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st: How to determine lag structure of VAR?


From   Jason R Franken <JR-Franken@wiu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: How to determine lag structure of VAR?
Date   Thu, 28 Feb 2013 11:43:36 -0600 (CST)

I want to determine the appropriate lag structure for a VAR of 3 price series - C, F1, and E. A prior study used these variables and determined the structure using Akaiki's Final Prediction Error (FPE), which can be obtained with the  below commands.

My problem is that the prior study was able to ascertain how the lag length differed for each variable and in each equation (that is 4 lags of each variable in each equation might not be appropriate), and I'm not sure how to investigate this with the below commands. Specifically, the prior study finds (for a shorter time period) that the F1 equation has lag 1 of F1 and lags 1 and 2 of C; the E equation has only lags 1 through 4 of C; and the C equation has only lag1 of F1.

Can I examine this by estimating a VAR with commands for seemingly unrelated regression (reg3, sur; suest; sureg)?

Thanks in advance,
Jason Franken

RESULTS:
.  var C F1 E, lags(1/4)

Vector autoregression

Sample:  1976q1   2010q3                           No. of obs      =       139
Log likelihood =  -1096.43                         AIC             =  16.33712
FPE            =  2502.717                         HQIC            =   16.6717
Det(Sigma_ml)  =  1425.583                         SBIC            =  17.16046

Equation           Parms      RMSE     R-sq      chi2     P>chi2
----------------------------------------------------------------
C                    13     5.20584   0.5664   181.5755   0.0000
F1                   13     4.50839   0.6138   220.9116   0.0000
E                    13     3.64389   0.7331   381.8178   0.0000
----------------------------------------------------------------
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
C            |
           C |
         L1. |   .8522103   .1119234     7.61   0.000     .6328444    1.071576
         L2. |  -.2105517   .1371686    -1.53   0.125    -.4793972    .0582938
         L3. |   .4614619   .1400664     3.29   0.001     .1869368     .735987
         L4. |  -.0850031   .1404678    -0.61   0.545     -.360315    .1903088
          F1 |
         L1. |   .1405764    .136883     1.03   0.304    -.1277093    .4088621
         L2. |  -.3039644   .1454131    -2.09   0.037    -.5889687     -.01896
         L3. |   .0981597   .1456564     0.67   0.500    -.1873216     .383641
         L4. |   .0081719   .1410511     0.06   0.954    -.2682833     .284627
           E |
         L1. |  -.1111197   .1855016    -0.60   0.549    -.4746961    .2524566
         L2. |   .0254513   .1867506     0.14   0.892    -.3405732    .3914758
         L3. |  -.2986691   .1875468    -1.59   0.111    -.6662541     .068916
         L4. |   .0016383   .1617178     0.01   0.992    -.3153227    .3185994
       _cons |    18.8637   4.441675     4.25   0.000     10.15818    27.56923
-------------+----------------------------------------------------------------
F1           |
           C |
         L1. |    .728714   .0969286     7.52   0.000     .5387376    .9186905
         L2. |   -.221222   .1187916    -1.86   0.063    -.4540491    .0116052
         L3. |   .5090438   .1213011     4.20   0.000      .271298    .7467896
         L4. |  -.3071865   .1216488    -2.53   0.012    -.5456138   -.0687593
          F1 |
         L1. |   .3239146   .1185442     2.73   0.006     .0915722    .5562569
         L2. |   .0113203   .1259315     0.09   0.928    -.2355008    .2581414
         L3. |   .0733694   .1261422     0.58   0.561    -.1738648    .3206036
         L4. |   .3028863   .1221539     2.48   0.013      .063469    .5423036
           E |
         L1. |  -.3247369   .1606491    -2.02   0.043    -.6396034   -.0098704
         L2. |   -.225406   .1617309    -1.39   0.163    -.5423927    .0915807
         L3. |  -.0965215   .1624204    -0.59   0.552    -.4148596    .2218166
         L4. |  -.2100509   .1400518    -1.50   0.134    -.4845473    .0644455
       _cons |   19.94553   3.846605     5.19   0.000     12.40632    27.48473
-------------+----------------------------------------------------------------
E            |
           C |
         L1. |   .5893907   .0783421     7.52   0.000      .435843    .7429384
         L2. |  -.3047364   .0960128    -3.17   0.002     -.492918   -.1165548
         L3. |   .3976193   .0980411     4.06   0.000     .2054622    .5897763
         L4. |   .0127413   .0983221     0.13   0.897    -.1799665    .2054491
          F1 |
         L1. |   .4016804   .0958129     4.19   0.000     .2138907    .5894702
         L2. |  -.3147535   .1017836    -3.09   0.002    -.5142457   -.1152614
         L3. |  -.1558412   .1019539    -1.53   0.126    -.3556671    .0439848
         L4. |   .0926355   .0987304     0.94   0.348    -.1008726    .2861435
           E |
         L1. |   -.023602    .129844    -0.18   0.856    -.2780915    .2308876
         L2. |   .2505328   .1307183     1.92   0.055    -.0056704    .5067359
         L3. |  -.0338416   .1312756    -0.26   0.797    -.2911371    .2234539
         L4. |  -.1952189   .1131963    -1.72   0.085    -.4170795    .0266417
       _cons |   12.52217   3.109002     4.03   0.000     6.428634     18.6157
------------------------------------------------------------------------------

.   varsoc

   Selection order criteria
   Sample:  1976q1   2010q3                     Number of obs      =       139
  +---------------------------------------------------------------------------+
  |lag |    LL      LR      df    p      FPE       AIC      HQIC      SBIC    |
  |----+----------------------------------------------------------------------|
  |  0 |  -1236.7                      11201.5   17.8374   17.8632   17.9008  |
  |  1 | -1146.61  180.18    9  0.000  3488.08   16.6707   16.7736    16.924* |
  |  2 | -1125.79  41.648    9  0.000  2942.99   16.5006   16.6807   16.9439  |
  |  3 | -1111.73  28.119    9  0.001   2737.7   16.4278   16.6851   17.0611  |
  |  4 | -1096.43  30.599*   9  0.000  2502.72*  16.3371*  16.6717*  17.1605  |
  +---------------------------------------------------------------------------+
   Endogenous:  C F1 E
    Exogenous:  _cons





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