                SERIES G, MONTHLY INTERNATIONAL AIRLINE PASSENGERS              

                       SARIMA( 0, 1, 1)( 0, 1,  1)12

                     Length of the input time series =  144

                     Length of differenced time series =  131

                Modified Sum of Squares Estimation (McLeod Algorithm)



             Sum of Squares, S(แ)            Residual Variance, ๅ
             11935.4562950931D+00            1.35052911746864D-03

                     AIC                           BIC
                 670.113588D+00                720.600414D+00


                  BOX-COX TRANSFORMATION PARAMETERS
                lamda         SE(lamda)         cons
                .0000            .0000      0.000000D+00

                             Deterministic Component
            Series                              Trend
            Mean,ๆ          S.E.                Term               S.E.
      2.90879878D-04      8.58629748D-04      2.90879878D-04     8.58629748D-04


                        Estimated แ parameters
                       แ                      SE(แ)
       ma(1)         .3998                    .0801
  seasonal ma(1)     .5545                    .0727


           Correlation matrix of แ
   1.000
    .000  1.000



                       Residual Analysis
                       อออออออออออออออออ


           Skewness                    Kurtosis
         g1      S.L.                g2      S.L.
        .0430   .825879             .7851   .054040


      Test for heteroscedasticity depending on the current level
                         ็           SE(็)
                       -.117897        .312299

            Test for trends in the variance over time
                         ็           SE(็)
                       -.005790        .003267


                Residual and Squared-residual autocorrelations
     LAG       RA          SE           QA             RAA          QAA
      1      .01279      .03493         .02           .13744        2.78
      2      .02163      .08129         .09           .02692        2.88
      3     -.12334      .08643        2.36           .04653        3.21
      4     -.11140      .08722        4.23          -.01470        3.24
      5      .05806      .08735        4.74           .11738        5.32
      6      .05283      .08737        5.16          -.00300        5.33
      7     -.06753      .08737        5.86          -.04678        5.66
      8     -.02509      .08737        5.96           .05428        6.12
      9      .12030      .08737        8.21          -.06610        6.80
     10     -.06014      .08737        8.78           .21380       13.97
     11     -.00512      .08737        8.78           .06125       14.56
     12     -.08543      .04844        9.95           .09501       16.00
     13     -.00257      .08737        9.95           .07539       16.91
     14      .02428      .08737       10.04          -.09514       18.38
     15      .06100      .08737       10.65           .06457       19.05
     16     -.15767      .08737       14.73           .00415       19.06
     17      .03916      .08737       14.99           .05785       19.61
     18      .00708      .08737       14.99          -.00386       19.61
     19     -.10719      .08737       16.93          -.06552       20.34
     20     -.09923      .08737       18.60           .07369       21.26
     21     -.03746      .08737       18.84          -.03008       21.41
     22     -.05246      .08737       19.31          -.04756       21.80
     23      .22101      .08737       27.80           .13466       24.95
     24      .00288      .07751       27.80          -.05171       25.42

 Modified (Ljung-Box) Portmanteau Test - Residual Autocorrelations
    Q(24) =  27.80 ON 22 DF is not significant at the 5 percent level

 Modified (Li-McLeod) Portmanteau Test - Residual Autocorrelations
    Q(24) =  26.58 ON 22 DF is not significant at the 5 percent level

 Modified (Ljung-Box) Portmanteau Test - Squared-Residual Autocorrelations
    Q(24) =  25.42 ON 24 DF is not significant at the 5 percent level


            Residual and Squared-residual Seasonal Autocorrelations
               LAG        RAS          QAS             RAAS         QAAS
      1        12       -.08543        1.16           .09501        1.44
      2        24        .00288        1.16          -.05171        1.91
      3        36       -.03486        1.40          -.04172        2.25

 Modified (Ljung-Box) Portmanteau Test - Seasonal Residual Autocorrelations
    Q( 3) =   1.40 ON  3 DF is not significant at the 5 percent level

 Modified (Ljung-Box) Portmanteau Test - Seasonal Squared-Residual Autocorrelations
    Q( 3) =   2.25 ON  3 DF is not significant at the 5 percent level


           Test for Periodic Correlation at Lag 1

    Q1(periodic) =  13.84 ON 12 DF is not significant at the 5 percent level
