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112118132129121135

148148136119104118115126141135125149

170170158133114140145150178163172178199199184162146166171180193181183218230

242209191172194196196236235

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229243264272237211

180201204188235227234264302293259229

203229242233267269270315364347312274237278284277317313318374413405355306271

306

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MA3_airline

Forecasting Moving averages - 3 period moving average

DataPeriod DemandPeriod 1 112Period 2 118Period 3 132Period 4 129Period 5 121Period 6 135Period 7 148Period 8 148Period 9 136Period 10 119

Period 11 104Period 12 118Period 13 115Period 14 126Period 15 141Period 16 135Period 17 125Period 18 149Period 19 170Period 20 170Period 21 158Period 22 133Period 23 114

Period 24 140Period 25 145Period 26 150Period 27 178Period 28 163Period 29 172Period 30 178Period 31 199Period 32 199Period 33 184Period 34 162Period 35 146Period 36 166

Period 37 171Period 38 180Period 39 193Period 40 181Period 41 183Period 42 218Period 43 230Period 44 242

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Period 45 209Period 46 191Period 47 172Period 48 194Period 49 196Period 50 196

Period 51 236Period 52 235Period 53 229Period 54 243Period 55 264Period 56 272Period 57 237Period 58 211Period 59 180Period 60 201Period 61 204Period 62 188Period 63 235

Period 64 227Period 65 234Period 66 264Period 67 302Period 68 293Period 69 259Period 70 229Period 71 203Period 72 229Period 73 242Period 74 233Period 75 267Period 76 269

Period 77 270Period 78 315Period 79 364Period 80 347Period 81 312Period 82 274Period 83 237Period 84 278Period 85 284Period 86 277Period 87 317Period 88 313Period 89 318

Period 90 374Period 91 413Period 92 405Period 93 355Period 94 306Period 95 271Period 96 306

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100105110115120125130135

1 2 3

V a

l u e

Time

Forecasting

Demand

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es

Forecasting Exponential smoothing

Alpha 0.9Data Error AnalysisPeriod Demand Forecast Error Absolute SquaredPeriod 1 112Period 2 118Period 3 132Period 4 129Period 5 121Period 6 135Period 7 148Period 8 148Period 9 136

Period 10 119Period 11 104Period 12 118Period 13 115Period 14 126Period 15 141Period 16 135Period 17 125Period 18 149Period 19 170Period 20 170Period 21 158

Period 22 133Period 23 114Period 24 140Period 25 145Period 26 150Period 27 178Period 28 163Period 29 172Period 30 178Period 31 199Period 32 199Period 33 184Period 34 162Period 35 146Period 36 166Period 37 171Period 38 180Period 39 193Period 40 181Period 41 183Period 42 218

V a

l u e

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Period 43 230Period 44 242Period 45 209Period 46 191Period 47 172Period 48 194

Period 49 196Period 50 196Period 51 236Period 52 235Period 53 229Period 54 243Period 55 264Period 56 272Period 57 237Period 58 211Period 59 180Period 60 201

Period 61 204Period 62 188Period 63 235Period 64 227Period 65 234Period 66 264Period 67 302Period 68 293Period 69 259Period 70 229Period 71 203Period 72 229Period 73 242Period 74 233Period 75 267Period 76 269Period 77 270Period 78 315Period 79 364Period 80 347Period 81 312Period 82 274Period 83 237Period 84 278Period 85 284

Period 86 277Period 87 317Period 88 313Period 89 318Period 90 374Period 91 413Period 92 405Period 93 355Period 94 306

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Period 95 271Period 96 306

Next period 275.4 Not enough data to compute the s

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050

100150200250300350400450

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91

Time

Forecasting

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andard error

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Demand

Forecast

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266 1145.9 2183.1 3119.3 4180.3 5168.5 6

231.8 7224.5 8192.8 9122.9 10336.5 11185.9 12194.3 13149.5 14210.1 15273.3 16191.4 17

287 18

226 19303.6 20289.9 21421.6 22264.5 23342.3 24339.7 25440.4 26315.9 27439.3 28401.3 29437.4 30575.5 31407.6 32

682 33475.3 34581.3 35646.9 36

Sales Time.pd-no

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decomposition

Forecasting Multiplicative decomposition

12 seasons

DataPeriod Demand (y) Time (x) Average Ratio Seasonal Smoothed UnadjustePeriod 1 266 1 0.912466 291.5179 110.0947Period 2 145.9 2 0.912106 159.9594 121.8879Period 3 183.1 3 0.852224 214.8496 133.6811Period 4 119.3 4 1.07902 110.5633 145.4743Period 5 180.3 5 0.83468 216.011 157.2675Period 6 168.5 6 1.029401 163.6874 169.0607Period 7 231.8 7 196.4583 193.4708 1.198113 1.019365 227.3964 180.8539Period 8 224.5 8 190.4833 190.6333 1.177653 1.117693 200.8602 192.6471Period 9 192.8 9 190.7833 191.9083 1.004646 0.979826 196.7696 204.4403Period 10 122.9 10 193.0333 199.45 0.616195 0.977552 125.7223 216.2335Period 11 336.5 11 205.8667 206.3292 1.630889 1.21554 276.8316 228.0267Period 12 185.9 12 206.7917 211.7292 0.878008 0.93429 198.9747 239.8199Period 13 194.3 13 216.6667 216.425 0.897771 0.912466 212.9396 251.6131Period 14 149.5 14 216.1833 219.4792 0.681158 0.912106 163.9063 263.4063Period 15 210.1 15 222.775 226.8208 0.926282 0.852224 246.5314 275.1995Period 16 273.3 16 230.8667 243.3125 1.123247 1.07902 253.2854 286.9927Period 17 191.4 17 255.7583 252.7583 0.757245 0.83468 229.3095 298.7859Period 18 287 18 249.7583 256.275 1.119891 1.029401 278.8028 310.5791Period 19 226 19 262.7917 268.85 0.840617 1.019365 221.7066 322.3723Period 20 303.6 20 274.9083 287.0292 1.057732 1.117693 271.631 334.1655Period 21 289.9 21 299.15 303.5583 0.955006 0.979826 295.8688 345.9587Period 22 421.6 22 307.9667 314.8833 1.338909 0.977552 431.2816 357.7519Period 23 264.5 23 321.8 330.5458 0.800192 1.21554 217.5987 369.5451Period 24 342.3 24 339.2917 345.5583 0.990571 0.93429 366.3746 381.3383

Period 25 339.7 25 351.825 366.3875 0.92716 0.912466 372.288 393.1315Period 26 440.4 26 380.95 385.2833 1.143055 0.912106 482.8384 404.9247Period 27 315.9 27 389.6167 405.9542 0.778167 0.852224 370.6771 416.7179Period 28 439.3 28 422.2917 424.5292 1.034793 1.07902 407.1286 428.5111Period 29 401.3 29 426.7667 439.9667 0.912115 0.83468 480.7832 440.3043Period 30 437.4 30 453.1667 465.8583 0.938912 1.029401 424.9071 452.0975Period 31 575.5 31 478.55 1.019365 564.5669 463.8907Period 32 407.6 32 1.117693 364.6798 475.6839Period 33 682 33 0.979826 696.0419 487.4771Period 34 475.3 34 0.977552 486.2148 499.2703Period 35 581.3 35 1.21554 478.2235 511.0635Period 36 646.9 36 0.93429 692.3977 522.8567

Average Intercept 98.30152Slope 11.7932

RatiosSeason 1 Season 2 Season 3 Season 4 Season 5 Season 6 Season 7 Season 8

1.198113 1.1776530.89777059 0.681158 0.926282 1.123247 0.757245 1.119891 0.840617 1.0577320.92716045 1.143055 0.778167 1.034793 0.912115 0.938912

Average 0.91246552 0.912106 0.852224 1.07902 0.83468 1.029401 1.019365 1.117693

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ForecastsPeriod Unadjusted Seasonal Adjusted

37 534.649949 0.912466 487.849638 546.44315 0.912106 498.414339 558.236351 0.852224 475.742540 570.029551 1.07902 615.073441 581.822752 0.83468 485.635742 593.615953 1.029401 611.069143 605.409154 1.019365 617.133244 617.202355 1.117693 689.842645 628.995556 0.979826 616.306346 640.788757 0.977552 626.404147 652.581958 1.21554 793.239748 664.375159 0.93429 620.7188

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Error analysis Adjusted Error |Error| Error^2

100.4576 165.5424 165.5424 27404.28111.1748 34.72524 34.72524 1205.842113.9263 69.17371 69.17371 4785.003156.9697 -37.6697 37.66972 1419.008

131.268 49.03198 49.03198 2404.135174.0313 -5.53134 5.531342 30.59574184.3562 47.44376 47.44376 2250.911215.3203 9.179692 9.179692 84.26674

200.316 -7.51597 7.515967 56.48976211.3794 -88.4794 88.47942 7828.608277.1757 59.32431 59.32431 3519.374224.0613 -38.1613 38.16127 1456.283229.5883 -35.2883 35.2883 1245.264240.2546 -90.7546 90.75462 8236.4234.5317 -24.4317 24.4317 596.908309.6709 -36.3709 36.37094 1322.845249.3906 -57.9906 57.99058 3362.908319.7106 -32.7106 32.71059 1069.983328.6152 -102.615 102.6152 10529.88373.4944 -69.8944 69.89442 4885.23338.9794 -49.0794 49.0794 2408.788

349.721 71.87904 71.87904 5166.596449.197 -184.697 184.697 34112.99

356.2805 -13.9805 13.98046 195.4532

358.719 -19.019 19.01897 361.7214369.3345 71.06553 71.06553 5050.309355.1371 -39.2371 39.23712 1539.551462.3722 -23.0722 23.07216 532.3244367.5131 33.78686 33.78686 1141.552465.3898 -27.9898 27.98984 783.4311472.8742 102.6258 102.6258 10532.06531.6685 -124.069 124.0685 15393477.6428 204.3572 204.3572 41761.85488.0625 -12.7625 12.76251 162.8816621.2184 -39.9184 39.91838 1593.477488.4996 158.4004 158.4004 25090.67

Total -84.7027 2237.774 229520.9-2.35285 62.1604 6375.58

Bias MAD MSESE 102.1409

Season 9 Season 10 Season 11 Season 121.004646 0.616195 1.630889 0.8780080.955006 1.338909 0.800192 0.990571

0.979826 0.977552 1.21554 0.93429

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556068636561

545246423730374455535850

48454134302429344454575151534646463941535562555657

595855494757688481

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787464747163

555157637585807768726870

53505358737268636468605441354344443644505561504639

333740494445383634

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282927292829

363236343136394039334446

57596459515048514548525863615958524853554238485567

606565636154525147

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555989847566

575260544849535973726258

55565252433743556868646557595457434252515860615862

614951474045505852

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505046463837

342930404646474743463741

39364855565352535256514842424450606658595557575653

514558746565555259

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545745404747

605863646463555444