model ARIMA.xls

Mont Month h Pass Passen enge gers rs Log( Log(Pa Pass ssen enge gers rs)) Jan-49 112 4.718 Feb-49 118 4.771 Mar-49 132 4.883 Apr-49 129 4.860 May-49 121 4.796 Jun-49 135 4.905 Jul-49 148 4.997 Aug-49 148 4.997 Sep-49 136 4.913 Oct-49 119 4.779 Nov-49 104 4.644 Dec-49 118 4.771 Jan-50 115 4.745 Feb-50 126 4.836 Mar-50 141 4.949 Apr-50 135 4.905 May-50 125 4.828 Jun-50 149 5.004 Jul-50 170 5.136 Aug-50 170 5.136 Sep-50 158 5.063 Oct-50 133 4.890 Nov-50 114 4.736 Dec-50 140 4.942 Jan-51 145 4.977 Feb-51 150 5.011 Mar-51 178 5.182 Apr-51 163 5.094 May-51 172 5.147 Jun-51 178 5.182 Jul-51 199 5.293 Aug-51 199 5.293 Sep-51 184 5.215 Oct-51 162 5.088 Nov-51 146 4.984 Dec-51 166 5.112 Jan-52 171 5.142 Feb-52 180 5.193 Mar-52 193 5.263 Apr-52 181 5.198 May-52 183 5.209 Jun-52 218 5.384 Jul-52 230 5.438 Aug-52 242 5.489 Sep-52 209 5.342 Oct-52 191 5.252

Nov-52 Dec-52 Jan-53 Feb-53 Mar-53 Apr-53 May-53 Jun-53 Jul-53 Aug-53 Sep-53 Oct-53 Nov-53 Dec-53 Jan-54 Feb-54 Mar-54 Apr-54 May-54 Jun-54 Jul-54 Aug-54 Sep-54 Oct-54 Nov-54 Dec-54 Jan-55 Feb-55 Mar-55 Apr-55 May-55 Jun-55 Jul-55 Aug-55 Sep-55 Oct-55 Nov-55 Dec-55 Jan-56 Feb-56 Mar-56 Apr-56 May-56 Jun-56 Jul-56 Aug-56 Sep-56

172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355

5.147 5.268 5.278 5.278 5.464 5.460 5.434 5.493 5.576 5.606 5.468 5.352 5.193 5.303 5.318 5.236 5.460 5.425 5.455 5.576 5.710 5.680 5.557 5.434 5.313 5.434 5.489 5.451 5.587 5.595 5.598 5.753 5.897 5.849 5.743 5.613 5.468 5.628 5.649 5.624 5.759 5.746 5.762 5.924 6.023 6.004 5.872

Oct-56 Nov-56 Dec-56 Jan-57 Feb-57 Mar-57 Apr-57 May-57 Jun-57 Jul-57 Aug-57 Sep-57 Oct-57 Nov-57 Dec-57 Jan-58 Feb-58 Mar-58 Apr-58 May-58 Jun-58 Jul-58 Aug-58 Sep-58 Oct-58 Nov-58 Dec-58 Jan-59 Feb-59 Mar-59 Apr-59 May-59 Jun-59 Jul-59 Aug-59 Sep-59 Oct-59 Nov-59 Dec-59 Jan-60 Feb-60 Mar-60 Apr-60 May-60 Jun-60 Jul-60 Aug-60

306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606

5.724 5.602 5.724 5.753 5.707 5.875 5.852 5.872 6.045 6.142 6.146 6.001 5.849 5.720 5.817 5.829 5.762 5.892 5.852 5.894 6.075 6.196 6.225 6.001 5.883 5.737 5.820 5.886 5.835 6.006 5.981 6.040 6.157 6.306 6.326 6.138 6.009 5.892 6.004 6.033 5.969 6.038 6.133 6.157 6.282 6.433 6.407

Sep-60 Oct-60 Nov-60 Dec-60

508 461 390 432

6.230 6.133 5.966 6.068

XLSTAT 2012.1.01 - ARIMA - on 23/01/2012 at 15:25:40 Time series: Workbook = demoARIMA.xls / Sheet = Data / Range = Data!$C:$C / 144 rows Date data: Workbook = demoARIMA.xls / Sheet = Data / Range = Data!$A:$A / 144 rows a Confidence intervals (%): 95 Center: Yes Model parameters: p = 0 / d = 1 / q = 1 / P = 0 / D = 1 / Q = 1 / s = 12 Optimize: Likelihood (Convergence = 0,00001 / Iterations = 500) Validation: 12 Confidence intervals (%): 95 Seed (random numbers): 123456789

Summary statistics: Variable bservation with missing ithout missin Minimum Log(Passenger 144 0 144 4.644

Maximum 6.433

Mean 5.542

Results of ARIMA modeling of the Log(Passengers) series:

Results after optimization (Log(Passengers)): Goodness of fit statistics: Observations SSE MAPE(Diff) MAPE WN Variance WN Variance ( -2Log(Like.) FPE AIC AICC SBC

132.000 0.156 185.004 0.470 0.001 0.001 -447.253 0.001 -441.253 -441.045 -432.916

Model parameters: Parameter Constant

Value ian standard er bound (9 er bound ( pt. standard er bound ( 0.000 0.001 -0.002 0.002 0.031 -0.060

Parameter MA(1) SMA(1)

Value ian standard er bound (9 er bound ( pt. standard er bound ( -0.348 0.094 -0.533 -0.164 0.090 -0.525 -0.562 0.077 -0.714 -0.410 0.080 -0.720

Predictions and residuals: Observations g(Passenge A(Log(Passen Jan-49 4.718 4.718 Feb-49 4.771 4.771 Mar-49 4.883 4.883 Apr-49 4.860 4.860 May-49 4.796 4.796 Jun-49 4.905 4.905 Jul-49 4.997 4.997 Aug-49 4.997 4.997 Sep-49 4.913 4.913 Oct-49 4.779 4.779 Nov-49 4.644 4.644 Dec-49 4.771 4.771 Jan-50 4.745 4.745 Feb-50 4.836 4.804 Mar-50 4.949 4.938 Apr-50 4.905 4.919 May-50 4.828 4.845 Jun-50 5.004 4.952 Jul-50 5.136 5.083 Aug-50 5.136 5.117 Sep-50 5.063 5.046 Oct-50 4.890 4.918 Nov-50 4.736 4.763 Dec-50 4.942 4.882 Jan-51 4.977 4.907 Feb-51 5.011 5.028 Mar-51 5.182 5.131 Apr-51 5.094 5.127 May-51 5.147 5.039 Jun-51 5.182 5.253 Jul-51 5.293 5.321 Aug-51 5.293 5.303 Sep-51 5.215 5.219 Oct-51 5.088 5.062 Nov-51 4.984 4.934 Dec-51 5.112 5.136 Jan-52 5.142 5.132 Feb-52 5.193 5.194 Mar-52 5.263 5.333 Apr-52 5.198 5.227 May-52 5.209 5.197

Residuals ardized resi tandard erro er bound ( 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.032 0.889 0.011 0.299 -0.014 -0.390 -0.016 -0.447 0.052 1.435 0.053 1.460 0.018 0.508 0.016 0.450 -0.028 -0.775 -0.027 -0.738 0.060 1.647 0.070 1.925 -0.017 -0.466 0.051 1.402 -0.034 -0.931 0.109 3.006 -0.071 -1.962 -0.028 -0.772 -0.010 -0.269 -0.004 -0.103 0.026 0.718 0.049 1.364 -0.025 -0.676 0.010 0.269 -0.001 -0.015 -0.070 -1.935 -0.028 -0.784 0.012 0.344

Jun-52 Jul-52 Aug-52 Sep-52 Oct-52 Nov-52 Dec-52 Jan-53 Feb-53 Mar-53 Apr-53 May-53 Jun-53 Jul-53 Aug-53 Sep-53 Oct-53 Nov-53 Dec-53 Jan-54 Feb-54 Mar-54 Apr-54 May-54 Jun-54 Jul-54 Aug-54 Sep-54 Oct-54 Nov-54 Dec-54 Jan-55 Feb-55 Mar-55 Apr-55 May-55 Jun-55 Jul-55 Aug-55 Sep-55 Oct-55 Nov-55 Dec-55 Jan-56 Feb-56 Mar-56 Apr-56

5.384 5.438 5.489 5.342 5.252 5.147 5.268 5.278 5.278 5.464 5.460 5.434 5.493 5.576 5.606 5.468 5.352 5.193 5.303 5.318 5.236 5.460 5.425 5.455 5.576 5.710 5.680 5.557 5.434 5.313 5.434 5.489 5.451 5.587 5.595 5.598 5.753 5.897 5.849 5.743 5.613 5.468 5.628 5.649 5.624 5.759 5.746

5.299 5.467 5.449 5.396 5.219 5.115 5.287 5.294 5.337 5.407 5.382 5.431 5.563 5.604 5.609 5.498 5.360 5.238 5.346 5.333 5.353 5.420 5.409 5.407 5.538 5.647 5.714 5.570 5.444 5.302 5.435 5.449 5.456 5.631 5.567 5.591 5.704 5.842 5.879 5.737 5.621 5.487 5.598 5.650 5.622 5.783 5.751

0.085 -0.029 0.040 -0.054 0.033 0.032 -0.019 -0.016 -0.059 0.056 0.077 0.003 -0.070 -0.028 -0.003 -0.030 -0.008 -0.045 -0.043 -0.015 -0.117 0.040 0.016 0.048 0.038 0.063 -0.034 -0.014 -0.010 0.011 -0.001 0.040 -0.005 -0.044 0.028 0.007 0.048 0.055 -0.030 0.006 -0.008 -0.019 0.030 -0.001 0.002 -0.024 -0.004

2.348 -0.811 1.105 -1.483 0.905 0.890 -0.526 -0.437 -1.620 1.556 2.130 0.070 -1.923 -0.767 -0.077 -0.818 -0.217 -1.246 -1.174 -0.423 -3.221 1.096 0.432 1.325 1.061 1.737 -0.946 -0.376 -0.284 0.304 -0.028 1.098 -0.136 -1.201 0.771 0.192 1.328 1.509 -0.830 0.154 -0.219 -0.528 0.818 -0.028 0.056 -0.666 -0.121

May-56 Jun-56 Jul-56 Aug-56 Sep-56 Oct-56 Nov-56 Dec-56 Jan-57 Feb-57 Mar-57 Apr-57 May-57 Jun-57 Jul-57 Aug-57 Sep-57 Oct-57 Nov-57 Dec-57 Jan-58 Feb-58 Mar-58 Apr-58 May-58 Jun-58 Jul-58 Aug-58 Sep-58 Oct-58 Nov-58 Dec-58 Jan-59 Feb-59 Mar-59 Apr-59 May-59 Jun-59 Jul-59 Aug-59 Sep-59 Oct-59 Nov-59 Dec-59 Jan-60 Feb-60 Mar-60

5.762 5.924 6.023 6.004 5.872 5.724 5.602 5.724 5.753 5.707 5.875 5.852 5.872 6.045 6.142 6.146 6.001 5.849 5.720 5.817 5.829 5.762 5.892 5.852 5.894 6.075 6.196 6.225 6.001 5.883 5.737 5.820 5.886 5.835 6.006 5.981 6.040 6.157 6.306 6.326 6.138 6.009 5.892 6.004 6.033 5.969 6.038

5.753 5.887 6.035 6.007 5.890 5.754 5.598 5.740 5.757 5.728 5.863 5.856 5.863 6.012 6.146 6.124 6.016 5.872 5.728 5.854 5.858 5.805 5.934 5.888 5.879 6.045 6.171 6.178 6.076 5.885 5.755 5.859 5.855 5.826 5.977 5.969 6.003 6.195 6.283 6.305 6.147 6.009 5.872 5.987 6.039 5.989 6.146

0.009 0.037 -0.011 -0.003 -0.018 -0.030 0.004 -0.016 -0.004 -0.021 0.012 -0.004 0.009 0.033 -0.004 0.023 -0.014 -0.022 -0.007 -0.037 -0.029 -0.042 -0.042 -0.036 0.015 0.030 0.026 0.046 -0.075 -0.002 -0.018 -0.039 0.031 0.008 0.029 0.013 0.037 -0.038 0.024 0.021 -0.009 0.000 0.020 0.017 -0.006 -0.020 -0.108

0.249 1.017 -0.311 -0.091 -0.485 -0.838 0.105 -0.452 -0.123 -0.573 0.324 -0.102 0.240 0.901 -0.120 0.626 -0.400 -0.614 -0.199 -1.026 -0.812 -1.173 -1.170 -0.990 0.425 0.829 0.709 1.280 -2.061 -0.047 -0.498 -1.078 0.864 0.231 0.810 0.355 1.015 -1.036 0.653 0.580 -0.249 -0.009 0.542 0.473 -0.155 -0.555 -2.971

0.036 0.043 0.049

5.968 5.904 6.049

Apr-60 May-60 Jun-60 Jul-60 Aug-60 Sep-60 Oct-60 Nov-60 Dec-60

6.133 6.157 6.282 6.433 6.407 6.230 6.133 5.966 6.068

6.119 6.160 6.305 6.433 6.446 6.267 6.136 6.008 6.115

0.014 -0.003 -0.023 -0.001 -0.039 -0.036 -0.003 -0.042 -0.046

0.395 -0.077 -0.622 -0.014 -1.084 -1.006 -0.083 -1.159 -1.274

0.055 0.060 0.064 0.068 0.072 0.076 0.080 0.083 0.086

6.012 6.043 6.179 6.300 6.305 6.118 5.980 5.846 5.946

ARIMA (Log(Passengers)) 7

0.15

6.5

0.1

    )    s    r    e 6    g    n    e    s    s    a    P     ( 5.5    g    o    L

0.05     l    a    u     d    i    s    e    R

5

0

-0.05 4.5 Jul-46

Apr-49

Jan-52

Oct-54

Jun-57

Mar-60

-0.1

Month

Log(Passengers)

A RIMA (L og(Passen gers))

Lower bound (95%)

Upper bound (95%)

Dec-62

Valid ation

-0.15

nd 1 column d 1 column

Std. deviation 0.441

per bound (95%) 0.060

per bound (95%) -0.172 -0.405

per bound (95%)

6.110 6.074 6.242

6.226 6.276 6.430 6.567 6.588 6.416 6.292 6.171 6.284

Residuals

       9        4          n       a        J

       9        4            l      u        J

       0        5          n       a        J

       0        5            l      u        J

       1        5          n       a        J

       1        5            l      u        J

       2        5          n       a        J

       2        5            l      u        J

       3        5          n       a        J

       3        5            l      u        J

       4        5          n       a        J

       4        5            l      u        J

       5        5          n       a        J

       5        5            l      u        J

Month

       6        5          n       a        J

       6        5            l      u        J

       7        5          n       a        J

       7        5            l      u        J

       8        5          n       a        J

       8        5            l      u        J

       9        5          n       a        J

       9        5            l      u        J

       0        6          n       a        J

       0        6            l      u        J