TIME SERIES ANALYSIS OF DIVORCE DATA USING COCHRANE-ORCUTT, HILDRETH-LU, & FIRST DIFFERENCES

>USE "D:\mydocs\ys209\divorce.SYD"

SYSTAT Rectangular file D:\mydocs\ys209\divorce.SYD,
created Tue Apr 18, 2000 at 21:57:38, contains variables:
 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

>REM SUBMIT 'D:\mydocs\ys209\divorce.syc' /ECHO
>select year<=1970
>plot divmf unemp flfprt marumf*year/symbol line stick

Data for the following results were selected according to:
      year<=1970


 

>mglh
>model divmf=constant+unemp+flfprt+marumf
>save divres01/data
>estimate

Data for the following results were selected according to:
      year<=1970

Dep Var: DIVMF   N: 51   Multiple R: 0.866   Squared multiple R: 0.750
Adjusted squared multiple R: 0.734   Standard error of estimate: 1.207

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
CONSTANT            -9.243        2.118        0.000      .      -4.365    0.000
UNEMP                0.048        0.036        0.125     0.588    1.321    0.193
FLFPRT               0.240        0.029        0.673     0.778    8.141    0.000
MARUMF               0.137        0.019        0.607     0.727    7.097    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
Regression               205.765     3       68.588      47.092       0.000
Residual                  68.454    47        1.456

*** WARNING ***
Case           26 is an outlier        (Studentized Residual =        3.239)
Case           27 has large leverage   (Leverage =        0.347)
Case           27 is an outlier        (Studentized Residual =        3.956)

Durbin-Watson D Statistic     0.429
First Order Autocorrelation   0.711

Residuals have been saved.

Plot of Residuals against Predicted Values


>use divres01

SYSTAT Rectangular file d:\MYDOCS\YS209\divres01.SYD,
created Tue Apr 18, 2000 at 23:26:28, contains variables:
 ESTIMATE     RESIDUAL     LEVERAGE     COOK         STUDENT      SEPRED
 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

>plot residual/stick ylimit=0 smooth=lowess

>plot residual/stick ylimit=0 line dash=11
 

>use divorce

SYSTAT Rectangular file d:\MYDOCS\YS209\divorce.SYD,
created Tue Apr 18, 2000 at 21:57:38, contains variables:
 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

>rem Cochrane-Orcutt procedure with r=0.711
>basic

File in use is d:\MYDOCS\YS209\divorce.SYD.
Variables in the SYSTAT Rectangular file are:
 YEAR         DIVPOP       DIVMF        UNEMP        FLFPRT       MARUMF
 TREND

 BASIC statements cleared.

>let ldivmf=lag(divmf)
>let lunemp=lag(unemp)
>let lflfprt=lag(flfprt)
>let lmarumf=lag(marumf)
>let pdivmf=divmf-0.711*ldivmf
>let punemp=unemp-0.711*lunemp
>let pflfprt=flfprt-0.711*lflfprt
>let pmarumf=marumf-0.711*lmarumf
>run

SYSTAT file created.
  79 cases and 15 variables processed.
 BASIC statements cleared.

>page wide
>format 3
>list year divmf ldivmf pdivmf unemp lunemp punemp/n=10

  Case number         YEAR        DIVMF       LDIVMF       PDIVMF        UNEMP        LUNEMP       PUNEMP
        1         1920.000        8.000         .            .           5.200         .             .
        2         1921.000        7.200        8.000        1.512       11.700         5.200        8.003
        3         1922.000        6.600        7.200        1.481        6.700        11.700       -1.619
        4         1923.000        7.100        6.600        2.407        2.400         6.700       -2.364
        5         1924.000        7.200        7.100        2.152        5.000         2.400        3.294
        6         1925.000        7.200        7.200        2.081        3.200         5.000       -0.355
        7         1926.000        7.500        7.200        2.381        1.800         3.200       -0.475
        8         1927.000        7.800        7.500        2.468        3.300         1.800        2.020
        9         1928.000        7.800        7.800        2.254        4.200         3.300        1.854
       10         1929.000        8.000        7.800        2.454        3.200         4.200        0.214

>page narrow
>mglh
>select year<=1970
>model pdivmf=constant+punemp+pflfprt+pmarumf
>save divres02/data
>estimate

Data for the following results were selected according to:
      year<=1970

1 case(s) deleted due to missing data.

Dep Var: PDIVMF   N: 50   Multiple R: 0.771   Squared multiple R: 0.594
Adjusted squared multiple R: 0.568   Standard error of estimate: 0.776

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
CONSTANT            -2.792        0.860        0.000      .      -3.247    0.002
PUNEMP               0.056        0.044        0.143     0.692    1.268    0.211
PFLFPRT              0.264        0.058        0.485     0.774    4.543    0.000
PMARUMF              0.134        0.019        0.763     0.778    7.167    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
Regression                40.566     3       13.522      22.436       0.000
Residual                  27.724    46        0.603

*** WARNING ***
Case           27 has large leverage   (Leverage =        0.707)

Durbin-Watson D Statistic     1.016
First Order Autocorrelation   0.422

Residuals have been saved.

Plot of Residuals against Predicted Values

>rem since the DW test still indicates autocorrelation one could
>rem iterate the Cochrane-Orcutt procedure
>rem instead, use the Hildreth-Lu procedure with the nonlin module
>nonlin
>model divmf=rho*ldivmf+b0+bu*(unemp-rho*lunemp)+bf*(flfprt-rho*lflfprt),
>            +bm*(marumf-rho*lmarumf)
>estimate

Data for the following results were selected according to:
      year<=1970

 Iteration
 No.      Loss      RHO         B0          BU          BF          BM
   0 .454861D+03 .101000D+00 .102000D+00 .103000D+00 .104000D+00 .105000D+00
   1 .417908D+02 .834602D+00 .184446D+00 .488722D-01 .140217D+00 .879993D-01
   2 .273765D+02 .823208D+00-.170591D+01 .626686D-01 .279460D+00 .135843D+00
   3 .269325D+02 .825911D+00-.172630D+01 .601687D-01 .275435D+00 .134539D+00
   4 .269321D+02 .824001D+00-.174633D+01 .606591D-01 .274929D+00 .134712D+00
   5 .269321D+02 .824229D+00-.174405D+01 .605317D-01 .275015D+00 .134667D+00
   6 .269321D+02 .824024D+00-.174617D+01 .605792D-01 .274967D+00 .134684D+00
   7 .269321D+02 .824035D+00-.174603D+01 .605624D-01 .274978D+00 .134679D+00
   8 .269321D+02 .823989D+00-.174650D+01 .605705D-01 .274969D+00 .134682D+00
   9 .269321D+02 .824011D+00-.174627D+01 .605637D-01 .274975D+00 .134679D+00
  10 .269321D+02 .824005D+00-.174633D+01 .605642D-01 .274974D+00 .134679D+00
  11 .269321D+02 .824007D+00-.174631D+01 .605634D-01 .274975D+00 .134679D+00

Dependent variable is DIVMF

Zero weights, missing data or estimates reduced degrees of freedom

    Source   Sum-of-Squares    df  Mean-Square
 Regression        4822.208     5      964.442
   Residual          26.932    45        0.598
      Total        4849.140    50
Mean corrected      271.809    49

       Raw  R-square (1-Residual/Total)        =        0.994
Mean corrected R-square (1-Residual/Corrected) =        0.901
          R(observed vs predicted) square      =        0.901

                                                      Wald Confidence Interval
Parameter         Estimate       A.S.E.    Param/ASE        Lower < 95%> Upper
 RHO                 0.824        0.116        7.099        0.590        1.058
 B0                 -1.746        1.372       -1.273       -4.510        1.017
 BU                  0.061        0.050        1.218       -0.040        0.161
 BF                  0.275        0.085        3.225        0.103        0.447
 BM                  0.135        0.021        6.556        0.093        0.176

>rem calculate p-values assuming standard normal sampling dist.
>calc 2*zcf(-1.273)
           0.203
>calc 2*(1-zcf(1.218))
           0.223
>calc 2*(1-zcf(3.225))
           0.001
>calc 2*(1-zcf(6.556))
           0.000

>rem first differences procedure
>mglh
>let ddivmf=divmf-ldivmf
>let dunemp=unemp-lunemp
>let dflfprt=flfprt-lflfprt
>let dmarumf=marumf-lmarumf
>model ddivmf=dunemp+dflfprt+dmarumf
>estimate

Data for the following results were selected according to:
      year<=1970

1 case(s) deleted due to missing data.

Model contains no constant

Dep Var: DDIVMF   N: 50   Multiple R: 0.701   Squared multiple R: 0.492
Adjusted squared multiple R: 0.470   Standard error of estimate: 0.787

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
DUNEMP               0.061        0.049        0.160     0.637    1.227    0.226
DFLFPRT              0.259        0.136        0.284     0.492    1.914    0.062
DMARUMF              0.132        0.023        0.880     0.470    5.807    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
Regression                28.177     3        9.392      15.163       0.000
Residual                  29.113    47        0.619

*** WARNING ***
Case           24 has large leverage   (Leverage =        0.369)
Case           27 has large leverage   (Leverage =        0.593)
Case           28 is an outlier        (Studentized Residual =       -4.738)

Durbin-Watson D Statistic     1.198
First Order Autocorrelation   0.351

Plot of Residuals against Predicted Values

>rem must also run regression with constant to get DW statistic
>model ddivmf=constant+dunemp+dflfprt+dmarumf
>estimate

Data for the following results were selected according to:
      year<=1970

1 case(s) deleted due to missing data.

Dep Var: DDIVMF   N: 50   Multiple R: 0.699   Squared multiple R: 0.489
Adjusted squared multiple R: 0.456   Standard error of estimate: 0.791

Effect         Coefficient    Std Error     Std Coef Tolerance     t   P(2 Tail)
CONSTANT             0.091        0.126        0.000      .       0.725    0.472
DUNEMP               0.051        0.051        0.136     0.596    0.996    0.324
DFLFPRT              0.208        0.153        0.215     0.444    1.359    0.181
DMARUMF              0.127        0.024        0.851     0.428    5.285    0.000

                             Analysis of Variance

Source             Sum-of-Squares   df  Mean-Square     F-ratio       P
Regression                27.554     3        9.185      14.678       0.000
Residual                  28.784    46        0.626
-------------------------------------------------------------------------------

*** WARNING ***
Case           24 has large leverage   (Leverage =        0.386)
Case           27 has large leverage   (Leverage =        0.658)
Case           28 is an outlier        (Studentized Residual =       -5.117)

Durbin-Watson D Statistic     1.174
First Order Autocorrelation   0.367

Plot of Residuals against Predicted Values


>REM End of command batch file D:\MYDOCS\YS209\DIVORCE.SYC
 



Last modified 19 Apr 2000