27 | 2095.78335518648 | 154.48664481352 |
66 | 2346.9 | 2266.55877185315 | 80.3412281468532 |
67 | 2525.56 | 2402.05335518648 | 123.50664481352 |
68 | 2409.36 | 2476.41585518648 | -67.0558551864801 |
69 | 2394.36 | 2412.04418851981 | -17.6841885198132 |
70 | 2401.33 | 2410.83002185315 | -9.50002185314725 |
71 | 2354.32 | 2442.02710518648 | -87.70710518648 |
72 | 2450.41 | 2350.72418851981 | 99.6858114801862 |
73 | 2504.67 | 2480.93710518648 | 23.73289481352 |
74 | 2661.39 | 2557.76543851981 | 103.624561480186 |
75 | 2880.4 | 2680.32877185315 | 200.071228146853 |
76 | 3064.42 | 2875.63210518648 | 188.787894813519 |
77 | 3141.12 | 3008.02335518648 | 133.09664481352 |
78 | 3327.7 | 3157.40877185315 | 170.291228146853 |
79 | 3564.95 | 3382.85335518648 | 182.09664481352 |
80 | 3403.13 | 3515.80585518648 | -112.67585518648 |
81 | 3149.9 | 3405.81418851981 | -255.914188519813 |
82 | 3006.84 | 3166.37002185315 | -159.530021853147 |
83 | 3230.66 | 3047.53710518648 | 183.122894813519 |
84 | 3361.13 | 3227.06418851981 | 134.065811480187 |
85 | 3484.74 | 3391.65710518648 | 93.0828948135195 |
86 | 3411.13 | 3537.83543851981 | -126.705438519813 |
87 | 3288.18 | 3430.06877185315 | -141.888771853147 |
88 | 3280.37 | 3283.41210518648 | -3.04210518648051 |
89 | 3173.95 | 3223.97335518648 | -50.0233551864799 |
90 | 3165.26 | 3190.23877185315 | -24.9787718531466 |
91 | 3092.71 | 3220.41335518648 | -127.70335518648 |
92 | 3053.05 | 3043.56585518648 | 9.48414481351983 |
93 | 3181.96 | 3055.73418851981 | 126.225811480187 |
94 | 2999.93 | 3198.43002185315 | -198.500021853147 |
95 | 3249.57 | 3040.62710518648 | 208.94289481352 |
96 | 3210.52 | 3245.97418851981 | -35.4541885198137 |
97 | 3030.29 | 3241.04710518648 | -210.75710518648 |
98 | 2803.47 | 3083.38543851981 | -279.915438519814 |
99 | 2767.63 | 2822.40877185315 | -54.7787718531467 |
100 | 2882.6 | 2762.86210518648 | 119.737894813519 |
101 | 2863.36 | 2826.20335518648 | 37.1566448135204 |
102 | 2897.06 | 2879.64877185315 | 17.4112281468529 |
103 | 3012.61 | 2952.21335518648 | 60.3966448135202 |
104 | 3142.95 | 2963.46585518648 | 179.484144813519 |
105 | 3032.93 | 3145.63418851981 | -112.704188519813 |
106 | 3045.78 | 3049.40002185315 | -3.62002185314668 |
107 | 3110.52 | 3086.47710518648 | 24.0428948135195 |
108 | 3013.24 | 3106.92418851981 | -93.6841885198137 |
109 | 2987.1 | 3043.76710518648 | -56.6671051864801 |
110 | 2995.55 | 3040.19543851981 | -44.6454385198131 |
111 | 2833.18 | 3014.48877185315 | -181.308771853147 |
112 | 2848.96 | 2828.41210518648 | 20.5478948135196 |
113 | 2794.83 | 2792.56335518648 | 2.26664481352009 |
114 | 2845.26 | 2811.11877185315 | 34.1412281468533 |
115 | 2915.02 | 2900.41335518648 | 14.6066448135198 |
116 | 2892.63 | 2865.87585518648 | 26.7541448135198 |
117 | 2604.42 | 2895.31418851981 | -290.894188519813 |
118 | 2641.65 | 2620.89002185315 | 20.759978146853 |
119 | 2659.81 | 2682.34710518648 | -22.5371051864804 |
120 | 2638.53 | 2656.21418851981 | -17.6841885198132 |
121 | 2720.25 | 2669.05710518648 | 51.1928948135196 |
122 | 2745.88 | 2773.34543851981 | -27.4654385198132 |
123 | 2735.7 | 2764.81877185315 | -29.1187718531473 |
124 | 2811.7 | 2730.93210518648 | 80.7678948135194 |
125 | 2799.43 | 2755.30335518648 | 44.1266448135202 |
126 | 2555.28 | 2815.71877185315 | -260.438771853147 |
127 | 2304.98 | 2610.43335518648 | -305.45335518648 |
128 | 2214.95 | 2255.83585518648 | -40.8858551864805 |
129 | 2065.81 | 2217.63418851981 | -151.824188519813 |
130 | 1940.49 | 2082.28002185315 | -141.790021853147 |
131 | 2042 | 1981.18710518648 | 60.8128948135197 |
132 | 1995.37 | 2038.40418851981 | -43.0341885198136 |
133 | 1946.81 | 2025.89710518648 | -79.0871051864801 |
134 | 1765.9 | 1999.90543851981 | -234.005438519813 |
135 | 1635.25 | 1784.83877185315 | -149.588771853147 |
136 | 1833.42 | 1630.48210518648 | 202.93789481352 |
137 | 1910.43 | 1777.02335518648 | 133.40664481352 |
138 | 1959.67 | 1926.71877185315 | 32.9512281468531 |
139 | 1969.6 | 2014.82335518648 | -45.2233551864801 |
140 | 2061.41 | 1920.45585518648 | 140.95414481352 |
141 | 2093.48 | 2064.09418851981 | 29.3858114801869 |
142 | 2120.88 | 2109.95002185315 | 10.929978146853 |
143 | 2174.56 | 2161.57710518648 | 12.9828948135196 |
144 | 2196.72 | 2170.96418851981 | 25.7558114801864 |
145 | 2350.44 | 2227.24710518648 | 123.19289481352 |
146 | 2440.25 | 2403.53543851981 | 36.7145614801866 |
147 | 2408.64 | 2459.18877185315 | -50.5487718531472 |
148 | 2472.81 | 2403.87210518648 | 68.9378948135195 |
149 | 2407.6 | 2416.41335518648 | -8.81335518647984 |
150 | 2454.62 | 2423.88877185315 | 30.731228146853 |
151 | 2448.05 | 2509.77335518648 | -61.7233551864797 |
152 | 2497.84 | 2398.90585518648 | 98.9341448135197 |
153 | 2645.64 | 2500.52418851981 | 145.115811480186 |
154 | 2756.76 | 2662.11002185315 | 94.6499781468533 |
155 | 2849.27 | 2797.45710518648 | 51.8128948135195 |
156 | 2921.44 | 2845.67418851981 | 75.7658114801866 |
157 | 2981.85 | 2951.96710518648 | 29.8828948135197 |
158 | 3080.58 | 3034.94543851981 | 45.6345614801867 |
159 | 3106.22 | 3099.51877185315 | 6.70122814685283 |
160 | 3119.31 | 3101.45210518648 | 17.8578948135196 |
161 | 3061.26 | 3062.91335518648 | -1.65335518647953 |
162 | 3097.31 | 3077.54877185315 | 19.7612281468528 |
163 | 3161.69 | 3152.46335518648 | 9.22664481352012 |
164 | 3257.16 | 3112.54585518648 | 144.614144813519 |
165 | 3277.01 | 3259.84418851981 | 17.1658114801871 |
166 | 3295.32 | 3293.48002185315 | 1.8399781468529 |
167 | 3363.99 | 3336.01710518648 | 27.9728948135194 |
168 | 3494.17 | 3360.39418851981 | 133.775811480187 |
169 | 3667.03 | 3524.69710518648 | 142.33289481352 |
170 | 3813.06 | 3720.12543851981 | 92.9345614801864 |
171 | 3917.96 | 3831.99877185315 | 85.961228146853 |
172 | 3895.51 | 3913.19210518648 | -17.6821051864804 |
173 | 3801.06 | 3839.11335518648 | -38.0533551864801 |
174 | 3570.12 | 3817.34877185315 | -247.228771853147 |
175 | 3701.61 | 3625.27335518648 | 76.3366448135203 |
176 | 3862.27 | 3652.46585518648 | 209.80414481352 |
177 | 3970.1 | 3864.95418851981 | 105.145811480187 |
178 | 4138.52 | 3986.57002185315 | 151.949978146853 |
179 | 4199.75 | 4179.21710518648 | 20.5328948135202 |
180 | 4290.89 | 4196.15418851981 | 94.7358114801864 |
181 | 4443.91 | 4321.41710518648 | 122.492894813519 |
182 | 4502.64 | 4497.00543851981 | 5.63456148018759 |
183 | 4356.98 | 4521.57877185315 | -164.598771853148 |
184 | 4591.27 | 4352.21210518648 | 239.05789481352 |
185 | 4696.96 | 4534.87335518648 | 162.08664481352 |
186 | 4621.4 | 4713.24877185315 | -91.8487718531478 |
187 | 4562.84 | 4676.55335518648 | -113.71335518648 |
188 | 4202.52 | 4513.69585518648 | -311.17585518648 |
189 | 4296.49 | 4205.20418851981 | 91.2858114801857 |
190 | 4435.23 | 4312.96002185315 | 122.269978146853 |
191 | 4105.18 | 4475.92710518648 | -370.747105186479 |
192 | 4116.68 | 4101.58418851981 | 15.0958114801861 |
193 | 3844.49 | 4147.20710518648 | -302.717105186481 |
194 | 3720.98 | 3897.58543851981 | -176.605438519813 |
195 | 3674.4 | 3739.91877185315 | -65.518771853147 |
196 | 3857.62 | 3669.63210518648 | 187.987894813519 |
197 | 3801.06 | 3801.22335518648 | -0.163355186479748 |
198 | 3504.37 | 3817.34877185315 | -312.978771853147 |
199 | 3032.6 | 3559.52335518648 | -526.92335518648 |
200 | 3047.03 | 2983.45585518648 | 63.57414481352 |
201 | 2962.34 | 3049.71418851981 | -87.3741885198133 |
202 | 2197.82 | 2978.81002185315 | -780.990021853147 |
203 | 2014.45 | 2238.51710518648 | -224.06710518648 |
204 | 1862.83 | 2010.85418851981 | -148.024188519814 |
205 | 1905.41 | 1893.35710518648 | 12.05289481352 |
206 | 1810.99 | 1958.50543851981 | -147.515438519813 |
207 | 1670.07 | 1829.92877185315 | -159.858771853147 |
208 | 1864.44 | 1665.30210518648 | 199.13789481352 |
209 | 2052.02 | 1808.04335518648 | 243.97664481352 |
210 | 2029.6 | 2068.30877185315 | -38.708771853147 |
211 | 2070.83 | 2084.75335518648 | -13.92335518648 |
212 | 2293.41 | 2021.68585518648 | 271.72414481352 |
213 | 2443.27 | 2296.09418851981 | 147.175811480187 |
214 | 2513.17 | 2459.74002185315 | 53.429978146853 |
215 | 2466.92 | 2553.86710518648 | -86.9471051864803 |
216 | 2502.66 | 2463.32418851981 | 39.3358114801863 |
217 | 2539.91 | 2533.18710518648 | 6.72289481351982 |
218 | 2482.6 | 2593.00543851981 | -110.405438519813 |
219 | 2626.15 | 2501.53877185315 | 124.611228146853 |
220 | 2656.32 | 2621.38210518648 | 34.9378948135195 |
221 | 2446.66 | 2599.92335518648 | -153.26335518648 |
222 | 2467.38 | 2462.94877185315 | 4.4312281468533 |
223 | 2462.32 | 2522.53335518648 | -60.2133551864799 |
224 | 2504.58 | 2413.17585518648 | 91.4041448135195 |
225 | 2579.39 | 2507.26418851981 | 72.1258114801867 |
226 | 2649.24 | 2595.86002185315 | 53.3799781468529 |
227 | 2636.87 | 2689.93710518648 | -53.0671051864801 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
228 | 2633.27418851981 | 2375.29088812151 | 2891.25748891811 |
229 | 2663.80129370629 | 2298.95781141725 | 3028.64477599534 |
230 | 2716.89673222611 | 2270.05654843195 | 3163.73691602027 |
231 | 2735.83550407925 | 2219.86890328265 | 3251.80210487585 |
232 | 2731.06760926573 | 2154.19941251539 | 3307.93580601608 |
233 | 2674.67096445221 | 2042.74351631723 | 3306.5984125872 |
234 | 2690.95973630536 | 2008.40008104379 | 3373.51939156693 |
235 | 2746.11309149184 | 2016.42612691375 | 3475.80005606994 |
236 | 2696.96894667832 | 1923.01904548342 | 3470.91884787322 |
237 | 2699.65313519813 | 1883.83830765208 | 3515.46796274418 |
238 | 2716.12315705128 | 1860.48934745258 | 3571.75696664999 |
239 | 2756.82026223776 | 1863.13989464944 | 3650.50062982608 |