airline

19
Airline Data 1 112 2 118 3 132 4 129 5 121 6 135 7 148 8 148 9 136 10 119 11 104 12 118 1 115 2 126 3 141 4 135 5 125 6 149 7 170 8 170 9 158 10 133 11 114 12 140 1 145 2 150 3 178 4 163 5 172 6 178 7 199 8 199 9 184 10 162 11 146 12 166 1 171 2 180 3 193 4 181 5 183 6 218 7 230 8 242 9 209 10 191 11 172 12 194 1 196 2 196

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Page 1: Airline

Airline Data1 1122 1183 1324 1295 1216 1357 1488 1489 136

10 11911 10412 118

1 1152 1263 1414 1355 1256 1497 1708 1709 158

10 13311 11412 140

1 1452 1503 1784 1635 1726 1787 1998 1999 184

10 16211 14612 166

1 1712 1803 1934 1815 1836 2187 2308 2429 209

10 19111 17212 194

1 1962 1963 2364 2355 229

Page 2: Airline

6 2437 2648 2729 237

10 21111 18012 201

1 2042 1883 2354 2275 2346 2647 3028 2939 259

10 22911 20312 229

1 2422 2333 2674 2695 2706 3157 3648 3479 312

10 27411 23712 278

1 2842 2773 3174 3135 3186 3747 4138 4059 355

10 30611 27112 306

Page 3: Airline

7 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 870

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450Airline Passenger Traffic

Airline Passenger Traffic

Page 4: Airline

7 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 870

50

100

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300

350

400

450Airline Passenger Traffic

Airline Passenger Traffic

Page 5: Airline

Note: In both F'casts, Ft is the forecast obtain at time period t-1Note This block can be copied for carrying out the H-W forecast

Note the MSE's in row 7 are directly comparable so that we can see which Just put the new data in the left-hand columnmethod has done best.

Holt'sLinExpSmthgAlphaLES 1.406607 MSE(LES) 489.242

Orig. Data BetaLES -0.005785 MSE 538.4095 Orig. DataMonth t Yt Lt bt Ft Et Et*Et Yt

1 112 112 0 1122 118 120.4396 -0.048822 112 6 36 1183 132 136.7204 -0.143287 120.3908 11.60918 134.773 1324 129 125.9191 -0.081632 136.5771 -7.57709 57.4123 1295 121 119.0331 -0.042269 125.8375 -4.837468 23.40109 1216 135 141.5095 -0.172537 118.9908 16.00922 256.2951 1357 148 150.7093 -0.226755 141.3369 6.663071 44.39651 1488 148 146.9906 -0.206555 150.4825 -2.482499 6.1628 1489 136 131.6151 -0.118804 146.784 -10.78404 116.2956 136

10 119 113.9189 -0.017121 131.4963 -12.49632 156.1581 11911 104 99.97386 0.063451 113.9018 -9.901782 98.04528 10412 118 125.3038 -0.082713 100.0373 17.96269 322.6581 11813 115 110.844 0.000456 125.221 -10.22105 104.4698 11514 126 132.1623 -0.122865 110.8445 15.1555 229.6891 12615 141 144.6434 -0.195777 132.0395 8.960528 80.29107 14116 135 131.1585 -0.118901 144.4476 -9.44764 89.25789 13517 125 122.5442 -0.069756 131.0396 -6.039619 36.477 12518 149 159.7855 -0.285596 122.4745 26.52551 703.6027 14919 170 174.2694 -0.371036 159.4999 10.50013 110.2527 17020 170 168.4149 -0.339315 173.8984 -3.898393 15.19747 17021 158 153.9032 -0.257329 168.0756 -10.07557 101.5171 15822 133 124.6052 -0.089333 153.6459 -20.64587 426.2519 13323 114 109.7242 -0.003764 124.5159 -10.5159 110.5843 11424 140 152.3119 -0.250151 109.7204 30.27961 916.8547 14025 145 142.1286 -0.192689 152.0618 -7.06176 49.86846 14526 150 153.2789 -0.258307 141.9359 8.064053 65.02895 15027 178 188.1568 -0.461566 153.0206 24.9794 623.9706 17828 163 152.9587 -0.260619 187.6952 -24.69524 609.855 16329 172 179.8483 -0.41768 152.6981 19.30189 372.5628 17230 178 177.4183 -0.406039 179.4306 -1.430609 2.046643 17831 199 207.9404 -0.584954 177.0123 21.98774 483.4605 19932 199 195.6026 -0.516966 207.3554 -8.35542 69.81305 19933 184 179.4925 -0.426761 195.0857 -11.08566 122.8918 18434 162 155.0609 -0.287896 179.0657 -17.06573 291.2391 16235 146 142.4328 -0.216509 154.7731 -8.773053 76.96646 14636 166 175.6706 -0.410039 142.2163 23.7837 565.6643 16637 171 169.2676 -0.37537 175.2606 -4.260588 18.15261 17138 180 184.5165 -0.465755 168.8922 11.10776 123.3823 18039 193 196.6388 -0.538575 184.0507 8.949259 80.08924 19340 181 174.8601 -0.415704 196.1003 -15.10026 228.0178 18141 183 186.4788 -0.485321 174.4444 8.55558 73.19795 18342 218 231.0141 -0.74576 185.9934 32.00656 1024.42 21843 230 229.8909 -0.743577 230.2683 -0.268342 0.072007 230

Page 6: Airline

44 242 247.226 -0.84816 229.1473 12.85269 165.1916 24245 209 193.8019 -0.544014 246.3778 -37.37784 1397.103 20946 191 190.0819 -0.525642 193.2579 -2.257882 5.098032 19147 172 164.8615 -0.382785 189.5563 -17.55629 308.2232 17248 194 206.0036 -0.623002 164.4787 29.5213 871.5072 19449 196 192.1858 -0.546671 205.3806 -9.380576 87.99521 19650 196 197.7732 -0.582156 191.6391 4.360883 19.0173 19651 236 251.78 -0.897947 197.191 38.80899 1506.138 23652 235 228.5422 -0.768714 250.8821 -15.88207 252.2403 23553 229 229.4987 -0.778694 227.7735 1.226482 1.504257 22954 243 248.8064 -0.894891 228.72 14.28 203.9183 24355 264 270.5417 -1.025805 247.9115 16.08854 258.8411 26456 272 273.01 -1.046018 269.5159 2.484086 6.170684 27257 237 222.7834 -0.761513 271.964 -34.96403 1222.483 23758 211 206.5184 -0.671828 222.0219 -11.02185 121.4813 21159 180 169.4906 -0.461512 205.8466 -25.84661 668.047 18060 201 213.9996 -0.721662 169.0291 31.97093 1022.14 20161 204 200.2275 -0.646166 213.278 -9.277955 86.08044 20462 188 183.2909 -0.551928 199.5813 -11.58135 134.1276 18863 235 256.2497 -0.977179 182.739 52.26099 2731.211 23564 227 215.5042 -0.747124 255.2725 -28.27252 799.3356 22765 234 241.8243 -0.903705 214.7571 19.24294 370.2907 23466 264 273.3842 -1.091503 240.9206 23.07938 532.658 26467 302 314.0792 -1.333233 272.2927 29.70726 882.5211 30268 293 284.9711 -1.172559 312.746 -19.74596 389.9028 29369 259 248.9167 -0.970771 283.7986 -24.79859 614.9701 25970 229 221.2964 -0.816607 247.9459 -18.94594 358.9486 22971 203 195.8926 -0.674372 220.4798 -17.47983 305.5446 20372 229 242.7359 -0.949257 195.2182 33.7818 1141.21 22973 242 242.0867 -0.950993 241.7867 0.213328 0.045509 24274 233 229.6919 -0.884792 241.1357 -8.135748 66.19039 23375 267 282.5295 -1.19557 228.8072 38.19285 1458.694 26776 269 263.9849 -1.095208 281.3339 -12.33392 152.1257 26977 270 272.8911 -1.153064 262.8897 7.110272 50.55596 27078 315 332.5906 -1.50509 271.738 43.26198 1871.599 31579 364 377.3833 -1.772917 331.0855 32.91445 1083.361 36480 347 335.3668 -1.540113 375.6103 -28.61034 818.5516 34781 312 303.1251 -1.362507 333.8267 -21.82671 476.4053 31282 274 262.7115 -1.136601 301.7626 -27.76259 770.7615 27483 237 227.0077 -0.936634 261.5749 -24.57492 603.9269 23784 278 299.1147 -1.359183 226.071 51.92898 2696.619 27885 284 278.4069 -1.247254 297.7555 -13.75552 189.2144 28486 277 276.9351 -1.245955 277.1596 -0.15965 0.025488 27787 317 333.7973 -1.582104 275.6891 41.31087 1706.588 31788 313 305.187 -1.425748 332.2152 -19.2152 369.2239 31389 318 323.7896 -1.54161 303.7612 14.23879 202.7431 31890 374 395.0427 -1.96272 322.248 51.75201 2678.271 37491 413 421.0996 -2.12481 393.08 19.91997 396.8052 41392 405 399.3177 -2.011096 418.9748 -13.9748 195.2949 40593 355 337.7978 -1.666844 397.3066 -42.30665 1789.853 35594 306 293.7485 -1.421667 336.131 -30.13096 907.8748 306

Page 7: Airline

95 271 262.3283 -1.248129 292.3269 -21.32686 454.8351 27196 306 324.2647 -1.613644 261.0802 44.91979 2017.787 306

Page 8: Airline

Note This block can be copied for carrying out the H-W forecast Note This block can be copied for carrying out the H-W forecastJust put the new data in the left-hand column Just put the new data in the left-hand column

Holt-Winter's Forecast, Multiplicative ModelAlphaHW 0.8089818259BetaHW 0.0177493982GammaHW 1.0324535703 MSE(HW) 90.37307 Orig. DataLt bt St Ft Et Et*Et Yt

0.884211 1 1120.931579 2 1181.042105 3 1321.018421 4 1290.955263 5 1211.065789 6 1351.168421 7 1481.168421 8 1481.073684 9 1360.939474 10 1190.821053 11 104

126.6666666667 0.5454545455 0.931579 12 118129.5156181645 0.5863402301 0.888044 112.4823 2.517703 6.33883 13 115134.2700583815 0.6603214964 0.938629 121.2002 4.799755 23.03764 14 126135.2318472992 0.6656723617 1.042672 140.6117 0.388341 0.150809 15 141133.1960218291 0.617722401 1.013385 138.4009 -3.400895 11.56609 16 135131.4193604814 0.5752235304 0.95102 127.8273 -2.82734 7.993851 17 125

138.311021176 0.6873364887 1.077655 140.6784 8.321562 69.24839 18 149144.2544240903 0.7806285045 1.1788 162.4086 7.591393 57.62924 19 170145.4075425333 0.7872399768 1.169151 169.462 0.537991 0.289435 20 170146.9730879353 0.8010544297 1.07507 156.967 1.03297 1.067028 21 158142.7539935791 0.71194981 0.93142 138.8299 -5.829918 33.98794 22 133139.7286176093 0.6456145266 0.815699 117.7931 -3.79309 14.38753 23 114

148.389829338 0.7878865529 0.943846 130.7697 9.230321 85.19882 24 140160.5863213286 0.9903824335 0.903425 132.4764 12.52358 156.84 25 145160.1455060853 0.964979536 0.936584 151.6606 -1.660561 2.757462 26 150168.8806089773 1.1028945494 1.054367 167.9853 10.01467 100.2936 27 178

162.592224315 0.9717037916 1.002155 172.2588 -9.258818 85.7257 28 163177.5548413208 1.2200340811 0.969289 155.5526 16.44739 270.5167 29 172167.7715525244 1.0247317221 1.060425 192.6577 -14.65767 214.8473 30 178168.8120711841 1.0250119307 1.178826 198.977 0.023004 0.000529 31 199

170.137972798 1.0303525415 1.169655 198.5652 0.43485 0.189094 32 199171.1547917289 1.0301123281 1.07505 184.018 -0.017985 0.000323 33 184173.5950910461 1.0551422984 0.933264 160.3764 1.623616 2.636128 34 162178.1590878508 1.1174223542 0.819615 142.462 3.537989 12.51737 35 146176.5256049042 1.0685954407 0.940261 169.2095 -3.209506 10.30093 36 166187.0476098624 1.2363877703 0.914556 160.443 10.55703 111.4508 37 171191.4421001677 1.2924421897 0.94035 176.3438 3.656235 13.36806 38 180184.8985297667 1.1533576821 1.043473 203.2129 -10.21288 104.3028 39 193181.6501406456 1.0752293254 0.996235 186.4528 -5.45282 29.73325 40 181

187.638157953 1.1624283555 0.975476 177.1137 5.886302 34.64855 41 183202.3731841963 1.4033337997 1.077763 200.2088 17.79115 316.5252 42 218196.7648874104 1.2788815766 1.168586 240.2172 -10.21716 104.3903 43 230

Page 9: Airline

205.2072081161 1.40602831 1.179609 231.6428 10.35716 107.2707 44 242196.7407460102 1.2307975466 1.061898 222.1195 -13.11947 172.1206 45 209203.3807976333 1.326808551 0.939315 184.7597 6.240267 38.94093 46 191208.8713686769 1.4007128294 0.823599 167.7815 4.218493 17.79568 47 172207.0795612892 1.3440475169 0.936727 197.7106 -3.710592 13.76849 48 194

213.186991825 1.4285946988 0.919537 190.615 5.385014 28.99838 49 196209.613929449 1.3398182958 0.93488 201.8139 -5.813864 33.80102 50 196

223.2615838896 1.5582749802 1.057497 220.1246 15.87539 252.0279 51 236233.7739127736 1.7172040482 1.005537 223.9734 11.02663 121.5865 52 235

234.897409861 1.706666107 0.974875 229.7159 -0.715896 0.512507 53 229227.5944236327 1.5467502003 1.067362 255.0031 -12.00307 144.0738 54 243226.5305168098 1.5004126093 1.165303 267.7711 -3.771131 14.22143 55 264230.0970779643 1.5370855025 1.182191 268.9873 3.012734 9.076564 56 272224.7991124512 1.4157674605 1.054027 245.9719 -8.971931 80.49555 57 237224.9341320941 1.3930349575 0.938011 212.4871 -1.487087 2.211426 58 211220.0380772706 1.2814073988 0.81786 186.4027 -6.402721 40.99484 59 180215.8648941013 1.1845916989 0.930957 207.3159 -6.315917 39.8908 60 201220.9335936766 1.2535322762 0.923478 199.5851 4.41491 19.49143 61 204205.1241713017 0.9506751 0.915922 207.7184 -19.71839 388.8151 62 188219.1383205376 1.182543904 1.072865 217.9235 17.07651 291.607 63 235224.7129251482 1.2605003383 1.010328 221.5408 5.459184 29.80268 64 227237.3456070559 1.4623497171 0.986262 220.2958 13.70421 187.8052 65 234245.7092667186 1.5848438153 1.07467 254.8945 9.105513 82.91037 66 264256.8935059239 1.7552273063 1.175918 288.1725 13.82751 191.1999 67 302249.9086348684 1.6000958204 1.172112 305.7722 -12.77218 163.1287 68 293

246.829156147 1.5170361885 1.049156 265.097 -6.097045 37.17396 69 259244.9381945188 1.4565462783 0.93483 232.9516 -3.951561 15.61483 70 229247.8622707634 1.482594052 0.81904 201.5164 1.483635 2.201173 71 203

246.625615705 1.4343290168 0.928454 232.1292 -3.129246 9.792179 72 229259.379856192 1.6352506328 0.933303 229.078 12.92204 166.979 73 242

255.6542594136 1.5400988176 0.91124 239.0695 -6.069504 36.83888 74 233250.4571305638 1.4205170811 1.06583 275.9349 -8.934857 79.83166 75 267263.5046773948 1.6268898617 1.021196 254.4791 14.52087 210.8556 76 269272.1125607853 1.7507982955 0.99243 261.4892 8.510808 72.43385 77 270

289.436096309 2.0272050093 1.088766 294.3128 20.68719 427.9597 78 315306.0913669421 2.2868443706 1.189618 342.737 21.26303 452.1166 79 364298.4023904392 2.1097795537 1.162559 361.4537 -14.45369 208.9093 80 347297.9799157527 2.064833565 1.046982 315.284 -3.28404 10.78492 81 312294.4277931265 1.965135973 0.930482 280.4907 -6.490749 42.12982 82 274290.7058752577 1.8641941899 0.815134 242.7578 -5.757764 33.15185 83 237

298.113480427 1.9625863986 0.932663 271.6379 6.362076 40.47601 84 278303.4894851502 2.0231725196 0.935862 280.062 3.937981 15.50769 85 284304.2739026394 2.0011853633 0.910336 278.3953 -1.395338 1.946968 86 277299.1122228919 1.8740488184 1.059607 326.437 -9.437039 89.05771 87 317305.4494036971 1.9532667251 1.024834 307.3661 5.633914 31.74099 88 313317.9379135292 2.1402609499 1.000447 305.0757 12.92426 167.0366 89 318339.0325468815 2.4766896529 1.103605 348.4903 25.5097 650.7446 90 374346.0888970092 2.5579758701 1.193456 406.2656 6.734449 45.3528 91 413348.4224042344 2.5539916868 1.162376 405.3226 -0.322576 0.104055 92 405341.3441643945 2.3830253741 1.03978 367.466 -12.46601 155.4014 93 355331.7013717257 2.1695743413 0.922258 319.832 -13.83196 191.3232 94 306

Page 10: Airline

332.7299905642 2.1493230677 0.814453 272.1496 -1.149633 1.321655 95 271329.3891086222 2.051875233 0.928873 312.3296 -6.329576 40.06353 96 306

Page 11: Airline

Note This block can be copied for carrying out the H-W forecastJust put the new data in the left-hand column

Holt-Winter's Forecast Additive ModelAlphaHWA 0.265894BetaHWA 0.056343GammaHWA 1.200592 MSE(HW) 118.5619Lt bt St Ft Et Et*Et

-14.66667-8.6666675.3333332.333333

-5.6666678.33333321.3333321.333339.333333

-7.666667-22.66667

126.666667 0.545455 -8.666667127.864771 0.582227 -12.50333 112.5455 2.454545 6.024793130.100773 0.675405 -3.184892 119.7803 6.219669 38.68428132.076531 0.74867 9.643621 136.1095 4.890489 23.91689132.783048 0.746295 2.193607 135.1585 -0.158535 0.025133132.768173 0.703409 -8.189718 127.8627 -2.862676 8.194916135.384715 0.8112 14.6748 141.8049 7.195084 51.76924139.511817 0.998027 32.32457 157.5292 12.47075 155.5197142.678697 1.120226 28.52244 161.8432 8.156822 66.53375145.093229 1.193151 13.62357 153.1323 4.867743 23.69492

144.79213 1.108961 -12.61966 138.6197 -5.619713 31.58118143.445709 0.970618 -30.80553 123.2344 -9.234424 85.27458145.546468 1.034293 -4.920582 135.7497 4.25034 18.06539

149.48501 1.197926 -2.876601 134.0774 10.92256 119.3024151.348192 1.235409 -0.979765 147.498 2.501956 6.259783156.777494 1.471704 23.54514 162.2272 15.77278 248.7806158.929141 1.510014 4.44742 160.4428 2.557195 6.539248165.690719 1.805901 9.217661 152.2494 19.75056 390.0847166.387463 1.743408 10.99827 182.1714 -4.171421 17.40076167.743877 1.721604 31.0418 200.4554 -1.455441 2.118308169.734587 1.736766 29.41445 197.9879 1.012079 1.024303171.180219 1.720363 12.65855 185.0949 -1.094927 1.198865173.357676 1.746117 -11.10453 160.2809 1.719082 2.955243175.556275 1.771611 -29.30568 144.2983 1.701737 2.895907

175.62422 1.675622 -10.56773 172.4073 -6.407304 41.05354176.389621 1.624337 -5.893712 174.4232 -3.42324 11.71857

178.80255 1.668769 1.634182 177.0342 2.965806 8.796007177.542105 1.503729 13.83566 204.0165 -11.01645 121.3623178.382892 1.466377 2.249962 183.4933 -2.493254 6.216317178.236106 1.375487 3.870504 189.0669 -6.06693 36.80765186.894476 1.785824 35.13887 190.6099 27.39013 750.2194191.413136 1.9398 40.10034 219.7221 10.2779 105.6352

Page 12: Airline

198.46678 2.227928 46.36533 222.7674 19.23262 369.8936199.537202 2.162711 8.821757 213.3533 -4.353255 18.95083201.807499 2.168772 -10.74792 190.5954 0.404619 0.163716203.266177 2.128764 -31.65944 174.6706 -2.670586 7.132031

205.17499 2.116371 -11.2968 194.8272 -0.82721 0.684276205.856157 2.035508 -10.65099 201.3976 -5.397649 29.13462204.295218 1.832874 -10.28697 209.5258 -13.52585 182.9485

210.39204 2.073117 27.96939 219.9638 16.03625 257.1612217.858793 2.377009 20.12827 214.7151 20.28488 411.4764221.537007 2.450322 8.183617 224.1063 4.893694 23.94824219.699463 2.208732 20.92586 259.1262 -16.1262 260.0544222.437714 2.238567 41.85554 262.0085 1.991463 3.965924224.931111 2.252925 47.21002 271.0416 0.95839 0.918511

227.44839 2.267819 9.698013 236.0058 0.994207 0.988448227.597485 2.148444 -17.77086 218.9683 -7.968293 63.49369224.936832 1.877487 -47.60017 198.0865 -18.08649 327.1212222.954193 1.659997 -24.09198 215.5175 -14.51752 210.7583221.965031 1.510736 -19.43217 213.9632 -9.963199 99.26533216.778209 1.133377 -32.4874 213.1888 -25.18879 634.4753215.018397 0.970367 18.37932 245.881 -10.88097 118.3956213.564596 0.833783 12.09287 236.117 -9.117033 83.12028217.434362 1.004838 18.247 222.582 11.418 130.3708224.989491 1.3739 42.63814 239.3651 24.63494 606.88235.345587 1.879981 71.62886 268.2189 33.78107 1141.161239.502797 2.008286 54.75836 284.4356 8.564415 73.34921243.582641 2.125004 16.56461 251.2091 7.790903 60.69818245.990348 2.140932 -16.83378 227.9368 1.063215 1.130427248.787743 2.177919 -45.42419 200.5311 2.468889 6.095415251.531037 2.209774 -22.21793 226.8737 2.126316 4.52122255.785899 2.324999 -12.6533 234.3086 7.691357 59.15697260.072268 2.435508 -25.98604 225.6235 7.3765 54.41275258.815276 2.227463 6.139772 280.8871 -13.8871 192.8514259.943104 2.165506 8.447905 273.1356 -4.135609 17.10326259.355111 2.010367 9.119968 280.3556 -10.35561 107.2387264.289354 2.175106 52.32992 304.0036 10.99638 120.9204273.352899 2.563219 94.462 338.0933 25.90668 671.1559280.256983 2.807795 69.14704 330.6745 16.32552 266.5226286.354053 2.993122 27.46759 299.6294 12.37061 153.032289.742456 3.015393 -15.52354 272.5134 1.486608 2.210003290.010186 2.860583 -54.53188 247.3337 -10.33366 106.7846294.824336 2.970652 -15.74243 270.6528 7.347157 53.98071297.491421 2.953548 -13.65954 285.1417 -1.141684 1.303442301.120625 2.991616 -23.74644 274.4589 2.541069 6.457031305.906493 3.092709 12.08719 310.252 6.747987 45.53533307.816742 3.026086 4.528397 317.4471 -4.447107 19.77676310.320932 2.996681 7.390036 319.9628 -1.962795 3.852565315.538486 3.121811 59.69146 365.6475 8.352463 69.76363318.627778 3.119979 94.35421 413.1223 -0.1223 0.014957325.498251 3.331292 81.57882 390.8948 14.1052 198.9567328.484643 3.31186 26.32435 356.2971 -1.29713 1.682547329.064981 3.157958 -24.57773 316.273 -10.27296 105.5337

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330.443823 3.057718 -60.42912 277.6911 -6.691063 44.77033330.374859 2.881552 -26.10645 317.7591 -11.75911 138.2768

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