Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 1 |
beta | 0.156597557299119 |
gamma | FALSE |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
3 | 1206.41 | 1208.61 | -2.19999999999982 |
4 | 1192.72 | 1237.81548537394 | -45.095485373942 |
5 | 1214.82 | 1217.06364251916 | -2.24364251916450 |
6 | 1199.07 | 1238.81229358121 | -39.7422935812108 |
7 | 1157.47 | 1216.83874748493 | -59.3687474849287 |
8 | 1100.1 | 1165.94174664888 | -65.8417466488809 |
9 | 1095.63 | 1098.26108995536 | -2.63108995535822 |
10 | 1105.63 | 1093.37906769532 | 12.2509323046850 |
11 | 1137.79 | 1105.29753376887 | 32.4924662311341 |
12 | 1124.72 | 1142.54577461129 | -17.8257746112854 |
13 | 1152.6 | 1126.68430185019 | 25.9156981498065 |
14 | 1211.85 | 1158.62263687615 | 53.2273631238456 |
15 | 1239.62 | 1226.20791192282 | 13.4120880771782 |
16 | 1244.13 | 1256.07821215399 | -11.9482121539884 |
17 | 1198.42 | 1258.71715131658 | -60.2971513165824 |
18 | 1227.99 | 1203.56476470831 | 24.4252352916897 |
19 | 1304.92 | 1236.95969689144 | 67.9603031085551 |
20 | 1340.26 | 1324.53211435155 | 15.7278856484475 |
21 | 1307.32 | 1362.33506282558 | -55.0150628255792 |
22 | 1356.51 | 1320.77983837244 | 35.730161627564 |
23 | 1383.29 | 1375.56509440522 | 7.72490559478479 |
24 | 1437.87 | 1403.55479575172 | 34.3152042482752 |
25 | 1494.56 | 1463.50847291522 | 31.051527084775 |
26 | 1521.42 | 1525.06106620711 | -3.64106620710822 |
27 | 1498.76 | 1551.35088413311 | -52.5908841331109 |
28 | 1488.75 | 1520.45528014166 | -31.7052801416646 |
29 | 1524.62 | 1505.48031071800 | 19.1396892820042 |
30 | 1439.27 | 1544.34753930702 | -105.077539307022 |
31 | 1423.11 | 1442.54265332454 | -19.4326533245398 |
32 | 1466.85 | 1423.33954728208 | 43.5104527179237 |
33 | 1425.83 | 1473.89317789468 | -48.063177894682 |
34 | 1363.45 | 1425.34660164034 | -61.8966016403417 |
35 | 1389.18 | 1353.27374501835 | 35.9062549816524 |
36 | 1395.89 | 1384.62657684023 | 11.2634231597663 |
37 | 1368.43 | 1393.10040139388 | -24.6704013938795 |
38 | 1349.03 | 1361.77707679801 | -12.7470767980092 |
39 | 1299.88 | 1340.38091570874 | -40.5009157087366 |
40 | 1365.41 | 1284.88857124037 | 80.521428759629 |
41 | 1451.04 | 1363.02803029436 | 88.011969705636 |
42 | 1433.75 | 1462.44048976335 | -28.6904897633506 |
43 | 1464.65 | 1440.65762914869 | 23.9923708513056 |
44 | 1475.57 | 1475.31477581782 | 0.255224182176335 |
45 | 1471.16 | 1486.27474330132 | -15.1147433013159 |
46 | 1429.12 | 1479.49781142113 | -50.377811421127 |
47 | 1452.46 | 1429.56876921050 | 22.8912307894975 |
48 | 1538.09 | 1456.49348003571 | 81.5965199642917 |
49 | 1631.59 | 1554.90129574623 | 76.6887042537749 |
50 | 1665.5 | 1660.4105595048 | 5.08944049519914 |
51 | 1690.6 | 1695.11755345437 | -4.51755345436845 |
52 | 1711.74 | 1719.51011561845 | -7.77011561844597 |
53 | 1734.1 | 1739.43333449267 | -5.3333344926657 |
54 | 1748.09 | 1760.95814733886 | -12.8681473388551 |
55 | 1703.45 | 1772.93302689863 | -69.483026898625 |
56 | 1745.74 | 1717.41215461255 | 28.3278453874484 |
57 | 1751.01 | 1764.13822600377 | -13.1282260037731 |
58 | 1795.65 | 1767.35237787991 | 28.2976221200886 |
59 | 1852.13 | 1816.42371638129 | 35.7062836187092 |
60 | 1877.1 | 1878.49523317621 | -1.39523317621047 |
61 | 1989.31 | 1903.24674306895 | 86.0632569310471 |
62 | 2097.76 | 2028.93403887756 | 68.8259611224387 |
63 | 2154.87 | 2148.1620162681 | 6.70798373190019 |
64 | 2152.18 | 2206.32247013492 | -54.1424701349174 |
65 | 2250.27 | 2195.15389156565 | 55.1161084343512 |
66 | 2346.9 | 2301.8749395143 | 45.0250604856983 |
67 | 2525.56 | 2405.55575400361 | 120.004245996393 |
68 | 2409.36 | 2603.00812579216 | -193.648125792165 |
69 | 2394.36 | 2456.48330231756 | -62.1233023175591 |
70 | 2401.33 | 2431.75494492327 | -30.4249449232748 |
71 | 2354.32 | 2433.96047286733 | -79.6404728673292 |
72 | 2450.41 | 2374.47896935416 | 75.9310306458406 |
73 | 2504.67 | 2482.4595832765 | 22.2104167234979 |
74 | 2661.39 | 2540.197680282 | 121.192319718002 |
75 | 2880.4 | 2715.89610151325 | 164.503898486750 |
76 | 3064.42 | 2960.66701018246 | 103.752989817542 |
77 | 3141.12 | 3160.93447495037 | -19.8144749503658 |
78 | 3327.7 | 3234.53157657397 | 93.1684234260265 |
79 | 3564.95 | 3435.7015240999 | 129.248475900101 |
80 | 3403.13 | 3693.19151971049 | -290.061519710489 |
81 | 3149.9 | 3485.94859425736 | -336.048594257356 |
82 | 3006.84 | 3180.09420526285 | -173.254205262851 |
83 | 3230.66 | 3009.90301992689 | 220.756980073111 |
84 | 3361.13 | 3268.29302376307 | 92.836976236932 |
85 | 3484.74 | 3413.30106746881 | 71.4389325311913 |
86 | 3411.13 | 3548.09822979925 | -136.968229799249 |
87 | 3288.18 | 3453.0393395851 | -164.859339585103 |
88 | 3280.37 | 3304.27276970813 | -23.9027697081292 |
89 | 3173.95 | 3292.71965435915 | -118.769654359153 |
90 | 3165.26 | 3167.70061660525 | -2.44061660524858 |
91 | 3092.71 | 3158.62842200656 | -65.9184220065636 |
92 | 3053.05 | 3075.75575813932 | -22.7057581393228 |
93 | 3181.96 | 3032.54009187808 | 149.419908121919 |
94 | 2999.93 | 3184.84888450183 | -184.918884501832 |
95 | 3249.57 | 2973.86103889037 | 275.708961109633 |
96 | 3210.52 | 3266.67638872561 | -56.1563887256139 |
97 | 3030.29 | 3218.83243542444 | -188.542435424442 |
98 | 2803.47 | 3009.07715058975 | -205.607150589748 |
99 | 2767.63 | 2750.05957304416 | 17.5704269558391 |
100 | 2882.6 | 2716.97105898615 | 165.628941013852 |
101 | 2863.36 | 2857.87814656696 | 5.48185343304294 |
102 | 2897.06 | 2839.49659142404 | 57.5634085759561 |
103 | 3012.61 | 2882.21088059685 | 130.399119403151 |
104 | 3142.95 | 3018.18106416934 | 124.768935830661 |
105 | 3032.93 | 3168.05957474723 | -135.129574747231 |
106 | 3045.78 | 3036.87861342295 | 8.90138657705438 |
107 | 3110.52 | 3051.12254881749 | 59.3974511825118 |
108 | 3013.24 | 3125.16404458246 | -111.924044582463 |
109 | 2987.1 | 3010.35701259781 | -23.2570125978114 |
110 | 2995.55 | 2980.57502123492 | 14.9749787650808 |
111 | 2833.18 | 2991.37006633014 | -158.190066330138 |
112 | 2848.96 | 2804.22788835385 | 44.732111646148 |
113 | 2794.83 | 2827.01282777047 | -32.1828277704703 |
114 | 2845.26 | 2767.84307555464 | 77.4169244453637 |
115 | 2915.02 | 2830.39637681639 | 84.6236231836087 |
116 | 2892.63 | 2913.40822949675 | -20.7782294967451 |
117 | 2604.42 | 2887.76440951255 | -283.344409512554 |
118 | 2641.65 | 2555.18336710853 | 86.4666328914732 |
119 | 2659.81 | 2605.95383060721 | 53.8561693927886 |
120 | 2638.53 | 2632.54757517961 | 5.98242482039086 |
121 | 2720.25 | 2612.20440829321 | 108.045591706792 |
122 | 2745.88 | 2710.84408403143 | 35.0359159685700 |
123 | 2735.7 | 2741.96062288985 | -6.26062288984531 |
124 | 2811.7 | 2730.80022463812 | 80.8997753618755 |
125 | 2799.43 | 2819.46893184584 | -20.0389318458415 |
126 | 2555.28 | 2804.0608840679 | -248.780884067899 |
127 | 2304.98 | 2520.95240532015 | -215.972405320151 |
128 | 2214.95 | 2236.831654203 | -21.8816542029999 |
129 | 2065.81 | 2143.37504060515 | -77.5650406051459 |
130 | 1940.49 | 1982.08854471457 | -41.5985447145731 |
131 | 2042 | 1850.25431422507 | 191.745685774927 |
132 | 1995.37 | 1981.79122024007 | 13.5787797599289 |
133 | 1946.81 | 1937.28762398158 | 9.52237601842148 |
134 | 1765.9 | 1890.21880480575 | -124.318804805747 |
135 | 1635.25 | 1689.84078364682 | -54.5907836468211 |
136 | 1833.42 | 1550.64200027668 | 282.777999723316 |
137 | 1910.43 | 1793.09434429129 | 117.335655708713 |
138 | 1959.67 | 1888.47882135936 | 71.1911786406386 |
139 | 1969.6 | 1948.86718603573 | 20.7328139642691 |
140 | 2061.41 | 1962.04389405847 | 99.3661059415276 |
141 | 2093.48 | 2069.41438352724 | 24.0656164727588 |
142 | 2120.88 | 2105.25300028177 | 15.6269997182276 |
143 | 2174.56 | 2135.10015026556 | 39.4598497344386 |
144 | 2196.72 | 2194.95946634536 | 1.76053365463531 |
145 | 2350.44 | 2217.39516161522 | 133.044838384777 |
146 | 2440.25 | 2391.94965831754 | 48.3003416824645 |
147 | 2408.64 | 2489.32337384172 | -80.6833738417222 |
148 | 2472.81 | 2445.07855458346 | 27.731445416543 |
149 | 2407.6 | 2513.59123119606 | -105.991231196062 |
150 | 2454.62 | 2431.78326329563 | 22.8367367043679 |
151 | 2448.05 | 2482.37944048022 | -34.3294404802186 |
152 | 2497.84 | 2470.43353395757 | 27.4064660424287 |
153 | 2645.64 | 2524.51531959402 | 121.124680405983 |
154 | 2756.76 | 2691.28314867423 | 65.47685132577 |
155 | 2849.27 | 2812.65666365148 | 36.6133363485164 |
156 | 2921.44 | 2910.90022268823 | 10.5397773117679 |
157 | 2981.85 | 2984.72072606973 | -2.87072606973197 |
158 | 3080.58 | 3044.68117737954 | 35.8988226204633 |
159 | 3106.22 | 3149.03284531182 | -42.8128453118161 |
160 | 3119.31 | 3167.96845831496 | -48.6584583149602 |
161 | 3061.26 | 3173.43866260090 | -112.178662600896 |
162 | 3097.31 | 3097.82175805651 | -0.511758056514282 |
163 | 3161.69 | 3133.79161799494 | 27.8983820050644 |
164 | 3257.16 | 3202.54043646953 | 54.619563530473 |
165 | 3277.01 | 3306.56372669914 | -29.5537266991423 |
166 | 3295.32 | 3321.78568528897 | -26.4656852889711 |
167 | 3363.99 | 3335.95122362047 | 28.0387763795284 |
168 | 3494.17 | 3409.01202751116 | 85.1579724888388 |
169 | 3667.03 | 3552.52755798746 | 114.502442012541 |
170 | 3813.06 | 3743.31836071141 | 69.7416392885925 |
171 | 3917.96 | 3900.26973106604 | 17.6902689339631 |
172 | 3895.51 | 4007.93998396906 | -112.429983969060 |
173 | 3801.06 | 3967.88372311233 | -166.823723112327 |
174 | 3570.12 | 3847.30953557339 | -277.189535573391 |
175 | 3701.61 | 3572.96233139372 | 128.647668606279 |
176 | 3862.27 | 3724.59824204969 | 137.671757950309 |
177 | 3970.1 | 3906.81730305378 | 63.2826969462153 |
178 | 4138.52 | 4024.55721881486 | 113.962781185138 |
179 | 4199.75 | 4210.82351197147 | -11.07351197147 |
180 | 4290.89 | 4270.31942704601 | 20.5705729539859 |
181 | 4443.91 | 4364.68072852285 | 79.2292714771474 |
182 | 4502.64 | 4530.10783890276 | -27.4678389027613 |
183 | 4356.98 | 4584.53644242630 | -227.556442426305 |
184 | 4591.27 | 4403.24165939467 | 188.028340605334 |
185 | 4696.96 | 4666.97643823647 | 29.9835617635308 |
186 | 4621.4 | 4777.36179076777 | -155.961790767766 |
187 | 4562.84 | 4677.37855530154 | -114.538555301537 |
188 | 4202.52 | 4600.88209732475 | -398.362097324746 |
189 | 4296.49 | 4178.17956596314 | 118.310434036863 |
190 | 4435.23 | 4290.67669093631 | 144.553309063692 |
191 | 4105.18 | 4452.05338603519 | -346.873386035186 |
192 | 4116.68 | 4067.68386109 | 48.9961389099976 |
193 | 3844.49 | 4086.8565367604 | -242.366536760397 |
194 | 3720.98 | 3776.71252913267 | -55.7325291326706 |
195 | 3674.4 | 3644.47495120839 | 29.9250487916074 |
196 | 3857.62 | 3602.58114075122 | 255.038859248784 |
197 | 3801.06 | 3825.73960312593 | -24.6796031259287 |
198 | 3504.37 | 3765.3148375613 | -260.944837561297 |
199 | 3032.6 | 3427.76151340938 | -395.161513409382 |
200 | 3047.03 | 2894.11018567085 | 152.919814329151 |
201 | 2962.34 | 2932.48705505743 | 29.8529449425705 |
202 | 2197.82 | 2852.47195331362 | -654.651953313621 |
203 | 2014.45 | 1985.43505654361 | 29.0149434563889 |
204 | 1862.83 | 1806.60872581405 | 56.2212741859464 |
205 | 1905.41 | 1663.79284001982 | 241.617159980183 |
206 | 1810.99 | 1744.20949707426 | 66.7805029257358 |
207 | 1670.07 | 1660.24716070764 | 9.82283929235905 |
208 | 1864.44 | 1520.86539334657 | 343.574606653434 |
209 | 2052.02 | 1769.0383374985 | 282.9816625015 |
210 | 2029.6 | 2000.93257460668 | 28.6674253933215 |
211 | 2070.83 | 1983.00182339733 | 87.8281766026726 |
212 | 2293.41 | 2037.98550131534 | 255.424498684658 |
213 | 2443.27 | 2300.56435388371 | 142.705646116289 |
214 | 2513.17 | 2472.77170947831 | 40.3982905216853 |
215 | 2466.92 | 2548.99798309307 | -82.0779830930705 |
216 | 2502.66 | 2489.89477143266 | 12.7652285673425 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
217 | 2527.63377504467 | 2284.63452392379 | 2770.63302616555 |
218 | 2552.60755008934 | 2181.07147644691 | 2924.14362373176 |
219 | 2577.58132513400 | 2087.81880196094 | 3067.34384830707 |
220 | 2602.55510017867 | 1996.39543763519 | 3208.71476272216 |
221 | 2627.52887522334 | 1903.91174484606 | 3351.14600560063 |
222 | 2652.50265026801 | 1809.09287504923 | 3495.91242548679 |
223 | 2677.47642531268 | 1711.30847699307 | 3643.64437363229 |
224 | 2702.45020035735 | 1610.23264289000 | 3794.66775782469 |
225 | 2727.42397540201 | 1505.69888784677 | 3949.14906295725 |
226 | 2752.39775044668 | 1397.63003245447 | 4107.16546843889 |
227 | 2777.37152549135 | 1286.00121316659 | 4268.74183781611 |
228 | 2802.34530053602 | 1170.81908834718 | 4433.87151272486 |