| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.560350289484692 |
| beta | 0.0738144826327317 |
| gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 3 | 342435 | 339329 | 3106 |
| 4 | 354980 | 341421.918267745 | 13558.0817322549 |
| 5 | 339890 | 349932.452485157 | -10042.452485157 |
| 6 | 339890 | 344803.044936457 | -4913.04493645683 |
| 7 | 340471 | 342344.689191442 | -1873.68919144233 |
| 8 | 343833 | 341511.93784803 | 2321.06215197034 |
| 9 | 346109 | 343125.720329679 | 2983.27967032051 |
| 10 | 345455 | 345233.970903853 | 221.029096146638 |
| 11 | 350419 | 345803.535767277 | 4615.46423272329 |
| 12 | 344660 | 349026.428309554 | -4366.42830955406 |
| 13 | 341499 | 347035.710703258 | -5536.7107032584 |
| 14 | 342376 | 344160.215775073 | -1784.21577507275 |
| 15 | 344148 | 343313.633792691 | 834.366207308776 |
| 16 | 359079 | 343968.886009468 | 15110.1139905316 |
| 17 | 344090 | 353248.541661067 | -9158.54166106705 |
| 18 | 342681 | 348550.433797578 | -5869.43379757792 |
| 19 | 348552 | 345452.607152191 | 3099.39284780901 |
| 20 | 349867 | 347508.662097681 | 2358.33790231869 |
| 21 | 353247 | 349247.012183752 | 3999.98781624797 |
| 22 | 356048 | 352070.708637227 | 3977.29136277275 |
| 23 | 363887 | 355046.195719376 | 8840.80428062403 |
| 24 | 358905 | 361112.626725313 | -2207.62672531256 |
| 25 | 359647 | 360896.754435597 | -1249.75443559728 |
| 26 | 361488 | 361165.933859351 | 322.066140649258 |
| 27 | 363229 | 362329.20468701 | 899.795312989678 |
| 28 | 393301 | 363853.423527418 | 29447.5764725825 |
| 29 | 366190 | 382592.409482539 | -16402.409482539 |
| 30 | 363811 | 374960.906619835 | -11149.9066198354 |
| 31 | 366190 | 369811.463190322 | -3621.46319032187 |
| 32 | 372656 | 368730.794375981 | 3925.20562401932 |
| 33 | 371781 | 372041.257840757 | -260.257840756793 |
| 34 | 374306 | 372995.630865272 | 1310.36913472775 |
| 35 | 377689 | 374884.304614703 | 2804.69538529683 |
| 36 | 373240 | 377726.332228387 | -4486.33222838741 |
| 37 | 373456 | 376297.266883816 | -2841.26688381587 |
| 38 | 372610 | 375672.49399503 | -3062.4939950296 |
| 39 | 372209 | 374797.085655757 | -2588.08565575653 |
| 40 | 390212 | 374080.463853989 | 16131.5361460106 |
| 41 | 373113 | 384520.619608962 | -11407.6196089617 |
| 42 | 370518 | 379057.359881949 | -8539.35988194891 |
| 43 | 370469 | 374848.125604111 | -4379.12560411106 |
| 44 | 372493 | 372788.950560721 | -295.950560721394 |
| 45 | 369536 | 373005.542737671 | -3469.54273767106 |
| 46 | 368835 | 371300.304508341 | -2465.30450834124 |
| 47 | 366859 | 370055.82161852 | -3196.82161852048 |
| 48 | 356044 | 368269.20607488 | -12225.2060748802 |
| 49 | 346106 | 360917.87412083 | -14811.8741208303 |
| 50 | 333829 | 351504.453734112 | -17675.453734112 |
| 51 | 317388 | 339755.334153169 | -22367.3341531694 |
| 52 | 285871 | 324451.961090514 | -38580.9610905139 |
| 53 | 339729 | 298467.4930516 | 41261.5069483995 |
| 54 | 308216 | 318929.432168327 | -10713.4321683269 |
| 55 | 309137 | 309824.070480335 | -687.070480335096 |
| 56 | 311245 | 306308.564880352 | 4936.43511964829 |
| 57 | 319568 | 306148.37293633 | 13419.6270636703 |
| 58 | 329201 | 311296.802221782 | 17904.1977782181 |
| 59 | 339880 | 319698.714837843 | 20181.2851621573 |
| 60 | 342305 | 330211.331673746 | 12093.6683262535 |
| 61 | 346975 | 336692.26798114 | 10282.7320188603 |
| 62 | 355294 | 342583.759623913 | 12710.2403760868 |
| 63 | 360766 | 350361.226816715 | 10404.7731832851 |
| 64 | 392946 | 357277.18668268 | 35668.8133173204 |
| 65 | 352108 | 379825.19102037 | -27717.1910203704 |
| 66 | 358071 | 365708.39194584 | -7637.39194583986 |
| 67 | 365429 | 362527.416544091 | 2901.58345590893 |
| 68 | 378731 | 365371.974257898 | 13359.0257421021 |
| 69 | 384120 | 374628.918362084 | 9491.08163791569 |
| 70 | 391390 | 382111.028670542 | 9278.97132945794 |
| 71 | 403547 | 389858.079409498 | 13688.920590502 |
| 72 | 404124 | 400642.447171272 | 3481.5528287277 |
| 73 | 406439 | 405851.117325066 | 587.882674934401 |
| 74 | 412232 | 409462.634554138 | 2769.36544586159 |
| 75 | 419221 | 414411.09268679 | 4809.90731321037 |
| 76 | 450521 | 420701.916271689 | 29819.0837283107 |
| 77 | 430027 | 442240.015049099 | -12213.0150490995 |
| 78 | 433442 | 439720.260787032 | -6278.26078703185 |
| 79 | 439938 | 440266.366580056 | -328.366580055503 |
| 80 | 450200 | 444132.915426808 | 6067.08457319171 |
| 81 | 459279 | 451834.10372882 | 7444.89627117995 |
| 82 | 465090 | 460615.284766393 | 4474.71523360664 |
| 83 | 478567 | 467917.207022276 | 10649.792977724 |
| 84 | 475726 | 479119.832262293 | -3393.83226229344 |
| 85 | 480634 | 482312.732456595 | -1678.7324565954 |
| 86 | 486952 | 486397.253647528 | 554.746352471644 |
| 87 | 491912 | 491756.250735844 | 155.749264155864 |
| 88 | 517281 | 496898.111786098 | 20382.888213902 |
| 89 | 502379 | 514217.332346075 | -11838.3323460751 |
| 90 | 504942 | 512991.725929302 | -8049.72592930193 |
| 91 | 516387 | 513556.113718987 | 2830.88628101273 |
| 92 | 523270 | 520334.546734612 | 2935.4532653878 |
| 93 | 528995 | 527292.990010448 | 1702.00998955185 |
| 94 | 540850 | 533630.671470137 | 7219.32852986327 |
| 95 | 550679 | 543358.589597399 | 7320.41040260089 |
| 96 | 544432 | 553445.935552698 | -9013.93555269798 |
| 97 | 550296 | 554007.491921132 | -3711.49192113243 |
| 98 | 554659 | 557386.759508199 | -2727.75950819941 |
| 99 | 558856 | 561204.436339654 | -2348.43633965391 |
| 100 | 582661 | 565137.531072707 | 17523.4689272934 |
| 101 | 564317 | 580930.658813145 | -16613.6588131447 |
| 102 | 568569 | 576907.863539268 | -8338.86353926838 |
| 103 | 574693 | 577176.940396413 | -2483.94039641297 |
| 104 | 586558 | 580624.084471578 | 5933.91552842234 |
| 105 | 588751 | 589033.614967619 | -282.614967619185 |
| 106 | 598250 | 593948.021289731 | 4301.97871026944 |
| 107 | 607706 | 601609.344306624 | 6096.65569337609 |
| 108 | 603869 | 610528.484760373 | -6659.4847603729 |
| 109 | 607696 | 612024.268831183 | -4328.26883118262 |
| 110 | 613285 | 614647.324711452 | -1362.32471145201 |
| 111 | 617160 | 618875.999808443 | -1715.99980844255 |
| 112 | 647083 | 622835.515835497 | 24247.4841645026 |
| 113 | 621246 | 642346.601255671 | -21100.6012556709 |
| 114 | 623252 | 635574.111516346 | -12322.1115163458 |
| 115 | 632722 | 633210.984277337 | -488.984277336509 |
| 116 | 641716 | 637458.327960814 | 4257.67203918635 |
| 117 | 644953 | 644541.567574492 | 411.432425508392 |
| 118 | 652723 | 649486.583361506 | 3236.41663849447 |
| 119 | 660093 | 656148.444427322 | 3944.55557267845 |
| 120 | 657090 | 663370.265926191 | -6280.26592619147 |
| 121 | 657281 | 664602.841588062 | -7321.84158806223 |
| 122 | 661949 | 664948.924258252 | -2999.92425825191 |
| 123 | 665608 | 667592.711788023 | -1984.71178802312 |
| 124 | 697124 | 670723.282336468 | 26400.7176635325 |
| 125 | 671310 | 690851.622100395 | -19541.6221003949 |
| 126 | 674708 | 684427.878555198 | -9719.87855519785 |
| 127 | 681915 | 683105.718555557 | -1190.71855555731 |
| 128 | 690556 | 686513.625369519 | 4042.37463048089 |
| 129 | 692885 | 693021.098030079 | -136.09803007869 |
| 130 | 699740 | 697181.5330435 | 2558.46695649973 |
| 131 | 707885 | 702957.691552273 | 4927.30844772665 |
| 132 | 704785 | 710265.034244391 | -5480.03424439055 |
| 133 | 705363 | 711513.95445222 | -6150.95445221965 |
| 134 | 749101 | 712132.508754074 | 36968.4912459255 |
| 135 | 752891 | 738442.146439589 | 14448.8535604106 |
| 136 | 784662 | 752730.53162892 | 31931.4683710804 |
| 137 | 761914 | 778136.053420169 | -16222.0534201692 |
| 138 | 763768 | 775887.759302429 | -12119.7593024288 |
| 139 | 768877 | 775436.889800298 | -6559.88980029814 |
| 140 | 781031 | 777830.164839633 | 3200.83516036696 |
| 141 | 783454 | 785825.257773609 | -2371.25777360902 |
| 142 | 785988 | 790599.9469339 | -4611.94693389954 |
| 143 | 795068 | 793928.306079021 | 1139.69392097858 |
| 144 | 790001 | 800526.738824207 | -10525.7388242069 |
| 145 | 789721 | 800153.077694804 | -10432.0776948037 |
| 146 | 794064 | 799400.408356032 | -5336.40835603164 |
| 147 | 798690 | 801282.374461578 | -2592.37446157809 |
| 148 | 829281 | 804594.735048054 | 24686.264951946 |
| 149 | 806249 | 824213.761595818 | -17964.7615958183 |
| 150 | 807048 | 819190.215199619 | -12142.2151996188 |
| 151 | 819928 | 816927.108461178 | 3000.89153882163 |
| 152 | 821105 | 823273.568743254 | -2168.56874325383 |
| 153 | 828422 | 826633.624191619 | 1788.37580838124 |
| 154 | 835360 | 832284.925405621 | 3075.07459437882 |
| 155 | 844092 | 838784.419789845 | 5307.58021015534 |
| 156 | 837469 | 846754.431298115 | -9285.43129811541 |
| 157 | 836969 | 846163.180883019 | -9194.18088301935 |
| 158 | 838721 | 845242.773260816 | -6521.77326081577 |
| 159 | 840537 | 845550.096654822 | -5013.09665482189 |
| 160 | 863719 | 846495.455884778 | 17223.5441152224 |
| 161 | 845413 | 860613.522865741 | -15200.5228657412 |
| 162 | 844366 | 855934.031006882 | -11568.0310068819 |
| 163 | 848357 | 852811.530499262 | -4454.5304992618 |
| 164 | 858754 | 853490.833918111 | 5263.16608188918 |
| 165 | 862431 | 859833.146329608 | 2597.85367039207 |
| 166 | 871565 | 864789.402496791 | 6775.59750320867 |
| 167 | 880366 | 872366.910668464 | 7999.08933153597 |
| 168 | 874476 | 880960.860906975 | -6484.86090697476 |
| 169 | 882077 | 881170.498835492 | 906.501164508401 |
| 170 | 889199 | 885559.383311441 | 3639.61668855941 |
| 171 | 892665 | 891630.311566801 | 1034.68843319884 |
| 172 | 913625 | 896284.364268714 | 17340.6357312859 |
| 173 | 893597 | 910792.702057305 | -17195.7020573046 |
| 174 | 892114 | 905237.344912244 | -13123.3449122435 |
| 175 | 894801 | 901421.1269169 | -6620.12691689993 |
| 176 | 898843 | 900975.167538667 | -2132.1675386671 |
| 177 | 908135 | 902955.846854465 | 5179.15314553503 |
| 178 | 918920 | 909247.64679217 | 9672.35320783011 |
| 179 | 923125 | 918457.280236898 | 4667.71976310224 |
| 180 | 921770 | 925055.631951567 | -3285.63195156725 |
| 181 | 917843 | 927061.420531141 | -9218.42053114146 |
| 182 | 916761 | 925361.477309559 | -8600.47730955889 |
| 183 | 915087 | 923652.066094895 | -8565.06609489501 |
| 184 | 938173 | 921608.229585921 | 16564.7704140791 |
| 185 | 907953 | 934331.055721903 | -26378.0557219028 |
| 186 | 905374 | 921899.808538615 | -16525.8085386152 |
| 187 | 921867 | 914305.730973904 | 7561.26902609575 |
| 188 | 927104 | 920521.603253173 | 6582.39674682729 |
| 189 | 930989 | 926461.225042508 | 4527.7749574919 |
| 190 | 936820 | 931436.816594476 | 5383.18340552354 |
| 191 | 944281 | 937114.395570748 | 7166.60442925233 |
| 192 | 945322 | 944087.739887775 | 1234.26011222496 |
| 193 | 944555 | 947787.944775108 | -3232.94477510825 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 194 | 948851.229156469 | 926266.743487383 | 971435.714825555 |
| 195 | 951726.09507845 | 925368.368548994 | 978083.821607905 |
| 196 | 954600.96100043 | 924506.745332807 | 984695.176668054 |
| 197 | 957475.826922411 | 923643.882995578 | 991307.770849245 |
| 198 | 960350.692844392 | 922756.932486505 | 997944.453202279 |
| 199 | 963225.558766373 | 921831.377883419 | 1004619.73964933 |
| 200 | 966100.424688353 | 920857.659082906 | 1011343.1902938 |
| 201 | 968975.290610334 | 919829.335189666 | 1018121.246031 |
| 202 | 971850.156532315 | 918742.014735591 | 1024958.29832904 |
| 203 | 974725.022454295 | 917592.69848013 | 1031857.34642846 |
| 204 | 977599.888376276 | 916379.358181232 | 1038820.41857132 |
| 205 | 980474.754298257 | 915100.657138078 | 1045848.85145844 |
