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  • AR model result interpretation

    Hi,

    I have tried modelling my regression into AR models with different lags, as far as I am concerned, the ADF tests if the lagged component of the dependant variable is equal to one (unit root), and in my first regression, I could see that L1=0.6435 and it is statistically significant, which clearly means that there is no unit root, is this equivalent to another form of 'ADF' test too?

    Another interesting fact is that my results become insignificant when the fourth lag is included, why is that so? What is the implication behind it?

    Code:
    . reg lkk L.lkk
    
          Source |       SS           df       MS      Number of obs   =     1,878
    -------------+----------------------------------   F(1, 1876)      =   1347.72
           Model |  683.656533         1  683.656533   Prob > F        =    0.0000
        Residual |  951.635002     1,876  .507268125   R-squared       =    0.4181
    -------------+----------------------------------   Adj R-squared   =    0.4178
           Total |  1635.29153     1,877  .871226177   Root MSE        =    .71223
    
    ------------------------------------------------------------------------------
             lkk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
             lkk |
             L1. |   .6435107   .0175289    36.71   0.000     .6091325     .677889
                 |
           _cons |   .5626007   .0330171    17.04   0.000     .4978467    .6273547
    ------------------------------------------------------------------------------
    
    . reg lkk L.lkk L2.lkk
    
          Source |       SS           df       MS      Number of obs   =     1,408
    -------------+----------------------------------   F(2, 1405)      =    584.82
           Model |  540.138103         2  270.069051   Prob > F        =    0.0000
        Residual |  648.822563     1,405  .461795419   R-squared       =    0.4543
    -------------+----------------------------------   Adj R-squared   =    0.4535
           Total |  1188.96067     1,407  .845032456   Root MSE        =    .67956
    
    ------------------------------------------------------------------------------
             lkk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
             lkk |
             L1. |   .5376675       .025    21.51   0.000     .4886262    .5867089
             L2. |   .1836253   .0248365     7.39   0.000     .1349046     .232346
                 |
           _cons |   .4363539   .0395376    11.04   0.000     .3587947     .513913
    ------------------------------------------------------------------------------
    
    
    . reg lkk L(1/3).lkk
    
          Source |       SS           df       MS      Number of obs   =       938
    -------------+----------------------------------   F(3, 934)       =    294.93
           Model |  414.185358         3  138.061786   Prob > F        =    0.0000
        Residual |  437.217421       934  .468112871   R-squared       =    0.4865
    -------------+----------------------------------   Adj R-squared   =    0.4848
           Total |  851.402779       937  .908647577   Root MSE        =    .68419
    
    ------------------------------------------------------------------------------
             lkk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
             lkk |
             L1. |   .5596522   .0327283    17.10   0.000     .4954228    .6238816
             L2. |   .1607176    .034937     4.60   0.000     .0921535    .2292817
             L3. |   .0930933   .0301917     3.08   0.002     .0338419    .1523446
                 |
           _cons |   .3121269   .0510917     6.11   0.000      .211859    .4123947
    ------------------------------------------------------------------------------
    
    
    . reg lkk L(1/4).lkk
    
          Source |       SS           df       MS      Number of obs   =       469
    -------------+----------------------------------   F(4, 464)       =    124.46
           Model |  221.002183         4  55.2505458   Prob > F        =    0.0000
        Residual |  205.982645       464  .443928115   R-squared       =    0.5176
    -------------+----------------------------------   Adj R-squared   =    0.5134
           Total |  426.984829       468  .912360745   Root MSE        =    .66628
    
    ------------------------------------------------------------------------------
             lkk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
             lkk |
             L1. |   .6316919   .0442414    14.28   0.000     .5447535    .7186303
             L2. |   .0957735   .0523239     1.83   0.068    -.0070477    .1985946
             L3. |   .0360217   .0465455     0.77   0.439    -.0554444    .1274879
             L4. |   .0182292   .0413091     0.44   0.659    -.0629469    .0994053
                 |
           _cons |   .3351893   .0729343     4.60   0.000     .1918668    .4785118
    ------------------------------------------------------------------------------
    
    .
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