| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.785955903365853 |
| beta | 0.0130978913377891 |
| gamma | 0.933597389032669 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 254811 | 252764.670405983 | 2046.32959401695 |
| 14 | 254895 | 254380.220568082 | 514.779431918258 |
| 15 | 258325 | 258119.089166354 | 205.910833645787 |
| 16 | 257608 | 257519.028721066 | 88.9712789337209 |
| 17 | 258759 | 258818.68317857 | -59.683178570267 |
| 18 | 258621 | 258690.137387212 | -69.1373872116965 |
| 19 | 257852 | 257415.865945926 | 436.134054073947 |
| 20 | 260560 | 258903.205299871 | 1656.79470012937 |
| 21 | 262358 | 263189.652410659 | -831.652410659473 |
| 22 | 260812 | 261322.478491026 | -510.478491026297 |
| 23 | 261165 | 264203.894724282 | -3038.8947242818 |
| 24 | 257164 | 254467.845467966 | 2696.15453203395 |
| 25 | 260720 | 260758.175672043 | -38.1756720430858 |
| 26 | 259581 | 260440.161925056 | -859.161925056396 |
| 27 | 264743 | 263034.124350974 | 1708.87564902613 |
| 28 | 261845 | 263604.104565919 | -1759.10456591874 |
| 29 | 262262 | 263414.667105948 | -1152.66710594838 |
| 30 | 261631 | 262407.063298019 | -776.063298018824 |
| 31 | 258953 | 260652.739210333 | -1699.73921033289 |
| 32 | 259966 | 260657.905797857 | -691.905797856569 |
| 33 | 262850 | 262529.534193008 | 320.465806991677 |
| 34 | 262204 | 261572.340426923 | 631.659573076759 |
| 35 | 263418 | 264798.213961622 | -1380.21396162163 |
| 36 | 262752 | 257480.973508101 | 5271.0264918989 |
| 37 | 266433 | 265244.260417286 | 1188.73958271352 |
| 38 | 267722 | 265734.744612777 | 1987.25538722344 |
| 39 | 266003 | 271116.596296056 | -5113.59629605623 |
| 40 | 262971 | 265598.728631334 | -2627.72863133362 |
| 41 | 265521 | 264806.158245413 | 714.84175458661 |
| 42 | 264676 | 265319.198264201 | -643.198264200531 |
| 43 | 270223 | 263463.695999082 | 6759.30400091829 |
| 44 | 269508 | 270384.749237451 | -876.749237451353 |
| 45 | 268457 | 272377.554567917 | -3920.55456791702 |
| 46 | 265814 | 268169.785842411 | -2355.78584241075 |
| 47 | 266680 | 268635.364319331 | -1955.36431933095 |
| 48 | 263018 | 262179.024357523 | 838.975642476755 |
| 49 | 269285 | 265581.341287912 | 3703.65871208755 |
| 50 | 269829 | 268172.092800152 | 1656.90719984833 |
| 51 | 270911 | 271836.017849589 | -925.017849588767 |
| 52 | 266844 | 270110.74317876 | -3266.74317876005 |
| 53 | 271244 | 269481.108094969 | 1762.89190503105 |
| 54 | 269907 | 270554.503161704 | -647.503161703527 |
| 55 | 271296 | 270182.834976573 | 1113.16502342653 |
| 56 | 270157 | 271090.196346848 | -933.196346847981 |
| 57 | 271322 | 272379.65358028 | -1057.65358027961 |
| 58 | 267179 | 270713.4233835 | -3534.42338349967 |
| 59 | 264101 | 270299.263321574 | -6198.26332157373 |
| 60 | 265518 | 260989.511623887 | 4528.48837611321 |
| 61 | 269419 | 267824.980575222 | 1594.01942477789 |
| 62 | 268714 | 268287.832014308 | 426.167985691573 |
| 63 | 272482 | 270395.01974451 | 2086.98025548994 |
| 64 | 268351 | 270526.618157502 | -2175.61815750215 |
| 65 | 268175 | 271728.39345153 | -3553.39345153014 |
| 66 | 270674 | 268055.780364755 | 2618.21963524504 |
| 67 | 272764 | 270550.310320995 | 2213.6896790046 |
| 68 | 272599 | 271872.686213764 | 726.313786235522 |
| 69 | 270333 | 274417.635553012 | -4084.63555301249 |
| 70 | 270846 | 269822.295471992 | 1023.70452800824 |
| 71 | 270491 | 272450.128035602 | -1959.1280356021 |
| 72 | 269160 | 268651.149480076 | 508.850519924366 |
| 73 | 274027 | 271735.04493181 | 2291.95506818977 |
| 74 | 273784 | 272514.337378467 | 1269.6626215335 |
| 75 | 276663 | 275626.307032504 | 1036.69296749582 |
| 76 | 274525 | 274079.76510795 | 445.23489204963 |
| 77 | 271344 | 277092.211619592 | -5748.21161959181 |
| 78 | 271115 | 272931.372172079 | -1816.37217207882 |
| 79 | 270798 | 271817.543842245 | -1019.5438422446 |
| 80 | 273911 | 270226.105802973 | 3684.89419702732 |
| 81 | 273985 | 274090.037591489 | -105.037591489323 |
| 82 | 271917 | 273639.303786127 | -1722.30378612719 |
| 83 | 273338 | 273480.577057715 | -142.577057715331 |
| 84 | 270601 | 271588.950948953 | -987.950948953046 |
| 85 | 273547 | 273823.782246879 | -276.782246878603 |
| 86 | 275363 | 272324.467399564 | 3038.53260043578 |
| 87 | 281229 | 276742.938382715 | 4486.06161728455 |
| 88 | 277793 | 277787.567594986 | 5.43240501423134 |
| 89 | 279913 | 279210.489736083 | 702.51026391692 |
| 90 | 282500 | 280965.526427325 | 1534.47357267537 |
| 91 | 280041 | 282739.230677265 | -2698.23067726492 |
| 92 | 282166 | 280845.914974458 | 1320.08502554154 |
| 93 | 290304 | 282146.92448993 | 8157.07551006973 |
| 94 | 283519 | 288004.779874211 | -4485.779874211 |
| 95 | 287816 | 286099.425516179 | 1716.57448382111 |
| 96 | 285226 | 285628.881731369 | -402.881731368543 |
| 97 | 287595 | 288600.491223598 | -1005.49122359796 |
| 98 | 289741 | 287318.270400616 | 2422.7295993836 |
| 99 | 289148 | 291662.99369682 | -2514.99369682011 |
| 100 | 288301 | 286358.647208385 | 1942.35279161501 |
| 101 | 290155 | 289512.054212609 | 642.945787390927 |
| 102 | 289648 | 291454.767820005 | -1806.76782000484 |
| 103 | 288225 | 289790.422050066 | -1565.42205006647 |
| 104 | 289351 | 289635.933546634 | -284.933546633692 |
| 105 | 294735 | 291070.694792496 | 3664.30520750378 |
| 106 | 305333 | 290853.728899927 | 14479.2711000728 |
| 107 | 309030 | 305271.456826872 | 3758.54317312763 |
| 108 | 310215 | 306181.263863219 | 4033.73613678146 |
| 109 | 321935 | 312764.098011283 | 9170.90198871703 |
| 110 | 325734 | 320514.556558218 | 5219.44344178151 |
| 111 | 320846 | 326448.871990857 | -5602.87199085701 |
| 112 | 323023 | 319954.726245822 | 3068.27375417849 |
| 113 | 319753 | 324091.407172788 | -4338.40717278805 |
| 114 | 321753 | 321936.199914176 | -183.199914175784 |
| 115 | 320757 | 321919.580537472 | -1162.58053747244 |
| 116 | 324479 | 322665.181251407 | 1813.81874859333 |
| 117 | 324641 | 326887.847185423 | -2246.84718542261 |
| 118 | 322767 | 324474.48773232 | -1707.48773232027 |
| 119 | 324181 | 324149.516711342 | 31.4832886579679 |
| 120 | 321389 | 322268.35700191 | -879.35700190952 |
| 121 | 327897 | 326049.050343981 | 1847.94965601887 |
| 122 | 334287 | 327211.750889872 | 7075.24911012792 |
| 123 | 332653 | 332418.501429552 | 234.49857044837 |
| 124 | 334819 | 332281.615277883 | 2537.38472211664 |
| 125 | 335264 | 334552.071072623 | 711.928927376517 |
| 126 | 339622 | 337279.649316558 | 2342.35068344203 |
| 127 | 342440 | 339161.394430547 | 3278.60556945315 |
| 128 | 346585 | 344147.17135697 | 2437.82864303043 |
| 129 | 335378 | 348210.081262065 | -12832.0812620653 |
| 130 | 337010 | 337637.253763321 | -627.253763321089 |
| 131 | 339130 | 338572.198086404 | 557.801913595642 |
| 132 | 341193 | 336991.504332397 | 4201.49566760322 |
| 133 | 343507 | 345431.64527965 | -1924.64527965017 |
| 134 | 348915 | 344756.113635797 | 4158.88636420271 |
| 135 | 346431 | 346356.000011242 | 74.9999887577142 |
| 136 | 348322 | 346604.563576247 | 1717.43642375304 |
| 137 | 348288 | 347907.973147118 | 380.026852881711 |
| 138 | 346597 | 350739.262757413 | -4142.26275741257 |
| 139 | 351076 | 347683.488373318 | 3392.51162668184 |
| 140 | 355215 | 352563.957683735 | 2651.04231626453 |
| 141 | 350562 | 353718.418066229 | -3156.41806622909 |
| 142 | 355266 | 353264.118434385 | 2001.88156561542 |
| 143 | 361565 | 356604.303597474 | 4960.69640252588 |
| 144 | 363462 | 359359.584298995 | 4102.41570100514 |
| 145 | 366183 | 366644.010402812 | -461.010402812331 |
| 146 | 365423 | 368495.92726634 | -3072.92726634024 |
| 147 | 369208 | 363682.810723715 | 5525.18927628529 |
| 148 | 366713 | 368686.269537952 | -1973.26953795168 |
| 149 | 369354 | 366926.774664258 | 2427.22533574194 |
| 150 | 371970 | 370589.536515362 | 1380.46348463756 |
| 151 | 371824 | 373563.074164244 | -1739.07416424406 |
| 152 | 373187 | 374392.359517305 | -1205.35951730516 |
| 153 | 367270 | 371445.832982126 | -4175.83298212575 |
| 154 | 368140 | 371301.097715477 | -3161.09771547699 |
| 155 | 373742 | 371201.513509144 | 2540.48649085616 |
| 156 | 364815 | 371885.032038681 | -7070.03203868051 |
| 157 | 368558 | 369363.406779708 | -805.406779707642 |
| 158 | 371503 | 370306.069890998 | 1196.93010900164 |
| 159 | 372611 | 370494.367337678 | 2116.63266232202 |
| 160 | 370197 | 371212.661504701 | -1015.66150470084 |
| 161 | 375441 | 370987.25276047 | 4453.7472395295 |
| 162 | 375888 | 375956.550852258 | -68.5508522579912 |
| 163 | 375132 | 377075.884952928 | -1943.88495292811 |
| 164 | 381142 | 377756.78057963 | 3385.21942036977 |
| 165 | 372024 | 377777.840828949 | -5753.84082894865 |
| 166 | 376070 | 376532.578844216 | -462.578844215546 |
| 167 | 376864 | 379657.986634237 | -2793.98663423723 |
| 168 | 371401 | 374138.171714183 | -2737.17171418271 |
| 169 | 375687 | 376228.260859157 | -541.260859157366 |
| 170 | 384304 | 377735.790095129 | 6568.20990487112 |
| 171 | 380738 | 382341.885687475 | -1603.88568747503 |
| 172 | 379908 | 379484.210605264 | 423.789394736232 |
| 173 | 384007 | 381472.046115779 | 2534.95388422121 |
| 174 | 384499 | 383998.750939933 | 500.249060066941 |
| 175 | 385106 | 385165.431307891 | -59.4313078908599 |
| 176 | 387935 | 388386.788488548 | -451.788488548133 |
| 177 | 380435 | 383520.80630177 | -3085.80630177015 |
| 178 | 379281 | 385412.269969669 | -6131.26996966865 |
| 179 | 384153 | 383540.50329715 | 612.496702850447 |
| 180 | 380599 | 380668.509396041 | -69.5093960405211 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 181 | 385280.658408888 | 379023.093285725 | 391538.223532051 |
| 182 | 388626.443308082 | 380627.486904959 | 396625.399711205 |
| 183 | 386361.717660937 | 376903.622253029 | 395819.813068844 |
| 184 | 385110.869570794 | 374359.952579282 | 395861.786562307 |
| 185 | 387124.190002245 | 375192.235214839 | 399056.144789652 |
| 186 | 387162.528562 | 374130.573425271 | 400194.48369873 |
| 187 | 387729.636813781 | 373659.404252121 | 401799.869375441 |
| 188 | 390825.354136507 | 375765.51969921 | 405885.188573804 |
| 189 | 385698.80510204 | 369688.756358384 | 401708.853845696 |
| 190 | 389349.47054797 | 372421.715643812 | 406277.225452129 |
| 191 | 393649.815116504 | 375831.605652263 | 411468.024580744 |
| 192 | 390159.424293501 | 371473.893332545 | 408844.955254457 |
