| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.661999366866233 |
| beta | 0.121510167209329 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 423113 | 411328.029380342 | 11784.970619658 |
| 14 | 418873 | 415710.814012727 | 3162.18598727311 |
| 15 | 405733 | 405479.852490458 | 253.147509542119 |
| 16 | 397812 | 398418.722435759 | -606.722435759439 |
| 17 | 389918 | 390636.84614569 | -718.846145689662 |
| 18 | 391116 | 391798.253628902 | -682.25362890237 |
| 19 | 443814 | 446728.130089375 | -2914.13008937461 |
| 20 | 460373 | 456531.052464022 | 3841.94753597805 |
| 21 | 455422 | 456355.705545378 | -933.70554537815 |
| 22 | 456288 | 454198.814026386 | 2089.18597361393 |
| 23 | 452233 | 453786.419842097 | -1553.41984209727 |
| 24 | 459256 | 459798.458026488 | -542.458026488195 |
| 25 | 461146 | 464463.236354482 | -3317.23635448195 |
| 26 | 451391 | 455779.233312991 | -4388.23331299104 |
| 27 | 443101 | 438804.65947924 | 4296.34052076016 |
| 28 | 438810 | 433692.734430221 | 5117.26556977927 |
| 29 | 430457 | 429685.922682176 | 771.077317824413 |
| 30 | 435721 | 431989.561767644 | 3731.43823235593 |
| 31 | 488280 | 489585.494553109 | -1305.49455310899 |
| 32 | 505814 | 503364.85999873 | 2449.14000127045 |
| 33 | 502338 | 501169.233502547 | 1168.76649745274 |
| 34 | 500910 | 502110.970408974 | -1200.97040897352 |
| 35 | 501434 | 498709.686687217 | 2724.31331278273 |
| 36 | 515476 | 508659.781596033 | 6816.21840396733 |
| 37 | 520862 | 518614.545965016 | 2247.45403498434 |
| 38 | 519517 | 515056.412291032 | 4460.58770896809 |
| 39 | 511805 | 509390.985427763 | 2414.01457223657 |
| 40 | 508607 | 505674.862933475 | 2932.13706652547 |
| 41 | 505327 | 500941.140093216 | 4385.85990678408 |
| 42 | 511435 | 509117.795661567 | 2317.20433843293 |
| 43 | 570158 | 566440.688383568 | 3717.31161643239 |
| 44 | 591665 | 587583.918328519 | 4081.08167148125 |
| 45 | 593572 | 588936.843091386 | 4635.15690861433 |
| 46 | 586346 | 594552.164886597 | -8206.16488659685 |
| 47 | 586063 | 590456.509026776 | -4393.5090267756 |
| 48 | 591504 | 599121.435188072 | -7617.4351880718 |
| 49 | 594033 | 598859.605293953 | -4826.60529395333 |
| 50 | 585597 | 591680.175048705 | -6083.17504870472 |
| 51 | 572450 | 577808.58991659 | -5358.58991659037 |
| 52 | 562917 | 567962.4573061 | -5045.45730610029 |
| 53 | 554675 | 556637.539756475 | -1962.53975647478 |
| 54 | 553997 | 557600.29727847 | -3603.29727846989 |
| 55 | 601310 | 608688.761127991 | -7378.76112799149 |
| 56 | 622255 | 618928.490503715 | 3326.50949628546 |
| 57 | 616735 | 616227.607274152 | 507.392725847661 |
| 58 | 606480 | 610696.381503927 | -4216.38150392729 |
| 59 | 595079 | 606777.981212973 | -11698.9812129727 |
| 60 | 598588 | 605176.692076504 | -6588.69207650423 |
| 61 | 599917 | 602281.635229646 | -2364.63522964634 |
| 62 | 591573 | 592247.789742626 | -674.789742625551 |
| 63 | 575489 | 578576.994640837 | -3087.99464083742 |
| 64 | 567223 | 566898.011732237 | 324.988267763401 |
| 65 | 555338 | 557160.528664803 | -1822.52866480255 |
| 66 | 555252 | 554662.833632154 | 589.166367846192 |
| 67 | 608249 | 604589.274186315 | 3659.72581368487 |
| 68 | 630859 | 623981.472841771 | 6877.52715822915 |
| 69 | 628632 | 621190.750098392 | 7441.24990160821 |
| 70 | 624435 | 617723.10407399 | 6711.89592600998 |
| 71 | 609670 | 618459.169302084 | -8789.1693020839 |
| 72 | 615830 | 620694.595253202 | -4864.59525320167 |
| 73 | 621170 | 620690.449533188 | 479.550466811983 |
| 74 | 604212 | 613661.233566408 | -9449.23356640816 |
| 75 | 584348 | 593210.895747495 | -8862.89574749477 |
| 76 | 573717 | 578242.789623333 | -4525.78962333279 |
| 77 | 555234 | 563558.304963063 | -8324.30496306252 |
| 78 | 544897 | 556038.664333912 | -11141.6643339121 |
| 79 | 598866 | 596760.601215983 | 2105.39878401696 |
| 80 | 620081 | 613609.873514074 | 6471.12648592645 |
| 81 | 607699 | 608106.379958165 | -407.37995816546 |
| 82 | 589960 | 595930.810292937 | -5970.81029293686 |
| 83 | 578665 | 578745.756138239 | -80.7561382389395 |
| 84 | 580166 | 584487.350308881 | -4321.35030888114 |
| 85 | 579457 | 583107.55117556 | -3650.55117555987 |
| 86 | 571560 | 566114.445441427 | 5445.55455857259 |
| 87 | 560460 | 553046.932278956 | 7413.06772104371 |
| 88 | 551397 | 548952.982942141 | 2444.01705785899 |
| 89 | 536763 | 536792.788798516 | -29.7887985160341 |
| 90 | 540562 | 533673.234872344 | 6888.76512765617 |
| 91 | 588184 | 592120.573371061 | -3936.57337106112 |
| 92 | 607049 | 607271.421514756 | -222.421514756046 |
| 93 | 598968 | 595299.176063141 | 3668.82393685926 |
| 94 | 577644 | 584556.808426011 | -6912.80842601147 |
| 95 | 562640 | 569278.420739365 | -6638.42073936539 |
| 96 | 565867 | 569257.451913665 | -3390.45191366517 |
| 97 | 561274 | 568807.448937224 | -7533.448937224 |
| 98 | 554144 | 552092.829365779 | 2051.17063422105 |
| 99 | 539900 | 536944.686346823 | 2955.31365317723 |
| 100 | 526271 | 527363.013633158 | -1092.01363315841 |
| 101 | 511841 | 510884.233644638 | 956.766355361906 |
| 102 | 505282 | 509694.024547604 | -4412.02454760403 |
| 103 | 554083 | 555030.014895536 | -947.014895535889 |
| 104 | 584225 | 571684.552310671 | 12540.4476893289 |
| 105 | 568858 | 568772.420172094 | 85.5798279060982 |
| 106 | 539516 | 551088.972404021 | -11572.9724040207 |
| 107 | 521612 | 531451.063988142 | -9839.06398814183 |
| 108 | 525562 | 528784.389904822 | -3222.38990482199 |
| 109 | 526519 | 525434.130131746 | 1084.86986825382 |
| 110 | 515713 | 516746.516094134 | -1033.5160941339 |
| 111 | 503454 | 498695.858652149 | 4758.14134785102 |
| 112 | 489301 | 487918.621706468 | 1382.37829353189 |
| 113 | 479020 | 472948.379930739 | 6071.62006926077 |
| 114 | 475102 | 472918.986482007 | 2183.01351799263 |
| 115 | 523682 | 523912.006341023 | -230.006341022672 |
| 116 | 551528 | 545777.59280919 | 5750.40719080996 |
| 117 | 531626 | 533792.135380974 | -2166.13538097357 |
| 118 | 511037 | 510127.75878681 | 909.241213190078 |
| 119 | 492417 | 499793.498218874 | -7376.49821887363 |
| 120 | 492188 | 501645.937276817 | -9457.9372768167 |
| 121 | 492865 | 495774.476481916 | -2909.4764819165 |
| 122 | 480961 | 483556.158915661 | -2595.15891566087 |
| 123 | 461935 | 466133.2278117 | -4198.2278117002 |
| 124 | 456608 | 447269.371884024 | 9338.62811597629 |
| 125 | 441977 | 438774.628904162 | 3202.37109583814 |
| 126 | 439148 | 434924.141342997 | 4223.85865700297 |
| 127 | 488180 | 486009.46039585 | 2170.53960415063 |
| 128 | 520564 | 511235.552648733 | 9328.44735126675 |
| 129 | 501492 | 498980.737780233 | 2511.26221976697 |
| 130 | 485025 | 479866.301556162 | 5158.69844383816 |
| 131 | 464196 | 470300.445562592 | -6104.44556259213 |
| 132 | 460170 | 473149.630181608 | -12979.6301816076 |
| 133 | 467037 | 467735.086277662 | -698.086277662253 |
| 134 | 460070 | 457839.722094772 | 2230.27790522826 |
| 135 | 447988 | 444210.320208244 | 3777.67979175557 |
| 136 | 442867 | 436984.486583451 | 5882.51341654861 |
| 137 | 436087 | 425632.241078112 | 10454.7589218881 |
| 138 | 431328 | 429015.974649375 | 2312.02535062528 |
| 139 | 484015 | 480075.732455651 | 3939.26754434884 |
| 140 | 509673 | 510968.469030339 | -1295.46903033875 |
| 141 | 512927 | 490598.201392419 | 22328.7986075813 |
| 142 | 502831 | 488313.698634746 | 14517.301365254 |
| 143 | 470984 | 484704.986628235 | -13720.986628235 |
| 144 | 471067 | 483144.241787353 | -12077.2417873525 |
| 145 | 476049 | 485506.868511864 | -9457.86851186352 |
| 146 | 474605 | 473126.309601372 | 1478.6903986283 |
| 147 | 470439 | 461785.90925735 | 8653.09074264951 |
| 148 | 461251 | 461154.735240574 | 96.2647594260634 |
| 149 | 454724 | 449707.680372277 | 5016.31962772313 |
| 150 | 455626 | 448491.717006656 | 7134.28299334354 |
| 151 | 516847 | 505434.511481263 | 11412.4885187367 |
| 152 | 525192 | 542247.010910813 | -17055.0109108132 |
| 153 | 522975 | 520903.101430467 | 2071.89856953284 |
| 154 | 518585 | 502412.942119597 | 16172.0578804035 |
| 155 | 509239 | 490332.916159448 | 18906.0838405523 |
| 156 | 512238 | 513529.165861684 | -1291.16586168431 |
| 157 | 519164 | 527387.453811535 | -8223.45381153515 |
| 158 | 517009 | 523089.872344301 | -6080.87234430056 |
| 159 | 509933 | 512131.141356827 | -2198.14135682659 |
| 160 | 509127 | 503512.519855095 | 5614.4801449047 |
| 161 | 500857 | 499913.658968299 | 943.341031700955 |
| 162 | 506971 | 498921.787550894 | 8049.21244910639 |
| 163 | 569323 | 560194.425772346 | 9128.57422765368 |
| 164 | 579714 | 587967.350131651 | -8253.35013165069 |
| 165 | 577992 | 581717.452149674 | -3725.4521496743 |
| 166 | 565464 | 566491.386343911 | -1027.38634391106 |
| 167 | 547344 | 544901.997600437 | 2442.00239956263 |
| 168 | 554788 | 550000.54351328 | 4787.45648672013 |
| 169 | 562325 | 565656.911057616 | -3331.91105761589 |
| 170 | 560854 | 565832.348858958 | -4978.34885895811 |
| 171 | 555332 | 557515.167030231 | -2183.1670302311 |
| 172 | 543599 | 552147.647844332 | -8548.64784433227 |
| 173 | 536662 | 537055.198413566 | -393.198413566104 |
| 174 | 542722 | 536934.058192907 | 5787.94180709287 |
| 175 | 593530 | 596246.396243316 | -2716.39624331577 |
| 176 | 610763 | 608521.885486027 | 2241.11451397301 |
| 177 | 612613 | 609812.949216487 | 2800.05078351288 |
| 178 | 611324 | 599406.81974488 | 11917.1802551195 |
| 179 | 594167 | 588188.747514827 | 5978.25248517317 |
| 180 | 595454 | 597334.874472989 | -1880.874472989 |
| 181 | 590865 | 606209.882300872 | -15344.8823008724 |
| 182 | 589379 | 597287.347005847 | -7908.34700584714 |
| 183 | 584428 | 587150.69673046 | -2722.69673045946 |
| 184 | 573100 | 578406.488340622 | -5306.4883406224 |
| 185 | 567456 | 567609.707368981 | -153.707368980744 |
| 186 | 569028 | 569148.417802284 | -120.41780228389 |
| 187 | 620735 | 620611.76591138 | 123.234088619705 |
| 188 | 628884 | 635607.961316141 | -6723.9613161413 |
| 189 | 628232 | 629597.154645877 | -1365.15464587719 |
| 190 | 612117 | 617624.292978065 | -5507.29297806451 |
| 191 | 595404 | 589571.286186606 | 5832.71381339431 |
| 192 | 597141 | 592660.386701409 | 4480.61329859053 |
| 193 | 593408 | 598403.278062761 | -4995.2780627613 |
| 194 | 590072 | 596885.67226689 | -6813.67226689041 |
| 195 | 579799 | 587354.448717058 | -7555.4487170584 |
| 196 | 574205 | 572276.89314039 | 1928.10685961077 |
| 197 | 572775 | 566332.255943292 | 6442.74405670806 |
| 198 | 572942 | 571100.884308957 | 1841.11569104309 |
| 199 | 619567 | 622954.725287527 | -3387.72528752661 |
| 200 | 625809 | 632039.495515016 | -6230.49551501614 |
| 201 | 619916 | 626933.521247073 | -7017.52124707308 |
| 202 | 587625 | 608130.954983854 | -20505.9549838543 |
| 203 | 565742 | 571087.48963205 | -5345.48963205004 |
| 204 | 557274 | 562526.161614463 | -5252.16161446262 |
| 205 | 560576 | 554046.749723003 | 6529.25027699675 |
| 206 | 548854 | 555894.429925729 | -7040.42992572894 |
| 207 | 531673 | 542294.805658476 | -10621.805658476 |
| 208 | 525919 | 524478.548445565 | 1440.45155443484 |
| 209 | 511038 | 515783.584080567 | -4745.58408056712 |
| 210 | 498662 | 506736.75786489 | -8074.75786488969 |
| 211 | 555362 | 544607.880693489 | 10754.1193065105 |
| 212 | 564591 | 557580.18546178 | 7010.81453822006 |
| 213 | 541657 | 557525.56177582 | -15868.5617758202 |
| 214 | 527070 | 524144.165413886 | 2925.83458611381 |
| 215 | 509846 | 505461.274119888 | 4384.72588011192 |
| 216 | 514258 | 501880.080017102 | 12377.9199828981 |
| 217 | 516922 | 508979.245796122 | 7942.75420387834 |
| 218 | 507561 | 507215.156106733 | 345.843893267447 |
| 219 | 492622 | 497927.934377748 | -5305.93437774765 |
| 220 | 490243 | 488768.639219014 | 1474.36078098568 |
| 221 | 469357 | 479068.774482755 | -9711.774482755 |
| 222 | 477580 | 466273.127585168 | 11306.8724148318 |
| 223 | 528379 | 525562.158488913 | 2816.84151108749 |
| 224 | 533590 | 533599.387818635 | -9.38781863509212 |
| 225 | 517945 | 522184.085108738 | -4239.08510873828 |
| 226 | 506174 | 504809.318055039 | 1364.68194496143 |
| 227 | 501866 | 487415.877552079 | 14450.1224479209 |
| 228 | 516141 | 495839.157956837 | 20301.8420431633 |
| 229 | 528222 | 509961.747513333 | 18260.2524866667 |
| 230 | 532638 | 516566.891881333 | 16071.1081186666 |
| 231 | 536322 | 521151.2325104 | 15170.7674895995 |
| 232 | 536535 | 534858.135919178 | 1676.8640808221 |
| 233 | 523597 | 528546.587572391 | -4949.58757239091 |
| 234 | 536214 | 533426.070154232 | 2787.92984576803 |
| 235 | 586570 | 590938.918660304 | -4368.91866030393 |
| 236 | 596594 | 599418.879953302 | -2824.87995330198 |
| 237 | 580523 | 590638.573608359 | -10115.5736083586 |
| 238 | 564478 | 576723.439737901 | -12245.4397379007 |
| 239 | 557560 | 559103.989034245 | -1543.98903424502 |
| 240 | 575093 | 561991.496464 | 13101.503536 |
| 241 | 580112 | 573152.648960029 | 6959.35103997099 |
| 242 | 574761 | 573122.871978533 | 1638.12802146666 |
| 243 | 563250 | 568273.489732491 | -5023.48973249085 |
| 244 | 551531 | 562851.657205295 | -11320.6572052952 |
| 245 | 537034 | 543451.294485051 | -6417.2944850506 |
| 246 | 544686 | 547611.66131331 | -2925.66131330968 |
| 247 | 600991 | 596100.716975803 | 4890.2830241971 |
| 248 | 604378 | 609154.577172334 | -4776.57717233396 |
| 249 | 586111 | 594383.422774296 | -8272.42277429625 |
| 250 | 563668 | 578882.253245284 | -15214.2532452842 |
| 251 | 548604 | 560589.432418602 | -11985.4324186022 |
| 252 | 551174 | 558349.876035365 | -7175.87603536528 |
| 253 | 555654 | 549215.238604417 | 6438.7613955827 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 254 | 542204.252751328 | 528495.462982631 | 555913.042520025 |
| 255 | 529049.027215523 | 511975.02977137 | 546123.024659677 |
| 256 | 520258.610334516 | 499794.619488517 | 540722.601180515 |
| 257 | 506354.800183125 | 482435.696039602 | 530273.904326649 |
| 258 | 512804.736029169 | 485345.688667438 | 540263.7833909 |
| 259 | 562968.860855384 | 531874.903781056 | 594062.817929713 |
| 260 | 566221.06833803 | 531392.054214057 | 601050.082462004 |
| 261 | 550517.74960974 | 511851.103968089 | 589184.395251392 |
| 262 | 535899.349081861 | 493291.674001338 | 578507.024162384 |
| 263 | 527746.300474267 | 481094.336690745 | 574398.264257788 |
| 264 | 535007.432619983 | 484208.645619782 | 585806.219620184 |
| 265 | 535742.908390011 | 480695.845693572 | 590789.971086451 |
